Assignment title: Information


MODULE TITLE : MASS AND ENERGY BALANCE TOPIC TITLE : EXAMPLES OF MASS BALANCE LESSON 2 : CHEMICAL CHANGES MAEB - 2 - 2 © Teesside University 2011 Published by Teesside University Open Learning (Engineering) School of Science & Engineering Teesside University Tees Valley, UK TS1 3BA +44 (0)1642 342740 All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise without the prior permission of the Copyright owner. This book is sold subject to the condition that it shall not, by way of trade or otherwise, be lent, re-sold, hired out or otherwise circulated without the publisher's prior consent in any form of binding or cover other than that in which it is published and without a similar condition including this condition being imposed on the subsequent purchaser. 1 ________________________________________________________________________________________ INTRODUCTION ________________________________________________________________________________________ In this lesson we will look at solving further examples of mass balances involving both non-reacting (physical changes) and reacting (chemical changes) systems. The principles used to solve the problems can be applied to most processes as we will be simply using blocks to indicate processes, thus the method is independent of the process actually occurring. The problems will all be steady state problems where the conditions within the process do not change and will involve both overall, component and atomic (of individual elements) mass balances. Some of the work will reinforce the work already done in earlier lessons. ________________________________________________________________________________________ YOUR AIMS ________________________________________________________________________________________ At the end of this lesson, you should be able to solve mass balance problems for physical and chemical changes involving: • stoichiometric and non-stoichiometric (limiting and excess reactants) reactions • reactions which have less than 100% conversion • recycle streams • purge streams. Teesside University Open Learning (Engineering) © Teesside University 2011 2 ________________________________________________________________________________________ STUDY ADVICE ________________________________________________________________________________________ The examples will involve both simple mathematics and the use of simultaneous equations and you should be familiar with solving these equations. You will need a copy of the Periodic Table and a calculator to solve the problems in this lesson. Note that in this lesson the phase (solid(s) solution (aq) others it has. When balancing chemical equations and in some calculations the phase is unimportant. However, when describing a process or in certain calculations, the phase may be important and as you progress through this module this importance will become clearer. , liquid(l) , gas(g) or in water ) of a material has not been included in some equations whilst in Teesside University Open Learning (Engineering) © Teesside University 2011 3 ________________________________________________________________________________________ SIMPLE BALANCE INVOLVING STOICHIOMETRIC QUANTITIES ________________________________________________________________________________________ Example 1 15 m3 h–1 of an acidic effluent contains 12 grams per litre (g l–1) of hydrochloric acid (HCl) and 5.5 g l–1 of sulphuric acid (H2SO4). It is to be neutralised using 1 molar sodium hydroxide (NaOH) solution. The reaction equations (not balanced) are HCl NaOH NaCl H O + ⎯→⎯ + 2 H SO NaOH Na SO H O + ⎯→⎯ + 24 24 2 Calculate the rate of addition of sodium hydroxide solution. Solution The first thing to notice here is that the units used for concentrations are different; two values are in g l–1 and the other in moles. The first thing we need to do is to standardise the units. We will do this both ways to show that, whichever unit is used, it will produce the same result. What is the formula for changing g l–1 to molarity or vice versa? ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... ________________________________________________________________________________________ Teesside University Open Learning (Engineering) © Teesside University 2011 4 molarity g l of A = ( ) molecular mass of A 1 – Mr or gl molarity –1 = × Mr For HCl, from the Periodic Table, H = 1, Cl = 35.5 so the Mr of HCl = 1 + 35.5 = 36.5 molarity of HCl solution in the effluent 12 = .0 36.5 = 0 329 . For H2SO4, from the Periodic Table, H = 1, S = 32, O = 16, so the Mr of H2SO4 = 2 × 1 + 32 + 4 × 16 = 98 molarity of H SO solution in the effluent 2 4 = 5.5 98 = 0 056 . For NaOH, from the Periodic Table, H = 1, Na = 23, O = 16, so the Mr of NaOH = 23 + 16 + 1 = 40 Amount of NaOH molarity g l 1 = × =× = Mr 1 40 40 – We now need to check that the equations for neutralisation are balanced. HCl NaOH NaCl H O2 + ⎯→⎯ + This equation is balanced as it has 1 Na, 1 O, 2 H and 1 Cl atoms on both sides. Teesside University Open Learning (Engineering) © Teesside University 2011 5 H SO NaOH Na SO H O 24 24 2 + ⎯→⎯ + This equation is not balanced as it has only 1 Na on the left and two on the right and unequal numbers of Hs. We balance the Na by putting a 2 in front of the NaOH and then balance the Hs and Os by putting a 2 in front of the H2O to H SO NaOH Na SO H O 24 24 2 + ⎯→ 2 2 ⎯ + Doing the calculation based on molarity: for the HCl HCl + NaOH NaCl H O 1 mole 1 mole 0.329 mols re But as the NaOH is 1 mole per litre, we require 1 × 0.329 litre = 0.329 litres per litre of effluent for neutralisation of the HCl. But we have15 m3 h–1 (15 000 litres h–1) of effluent, so ⎯ →⎯ + 2 quires 0.329 mols volume of NaOH required 0.329 15 000 = × = 4935 itres h l – = 4 935 . 1 1 – m h 3 1 Teesside University Open Learning (Engineering) © Teesside University 2011 6 Similarly for H SO + 2NaOH Na SO 2H O 24 24 2 ⎯ →⎯ + 1 mole 2 moles 6 mols requires 2 0.056 0.112 mols × = But the NaOH is 1 mole per litre so we only require 0.112 litres per litre of effluent for neutralisation of the H2SO4. But we have 15 m3 h–1 not just 1 litre, so volume of NaOH required 0.112 15 000 = × 1 1 – = 1680 tres h li – = 1 68 . m h 3 1 Therefore total amount of 1 molar NaOH required = += 4 935 1 68 6 615 . .. m h 3 1– Repeating this calculation but this time using mass rather than moles: HCl + NaOH NaCl H O 1 mole 1 mole ⎯ →⎯ + 2 36.5g require s 40 g Teesside University Open Learning (Engineering) © Teesside University 2011 7 There are 12 grams HCl present in 1 litre of effluent and we have 15 m3 h–1 = 15 000 litres. So mass of HCl = 12 × 15 000 g = 180 000 g mass of NaOH required 40 180 000 ∴ = × 36.5 197 260 g = The NaOH solution is 40 g l–1, so number of litres 197 260 m3 = == 4932 4 932 . 40 Similarly for H SO + 2NaOH Na SO 2H O 24 24 2 ⎯ →⎯ + 1 mole 2 moles 98 g There are 5.5 g l–1 of H2SO4 and we have 15 m3 h–1 (15 000 l h–1), so requires 2 4 8 g × = 0 0 mass of ∴ mass of H SO g NaOH required 80 82 500 5 5 15 000 82 500 . 2 4 =× = × = 67 347 98 = g Teesside University Open Learning (Engineering) © Teesside University 2011 8 The NaOH solution is 40 gl–1, so number of litres 67 347 3 = == t otal amount of 1 molar NaOH required 4.932 = + 1684 1 684 . 40 1.684 6.616 m h 3 –1 = This figure is basically the same as calculated on a mole basis, the slight differences being due to rounding errors. This is a simple example where the reactants are present in stoichiometric quantities. Let us now move on to look at another question where non- stoichiometric quantities are present. Teesside University Open Learning (Engineering) © Teesside University 2011 9 ________________________________________________________________________________________ NON-STOICHIOMETRIC BALANCE ________________________________________________________________________________________ Example 2 2600 kg of a 20% w/w sulphuric acid (H2SO4) solution in water is mixed with 7200 kg of a 10% w/w solution of potassium hydroxide (KOH) in water. The balanced reaction equation is H SO KOH K SO H O 2 4 ( ) ( ) ( ) () aq aq aq l 2 4 2 + ⎯→ 2 ⎯ + (a) Determine the limiting reactant and the excess reactant (show your calculations). (b) Calculate the % excess of the excess reactant. (c) Assuming 100% conversion of the limiting reactant, determine the composition of the final mixture as percentages by weight (i.e. % w/w). Solution (a) The limiting reactant is the one that determines the amount of product formed and the excess reactant is present in greater amounts than that required by stoichiometry to react with the limiting reactant. The first step, therefore, is to determine the amounts of each material that react together. To do this we need to calculate the relative molecular masses (Mr) of each reactant. As the question later asks for the composition of the final product, we will also determine the relative molecular masses of the products. Teesside University Open Learning (Engineering) © Teesside University 2011 10 For this we need the Periodic Table to find the values of relative atomic mass (Ar Look up the relative atomic mass of each element present from your Periodic Table and use these values to calculate the relative molecular mass of each reactant and product. The answers are in the text that follows. ) of each element present. ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... ________________________________________________________________________________________ The elements present are hydrogen (H), sulphur (S), oxygen (O), and potassium (K). The Ar values are H = 1, S = 32, O = 16 and K = 39. of H SO M r M r of K SO M r M 2 4 = ×+ + × = of KOH 2 4 of H O 2 ×+ = 1 16 18 r 2 1 32 4 16 98 39 16 1 = = ++ 2 39 32 4 16 174 =× + +× = 2 = 56 Teesside University Open Learning (Engineering) © Teesside University 2011 11 From the balanced equation, and substituting the Mr values to find the reacting masses by stoichiometry: H SO 2KOH K SO H O 2 4 aq aq ( ) ( ) ( ) () 2 4 aq 2 + ⎯→⎯ + 2 l 1 mol e 2 moles 1 mole 2 moles 98 2 56 112 2 18 36 × = ×= 174 We now need to calculate the actual masses of reactants present and see how they compare with the stoichiometric quantities. 2600 kg of 20% w/w H2SO4 will contain 0 2 2600 520 . × = kg H SO 2 4 7200 kg of 10% w/w KOH will contain 0 1 7200 720 . × = kg KOH From the equation, 98 kg H2SO4 requires 112 kg KOH 1 kg H2SO4 requires kg KOH 112 98 112 520 594 3 × = . 98 520 kg H2SO4 requires kg KOH As we have 720 kg of KOH, H2SO4 is the limiting reactant and KOH is present in excess. Teesside University Open Learning (Engineering) © Teesside University 2011 12 (b) We found in part (a) that the KOH was the excess reactant, only 594.3 kg being required but 720 kg was available. The excess is therefore 720 – 594.3 = 125.7 kg KOH The % excess is given by amount of excess 100 stoichiometric amount r equired = × = 127 5 100 × 21 15 . . . % 594 3 (c) To find the composition of the final mixture we need to look at what (materials and amounts) is produced in the reaction and what is unchanged. We know that: • all the sulphuric acid is used up as the reaction has 100% conversion of the limiting reactant so it will not be present in the product solution • some KOH is un-reacted and will be present in the product solution • the water present in the reactants will be unchanged in the reaction • the products of the reaction (K2SO4 and water) will be present in the product solution. Let us draw a diagram to summarise this information. Teesside University Open Learning (Engineering) © Teesside University 2011 13 2600 kg 20% w/w H2 80% w/w H2 SO4 O Reaction 7200 kg 10% w/w KOH 90% w/w H2 T kg x% w/w K2 y% w/w H2 z% w/w KOH O If we let the amount of product solution formed = T Doing an overall mass balance over the reactor T =+= 2600 7200 9800 kg Thus we know the total amount of solution. We can convert the masses out into % w/w composition using the formula % w/w composition of A amount of material A = × 100 total amount of material In part (b), we calculated that the amount of un-reacted KOH = 125.7 kg so the % KOH in the product solution is = 1.28%. We now need to calculate the amounts of product formed in the reaction. From the balanced equation earlier: 125 7 100 . × 9800 H SO 2KOH K SO 2H O 2 4 ( ) ( ) ( ) () aq aq aq l 2 4 2 + ⎯→⎯ + 98 174 2 18 36 × = Teesside University Open Learning (Engineering) © Teesside University 2011 14 We have 520 kg of H2SO4 (20% w/w of 2600 kg) present so amount of K SO formed 174 520 2 4 = × = 923 3. 98 kg %K 2 4 = × = 923 3 100 SO 9 42 . . % 9800 amount of water for med 36 520 98 = kg × = 191 0. and we also have the water in the reactant solutions, which remains unchanged, so the amount entering = amount leaving. Water entering = 80% w/w of 2600 kg (in acid solution) + 90% w/w of 7200 kg (in the KOH solution) = 0.8 × 2600 + 0.9 × 7200 = 8560 kg. This will leave unchanged and will need to be added to the water formed in the reaction to give the total 8560 191 0 8751 + = % water 8751 100 kg . = × = 89 30 % . 9800 Putting these values into a table to summarise the process gives us: Material KOH H2 SO4 K2 SO4 H2 O Total IN (kg) Out 720 520 0 8560 9800 (kg) % composition 125.7 0 923.3 8751 9800 1.28 0 9.42 89.30 100 Teesside University Open Learning (Engineering) © Teesside University 2011 15 Let us look at a slightly more complex example. Example 3 Butane (C4H10) is burned with 15% excess air based on the complete combustion of butane to carbon dioxide and water. However, the combustion is incomplete and only 90% of the carbon is converted to carbon dioxide, the other 10% forming carbon monoxide. The unbalanced reaction equations are: C H O CO H O + ⎯→⎯ + 4 10 2 2 2 C H O CO H O + ⎯→⎯ + 4 10 2 2 (a) Balance the reaction equations. (b) Determine the molar composition of the product gases. Assume the water formed is a vapour and that air contains 79 mol% nitrogen and 21 mol% oxygen. Teesside University Open Learning (Engineering) © Teesside University 2011 16 Solution (a) First we need to balance the equations, i.e. the number of atoms of each element present must be the same either side of the arrow. Looking at the first equation, balance the carbons first. There are 4 on the left and only 1 on the right so we need to put a 4 in front of the carbon dioxide. The hydrogens are next with 10 on the left and 2 on right, so we need to put a 5 in front of the water giving: C H O CO H O 4 10 2 2 2 + ⎯→⎯ + 4 5 That only leaves the oxygen, 2 on left and 13 on the right! We could put 6.5 in front of the O2 on the left to balance the oxygens but chemists do not normally like decimals or fractions in reaction equations so we double everything to give: 2C H O CO H O 4 10 2 2 2 + ⎯→ 13 8 10 ⎯ + Try to balance the second equation given below. C H + O CO + H O 4 10 2 2 ⎯ →⎯ ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... ________________________________________________________________________________________ Teesside University Open Learning (Engineering) © Teesside University 2011 17 Looking at the carbons first, there are 4 on the left and only 1 on the right so we need to put a 4 in front of the carbon monoxide. The hydrogens are next with 10 on the left and 2 on right, so we need to put a 5 in front of the water giving: C H O CO H O 4 10 2 2 + ⎯→⎯ + 4 5 That only leaves the oxygen, 2 on left and 9 on the right. We could put 4.5 in front of the O2 on the left to balance but, as before, we double everything to give: 2C H O CO H O 4 10 2 2 + ⎯→ 9 8 10 ⎯ + (b) Having balanced the equations we now need to look at the quantities involved in the complete combustion reaction in order to calculate the amount of excess air (15%) used. The answers required are in moles (% molar composition) and the composition of air is in moles so we will use moles in our answer. We will also assume that 100 moles of butane are available (to help with percentages). By stoichiometry 2C H O CO H O 4 10 2 2 2 2 moles 13 moles 8 mo + ⎯→ 13 8 10 ⎯ + les 10 moles We have available 100 moles butane and for this we need 13 100 650 × = moles O2 2 Teesside University Open Learning (Engineering) © Teesside University 2011 18 The question states that 15% excess air (oxygen) is used = 15% of 650 = 97.5 moles giving a total oxygen of 650 + 97.5 = 747.5 moles. As oxygen is 21 mol % of the air, the nitrogen present (79%) with the oxygen = × = 747 5 79 2812 . moles. 21 All this nitrogen takes no part in the reactions and so will pass through unchanged (it could be ignored from a mass balance point of view but will be required for the composition of product gases). It is an example of a tie substance. To see what we have let us put this information onto a diagram. Air 747.5 moles O2 2812 moles N2 Products Butane (C4 100 moles H10) Combustion Oxygen 2812 moles nitrogen Carbon dioxide Carbon monoxide Water As we are told in the question that 90% of the carbon forms carbon dioxide and 10% forms carbon monoxide we can say that 90% of butane forms carbon dioxide and 10% forms carbon monoxide (butane is the only source of carbon). Looking at the equation for producing carbon dioxide By stoichiometry 2C H O CO H O 4 10 2 2 2 2 moles 13 moles 8 mo + ⎯→ 13 8 10 ⎯ + les 10 moles Teesside University Open Learning (Engineering) © Teesside University 2011 19 If the reaction were complete, 100 moles of butane would produce 8 100 10 100 and require 13 100 × = 2 × = 2 650 mo × = les of oxygen 2 400 moles of carbon dioxide 500 moles of water However, only 90% conversion is achieved so: carbon dioxide actually produced 90% of 400 = = 360 moles water produced 90% of 500 4 0 mo 5 les oxygen used 90% of 650 5 moles = = 58 = = Similarly for the carbon monoxide reaction 2C H O CO H O 4 10 2 2 2 moles 9 moles 8 moles + ⎯→ 9 8 10 ⎯ + 10 moles If we have 100 moles of butane we would get 400 moles of carbon monoxide , 500 moles of water and use 450 moles of oxygen. However, as only 10% is converted: carbon monoxide produced 10% of 400 40 mole = = s water produced 10% of 500 0 moles oxygen = = 5 used 10% of 450 moles = = 45 Teesside University Open Learning (Engineering) © Teesside University 2011 20 From the above two sets of calculations the total oxygen used = 585 + 45 = 630 moles. Since we started with 747.5 moles oxygen, the amount un-reacted = 747.5 – 630 = 117.5 moles Adding these figures to the diagram and also putting the results into a table gives. Air 747.5 moles O2 2812 moles N2 Products Butane (C4 100 moles H10) Combustion 117.5 moles oxygen 2812 moles nitrogen 360 moles carbon dioxide 40 moles carbon monoxide 500 moles water Material Butane Oxygen Nitrogen Carbon dioxide Carbon monoxide Water Total IN OUT 100 747.5 2812 0 0 0 3659.5 Moles 0 117.5 2812 360 40 500 3829.5 Mol% We can complete the table by calculating the mol % composition using mol % composition of A moles of A 100 total = × number of moles Teesside University Open Learning (Engineering) © Teesside University 2011 21 Do this for yourself and check your answers with ours. ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... ________________________________________________________________________________________ Material Butane Oxygen Nitrogen Carbon dioxide Carbon monoxide Water Total IN OUT 100 747.5 2812 0 0 0 3659.5 Moles Mol% 0 117.5 2812 360 40 500 3829.5 0 3.07 73.43 9.40 1.04 13.06 100 Looking at this, there appears to be an 'imbalance'. The number of moles IN does not equal the number of moles OUT. This is because we have done the balance using individual materials and the stoichiometry of the reactions means there is a change in the number of moles during the reactions, e.g. for the formation of CO: 2C H 9O 8CO 10H O 4 10 2 2 + ⎯→⎯ + 2 moles 9 moles 8 moles 10 moles 11 moles IN produce 18 moles OUT Teesside University Open Learning (Engineering) © Teesside University 2011 22 We could have solved this problem in other ways. We could have done a balance on the moles of each element present (C, H, O, and N) or we could have converted moles to mass and done a mass balance. In both these cases the numbers in and out would be the same. We will do both the element and mass balance to check our answer is correct. We can ignore the nitrogen as it passes through the process unchanged. As the formula represents the number of atoms of each element present, e.g. C4H10 has 4 carbons and 10 hydrogens and O2 has 2 atoms of oxygen, on an element basis and using the figures in the previous table: Material IN (moles) OUT (moles) Butane (C4 Oxygen (O2 Carbon dioxide (CO2 Carbon monoxide (CO) Water (H2 Total Material C H O Material C H O H10) ) ) O) 100 400 0 747.5 0 0 0 0 0 0 847.5 400 1000 0 1495 0 0 0 1000 1495 0 0 117.5 360 0 40 0 500 0 1017.5 0 0 360 40 0 1000 400 1000 0 0 0 0 To do the mass balance we need the relative molecular mass Mr of each of the materials. (The Ar values from the Periodic Table are C = 12, O = 16, H = 1). Teesside University Open Learning (Engineering) © Teesside University 2011 23 M r of butane C H of oxyg M r 2 16 32 of carbon dioxide CO Mr 12 2 16 44 ( ) 4 10 = × + ×= 4 12 10 1 58 en O ( ) =× = 2 ( ) = 2 M ( ) = + r of carbon monoxide CO = +× = 12 16 28 M 2 1 16 18 r of water H O2 ( ) = ×+ = We can now calculate the mass of each material entering and leaving and put these into the new table. Material IN Butane (Mr Oxygen (Mr Carbon dioxide (Mr Carbon monoxide (Mr Water (Mr = 58) = 32) = 44) = 28) = 18) Total Moles Mass g 100 747.5 0 0 0 847.5 (Moles × Mr 5800 23920 0 0 0 29720 Moles Mass g ) 0 117.5 360 40 500 1017.5 OUT (Moles × Mr 0 3760 15840 1120 9000 29720 You can see from these two checks that we do have a balance. Teesside University Open Learning (Engineering) © Teesside University 2011 24 ________________________________________________________________________________________ CHEMICAL CHANGE WITH RECYCLE ________________________________________________________________________________________ Example 4 Propene (C3H6) is to be chlorinated to produce dichloro-propane (C3H6Cl2) in a reaction which has the balanced equation: C H Cl C H Cl 3 6 2 ( ) ( ) () gg l 3 6 2 + ⎯→⎯ An excess of propene is required in the reactor as this suppresses any side reactions and allows 96% conversion of the chlorine to dichloro-propane. The reaction mixture is then separated into product, un-reacted propene and chlorine, the latter two being recycled back to the reactor for further processing. (a) Draw a block diagram of the process. (b) If 500 kg h–1 of dichloro-propane is required as product, determine the mass of propene and chlorine required in the fresh feed at the steady state. (c) If the mole ratio of propene to chlorine at the reactor inlet is 5:1 determine: (i) the composition of the feed to the separator (ii) the flow rate and composition of the recycle stream. Data: The relative atomic masses (Ar ) of C = 12, H = 1 and Cl = 35.5. Teesside University Open Learning (Engineering) © Teesside University 2011 25 Solution As in a previous example, there appears to be a conflict of units. In part (b) we are given 500 kg h–1 of dichloro-propane but in part (c) we are given mole ratio. As we saw, the actual choice of unit is unimportant as they should give the same result. At this stage we will stick with mass as it demonstrates the alternative not covered earlier when we used moles. (a) The first thing the question asks for is the block diagram. Try to do this first for yourself before looking at our answer. ________________________________________________________________________________________ Teesside University Open Learning (Engineering) © Teesside University 2011 26 Reactor Product Propene Chlorine Dichloro-propane Feed Propene chlorine Reactor Separator Product Dichloro-propane Recycle Propene Chlorine We have not put any figures on it as yet as we are not given much in the question! (b) Where do we start? Well looking at our block diagram we see that, for mass, the feed in = product out as there are no other streams entering or leaving. So at the steady state the fresh feed in of propene and chlorine is all converted to dichloro-propane. We are given five bits of information in the question, the balanced reaction equation, excess propene present, 98% conversion of chlorine, 500 kg h–1 of dichloro-propane are required and the relative atomic masses of the elements present. Let us look at the equation C H Cl C H Cl 3 6 2 ( ) ( ) () gg l 3 6 2 + ⎯→⎯ 1 mole 1 mole 1 mo le From this equation we see that for every mole of product we need 1 mole of propene and 1 mole of chlorine. We require 500 kg h–1 of dichloro- propane, how is this changed into moles or how do we change moles into mass in kg? Well we use the equation we met earlier. Teesside University Open Learning (Engineering) © Teesside University 2011 27 moles of A mass of A in grams relative molec = ular mass of A ( ) M of propene C H3 6 M r ( ) = × 3 12 6 1 42 + ×= M ( ) = r of dichloro-propane C H Cl 36 2 3 12 6 1 2 35 5 113 × + ×+ × = . Mr of chlorine Cl2 35 5 71 . = ( ) = × 2 So we can now use grams instead of moles in our reaction C H Cl C H Cl 3 6 2 ( ) ( ) () gg l 3 6 2 + ⎯→⎯ 42 g 71 g 113 g So 42 g of propene + 71 g of chlorine will produce 113 g dichloro- propane. But the question says we need 500 kg h–1 of dichloro-propane. By ratio, to produce 500 kg h–1 of dichloro-propane we need and 71 42 500 185 84 × = . – kg h of propene 113 × = 500 113 kg h of chlorine 1 314 16 . – 1 These figures answer part (b) and we can now put them onto the block diagram. Teesside University Open Learning (Engineering) © Teesside University 2011 28 Feed 185.84 kg h–1 Propene 314.16 kg h–1 Chlorine Reactor Product Propene Chlorine Dichloro-propane Reactor Separator Product 500 kg h–1 Dichloro-propane Recycle Propene Chlorine (c) For part (c) we are told that the feed to the reactor is in the mole ratio of 5 moles propene to 1 mole chlorine (i.e. for every 6 moles of feed entering there are 5 moles propene and 1 mole chlorine) and that 96% of the chlorine is converted. From the reaction equation, we saw 1 mole of propene requires 1 mole of chlorine to produce 1 mole of dichloro-propane. Therefore for every 6 moles of feed, only 0.96 moles of chlorine along with 0.96 moles of the propene are converted to 0.96 moles of dichloro- propane. Thus the reactor product composition on this basis is 0.96 mole dichloro-propane formed ( ) = mole chlorine unreacted 1 0 96 0 04 –. . ( ) 5 0.96 = 4 04 . mole propene unreacted – Teesside University Open Learning (Engineering) © Teesside University 2011 29 Convert this to mol % ⎟ moles of A 100 ⎜ ⎞ ⎛ × = ⎝ total moles ⎠ Dichloro-propane is 0 96 100 ... . % × 19 05 . + + = 0 96 0 04 4 04 Chlorine is 0 04 100 ... . % × 0 79 . + + = 0 96 0 04 4 04 Propene is 4 04 100 ... . % × 80 16 . + + = 0 96 0 04 4 04 The dichloro-propane is removed by the separator and the composition of the recycle stream in terms of relative number of moles will be 4.04 moles propene to 0.04 moles of chlorine, which as a mole ratio of propene: chlorine = 4.04: 0.04 = 101:1. This recycle stream is mixed with 500 kg h–1 of fresh feed having a mole ratio of 1:1 to give a reactor feed which has a molar ratio of propene:chlorine = 5:1. Let us look at that part of the process more closely and put the figures on the diagram. Teesside University Open Learning (Engineering) © Teesside University 2011 30 Fresh feed 500 kg h–1 185.84 kg h–1 314.16 kg h–1 chlorine propene Unknown amount of reactor feed Propene: chlorine = 5:1 Unknown amount of recycle Propene: chlorine = 101:1 To solve this problem we need to convert all concentrations to the same units. We could use moles or mass. We used moles in the last example, let us now look at mass. mass number of moles = × Mr But the figures given are as ratios so we will need to work out relative masses and hence % w/w in the mixtures. Reactor feed relative mass of propene number of moles = × Mr of propene relative mass of chlor % w/w propene mass of propene =× = ine number of moles of chlorine = × =× = total mas = × 100 = × = 210 100 5 42 210 Mr 17 7 1 1 s of reactor feed 74 73 . % 281 Teesside University Open Learning (Engineering) © Teesside University 2011 31 % w/w chlorine mass of chlorine total ma = × 100 = × = 71 100 ss of reactor feed 25 27 . % 281 Recycle stream relative mass of propene number of moles = × Mr of propene relative mass of ch Mr 1 w/w propene mass of propene 100 % = ×= 01 242 1 42 4 lorine number of moles of chlorine = × 1 7 = × = × 1 = 7 total mass of recycle = × = 4242 100 98 35 . % 4313 % hlorine mass of chlorine w/w c total mass of = × 100 = × = 71 100 recycle 1 65 . % 4313 Teesside University Open Learning (Engineering) © Teesside University 2011 32 Redoing the diagram, and letting the amount of recycle be x kg h–1 Fresh feed 500 kg h–1 185.84 kg h–1 314.16 kg h–1 chlorine propene (500 + x) kg h–1reactor feed 74.73% w/w propene 25.27% w/w chlorine x kg h–1recycle 98.35% w/w propene 1.65% w/w chlorine Doing an overall mass balance gives: fresh feed recycle reactor feed + = 500 500 += + x x No help!! Doing a balance over propene gives: 185 84 98 35 74 73 500 . .% .% 185 84 185 84 0 9835 373 6 0 9835 0 7473 373 65 185 84 . –. . – . += + ( ) 0 9835 0 7473 500 + . . . + = 5 0 7473 .. . x x 0 23 . of of x x = ×+ ( ) x x x + . x = 62 187 81 x = 795 1 x = . . – kg h 1 Teesside University Open Learning (Engineering) © Teesside University 2011 33 The amount of recycle is 795.1 kg h–1 and it composition is 98.35% w/w propene and 1.65% w/w chlorine (mole ratio 101:1). To check do a mass balance on the chlorine 314 16 795 1 0 0165 1295 1 0 2527 +× = × . .. .. 327 27 327 = .27 . A balance! Try doing the last part using moles instead of mass. Remember this is just a mixing stage and what goes in as propene stays propene and the same with chlorine. Fresh feed 500 kg h–1 185.84 kg h–1 314.16 kg h–1 chlorine propene Unknown amount of reactor feed Propene: chlorine = 5:1 Unknown amount of recycle Propene: chlorine = 101:1 Teesside University Open Learning (Engineering) © Teesside University 2011 34 Fresh feed Convert mass rate into moles, remember the mass quoted in the feed is in kilograms and needs to be converted to grams: moles propene mass of propene in g moles chlorine mass of pro = Mr pene 185 84 1000 = × = 4425 . 42 of chlorine in g = M of chlorine r = 314 16 100 . × 0 71 = 4425 The feed is correct in mole terms (need to be equal), i.e moles propene = moles chlorine. Total feed = 8850 moles. Recycle This is 101 moles propene to 1 of chlorine by ratio which means for every 102 moles, 101 are propene and 1 is chlorine. mole fraction propene moles propene total mo = les 101 = = 102 0 99 . mole fraction chlorine mole s chlorine total moles = = 1 = 0 01 . 102 Teesside University Open Learning (Engineering) © Teesside University 2011 35 But we do not how many moles in total there are per hour. Let this be T. The amount of propene in moles in the recyle =× = T T mole fraction of propene 0.99 The amount of chlorine in moles in the recyle =× = T T mole fraction of chlorine 0.01 Reactor Feed The reactor feed is a molar ratio of propene:chlorine of 5:1 so for every 6 moles entering 5 are propene and 1 is chlorine. mole fraction of propene moles propene mole fraction of chlorine m total = moles oles chlorine total moles = = 1 = 5 0 833 . = = 6 0 167 . 6 The amount of reactor feed in moles = + =+ fresh feed recycle 8850 T Therefore, the amount of propene in moles will be ( ) 8850 8850 + T × = mole fraction of propene 0.833( ) + T and the amount of chlorine in moles will be ( ) 8850 885 + T × = mole fraction of chlorine 0.167 0 ( ) + T Teesside University Open Learning (Engineering) © Teesside University 2011 36 We now have consistent units so we can do balances. Over propene 4425 0 99 0 833 8850 4425 0 99 7372 0 + =× + ( ) T T . . T 833T + =+ . . Rearranging ( ) = 0 99 0 833 7372 4425 . –. – T 0 157 2947 T . T moles = 18 771 = Check using balance over chlorine: ×+ = × + ( ) 0 5 8850 0 01 0 167 8850 . .. 4425 0 01 147 T T T 8 0 167 + = . 2947 0 157 T moles + T = . 18 771 = T . (We may have used less significant figures in our calculation and ended up with not quite as good a balance.) Teesside University Open Learning (Engineering) © Teesside University 2011 37 We could do a further check by seeing if this matches the mass balance. If T = 18 771 moles, of which mole fraction chlorine is 0.01 and propene is moles chlorine ∴ == mass moles moles propene =× = mass 18 583 42 0 01 187 71 . . T = × 13327 4 . g 13.33 kg = = 0.99 18 771 18 583 = × 780 486 g 780.49 kg = = Mr = × 187 71 71 . total mass in recycle 780.49 13.33 79 = += 3.82 kg This compares to the 795.1 kg we calculated earlier, a difference of 0.15%. This difference would be due to rounding errors. The summary table is: Fresh feed Propene Chlorine Dichloropropane Total Moles Mass 4425 185.84 4425 314.16 0 0 8850 500 Final products Moles Mass 0 0 0 0 4425 500 4425 500 Reactor feed Moles 23010 4603 0 27613 Mass Moles 966.34 18585 327.49 185.7 0 4425 1293.8 23196 Reactor products Mass 780.5 13.33 500 1293.8 Recycle stream Moles 18585 185.7 0 18771 At this stage we should point out then when you solve problems, whilst we would expect enough explanation to enable us to see what you were trying to do, it would not need a lot of the additional explanation we have given here. You would also only need to do one check not all the ones we have done in this example!! Teesside University Open Learning (Engineering) © Teesside University 2011 38 ________________________________________________________________________________________ BALANCE INVOLVING A PURGE STREAM ________________________________________________________________________________________ Example 5 In the production of ethanol from ethene and steam, equimolar quantities of ethene and steam are passed into a high temperature catalytic converter and the resultant reaction conversion is 70%. Equation: C H H O C H OH 24 2 25 + ⎯→⎯ ethene steam ethanol 1 mole 1 mole 1 mole The ethanol is separated by absorption and the un-reacted ethene and steam are recycled to the reactor. The ethene contains 0.01% impurity, which if allowed to build up to above 1% in the feed to the catalytic converter causes the catalyst to be poisoned. Estimate the minimum % of the recycle stream leaving the separator that must be removed (purged) to prevent the catalyst being poisoned. Teesside University Open Learning (Engineering) © Teesside University 2011 39 Solution 50 moles ethene (0.01% impurity) 50 moles steam Reactor Separator Recycle Purge All we are given is that the feed is equimolar (equal quantities), with 0.01% impurity in the ethene, and that in the reactor, the conversion rate = 70%. To solve this we need to make some assumptions. Let the feed be 100 moles, 50 moles ethene and 50 moles steam. (We could have chosen any number of moles but 100 is used as it is a good number to work out values on!) There is 0.01% impurity in the feed ethene = 0.01% of 50 = 0.05 moles. We will assume that the ethene impurity is additional and not part of the ethene moles. If not then the problem is made much more difficult. The amount of ethene will only be 49.95 moles compared to 50 moles steam, and hence steam will build up in the recycle to produce a recycle stream richer in steam than ethene. This will be reflected in changes in the purge concentration and the amount of steam compared to ethene removed in the purge and entering the reactor. Let us remove that complication by making it extra – the question does say estimate not calculate! Let the amount of recycle entering the reactor = x moles and the amount of purge = y moles Teesside University Open Learning (Engineering) © Teesside University 2011 40 total moles entering reactor 100 = + x maximum m oles of impurity that can enter 1% of tota = l feed = + 0.01 100 moles ( ) x This stays with the un-reacted ethene and steam moles ethene and steam leaving system 30% o = f feed [70% is converted to ethanol which is removed] ∴ mole fraction of impurity in recycle = + ( ) 0 3 100 . x 0.01 = ( ) + ( ) + = 100 . x . 0 3 100 x 0 033 The purge rate must be such as to remove all the fresh impurity added = 0.05 moles. Thus (mole fraction of impur 0 05 0 033 . . = y ity purge rate in moles) × y = 1 515 . moles Teesside University Open Learning (Engineering) © Teesside University 2011 41 Doing a balance around the purge point: moles ethene and steam leaving reactor 0.3 1 = ( ) 00 + x This must equal the amount recycled + the amount of purge ( ) + = + 0.3 100 But 1 515 30 0 3 + = 28 485 0 7 . . = + x y x xy y = . . + x x 1 515 . % of reactor recyle leaving as purge 1.515 100 = x moles 40 69 = . 40.69 1. = × x + 515 = 3 59 . % This lesson has covered quite a lot of calculations and has offered several different alternative ways of solving the problems. If done correctly, the result should be independent of the method chosen and in practice engineers often use alternatives to check their answers. When dealing with the large quantities of potentially hazardous chemicals being processed, getting it wrong can have serious consequences, on both economic and safety issues. That completes our look at mass balances. Test your understanding of this lesson by attempting the Self-Assessment Question which follows. Teesside University Open Learning (Engineering) © Teesside University 2011 42 ________________________________________________________________________________________ SELF-ASSESSMENT QUESTION ________________________________________________________________________________________ Note: This is a complex problem incorporating all the types of calculation met during the lesson. It is not a real process. It is important to break it up into stages, calculating each answer in turn. 150 kg h–1 of tri-iron tetroxide (Fe3O4) is reacted with 10% excess hydrogen gas containing 0.01% v/v chlorine gas at 500°C to produce iron and water with 60% conversion of the tri-iron tetroxide. The resultant iron/tri-iron tetroxide /hydrogen/water mix is separated into hydrogen gas, liquid water and solid iron metal/tri-iron tetroxide mix. The solid is recycled back to the reactor and, at the steady state, the solid removed from the process is 95% w/w iron metal, 5% w/w Fe3O4. The hydrogen gas is also recycled back to the reactor taking with it the chlorine impurity. The level of chlorine leaving the reactor must not exceed 1% by volume to prevent side reactions. The unbalanced reaction is: Fe O H Fe H O 34 2 2 + ⎯→⎯ + Teesside University Open Learning (Engineering) © Teesside University 2011 43 (a) Balance the reaction equation. (b) Calculate: (i) the amount in kg h–1 of pure iron removed (ii) the composition of the solid feed to the reactor (iii) the amount in kg h–1 of recycled iron/ tri-iron tetroxide mix (iv) the amount in kg h–1 of hydrogen required in the reactor (v) the amount in kg h–1 of recycled hydrogen purged (vi) the amount in kg h–1 of hydrogen recycled to the reactor (vii) the amount in kg h–1 of fresh hydrogen feed. Data: Relative atomic mass of hydrogen (H) = 1, oxygen (O) = 16, iron (Fe) = 56, chlorine (Cl) = 35.5. Teesside University Open Learning (Engineering) © Teesside University 2011 44 ________________________________________________________________________________________ ANSWER TO SELF-ASSESSMENT QUESTION ________________________________________________________________________________________ (a) The unbalanced equation is Fe O H Fe H O 34 2 2 + ⎯→⎯ + First balance the Fe, 3 on the left 1 on the right, so multiply Fe on right by 3 Fe O H Fe H O 34 2 2 + ⎯→⎯ + 3 Now balance the O, 4 on left 1 on right, multiply H2O by 4 Fe O H Fe H O 34 2 2 + ⎯→⎯ + 3 4 Finally balance the H, 2 on left 8 on right, multiply H2 by 4 Fe O H Fe H O 34 2 2 + ⎯→ 4 34 ⎯ + (Your answer may be a single line: Multiply Fe by 3, H2O by 4 and H2 by 4.) Teesside University Open Learning (Engineering) © Teesside University 2011 45 (b) Diagram: 150 kg h–1 Fe3 99.99% v/v hydrogen 0.01% v/v chlorine O4 Reactor Separator 95% w/w Fe 5% w/w Fe3 Water Hydrogen purge Hydrogen recycle containing max 1% v/v chlorine First we need to determine the relative molecular masses (Mr within the equation: ) of materials a ( ) = M r of Fe O M r M ctually of Fe A r of H O2 M r =× + × = 3 4 of H = ×= 2 r = ×+ = 3 56 4 16 232 212 56 2 1 16 18 Teesside University Open Learning (Engineering) © Teesside University 2011 46 (i) To calculate the amount of iron produced we need to look at the balance over iron. 150 kg h–1 of Fe3O4 enter and the product is 95% w/w iron (Fe) and 5% w/w of Fe3O4 Do an element balance over Fe In Fe3O4, the amount of iron is 168 (3 × 56) out of a total of 232 = × = 168 100 72 41 . % 232 150 kg h–1 of Fe3O4 feed contains 72.41% of Fe, so the amount of Fe = 0.7241 × 150 = 108.62 kg h–1 The product out is 95% w/w pure iron and 5% w/w of Fe3O4. Let the total mass of solid out = x amount of Fe out 95% of of 72.41% of = + x x 5% 0 95 0 0362 = + . . x x 108 62 0 9862 ∴ = . . 110 14 x = x kg h –1 . 95% of this is pure iron 0.95 110.14 5 0 05 110 14 5 51 kg % . .. is Fe O =× = =× = 3 4 104.63 kg h 1 – Teesside University Open Learning (Engineering) © Teesside University 2011 47 (ii) To produce the reactor product, the Fe3O4 feed is 60% converted into pure iron. If we assume 100 kg of solid reactor product, 95 kg (95% w/w) are iron and 5 kg (5% w/w) are un-reacted Fe3O4. The 5 kg of un-reacted Fe3O4 in the product must therefore be 40% of the feed Fe3O4. (60% of the feed of Fe3O4 is converted.) Therefore, the total feed into the reactor of Fe3O4 to give 100 kg of final product is = 12.5 kg, 7.5 kg being converted to iron. The iron is produced according to the following reaction equation which, when Mr values and stoichiometry are considered, gives: Fe O 4H 3Fe 4H O 34 2 2 + ⎯→⎯ + 232 g 4 2 8 g 3 56 168 g 5 100 × 40 ×= × = 7.5 kg of Fe3O4 will produce 168 7 5 232 5 43 × = . . kg of Fe. But 95 kg of iron are in the reactor product so 95 – 5.43 = 89.57 kg must be present in reactor feed. Thus to give a reactor product composition of 95 kg iron, 5 kg Fe3O4, the feed must be 89.57 kg iron and 12.5 kg Fe3O4, giving a total reactor feed of 102.07 kg. The % composition of the reactor feed is Fe 89.57 100 = × = Fe O 1 100 = × 3 4 . . % 102 07 2 5 . .07 = 12 25 . % 102 87 75 This is on the basis of 100 kg of product but as we have converted to % these will be valid for any amount of product formed. Teesside University Open Learning (Engineering) © Teesside University 2011 48 (iii) At the junction of solid feed and recycle and let the recycle be y kg h–1. y kg h–1 95% w/w Fe 5% w/w Fe3 O4 150 kg h–1 100% w/w Fe3 O4 150 + y kg h–1 87.75% w/w Fe 12.25% w/w Fe3 Doing a balance over pure Fe, as it is only present in the recycle stream in and reactor feed out and no chemical change occurs: 95 87 75 % .% . y 0 0725 131 625 . . of of 150 y y = + ( ) 0 95 0 8775 150 = ×+ 0 8775 y . . y = = kg h 1 1815 5 y . – (iv) The reactor feed is 12.25% Fe3O4 and the total amount of feed is 150 150 1815 5 += + y . 1965 5 . – kg h = 1 amount of ∴ Fe O in reactor feed of 1965.5 kg h 3 4 = 12 25 . % –1 1 = 240 77 . kg h– Teesside University Open Learning (Engineering) © Teesside University 2011 49 According to the reaction equation Fe O 4H 3Fe H O 34 2 2 + ⎯→⎯ + 232 4 So for 240.77 kg Fe3O4, the amount of hydrogen required by stoichiometry = . A 10% excess is required so the actual amount of hydrogen required in the reactor = 8.30 + 10% of 8.30 = 9.13 kg h–1. 4 g 2 8 g × = 8 240 77 8 30 × = . . – kg h 1 232 (v) However, only 60% of the Fe3O4 is converted so only 60% of the stoichiometric quantity of hydrogen is used. Hydrogen used in reactor = 60% of 8.30 = 4.98 kg h–1 so hydrogen leaving the reactor = (9.13 – 4.98) = 4.15 kg h–1. Amount of fresh hydrogen entering reactor If the amount of purge kg h of hydrogen total hydrogen entering will be 4.98 kg h chlorine in this feed 0.01% by volume = + amount used purged hydrogen 1 = z – 1 = + ( )z – = = 0 0001 . er mole of hydrogen = mole p 1 mole hydrogen 2 g 1 mole chlorine 71 g = and Teesside University Open Learning (Engineering) © Teesside University 2011 50 so moles hydrogen in feed = ( ) + × = 4 98 1000 . z 2 24 90 500 + so moles chlorine in feed 2490 500 ( )z × = + z 0 0001 . mass of chlorine in feed = + = + ( ) × = + ( ) = 0 249 0 05 . . z 0 249 0 05 71 . . 17.68 3.55 g h 1 . . – ( ) + z kg h 1 7 68 3 55 1 1000 z – z This must be removed in the purge. The reactor outlet has 4.15 kg h–1 of hydrogen and the chlorine is 1% by volume. So moles of hydrogen in reactor outlet mass = of hydrogen in kg 1000 = × = and moles of chlori ne in reactor outlet (1%) = ⎡ × = molecular mass of h 4 15 1000 . 2 2075 ⎢ ⎤ 4 15 1000 . × ⎣ 2 20 75 . ydrogen 0 01 ⎥ ⎦ . Teesside University Open Learning (Engineering) © Teesside University 2011 51 mass of chlorine in recycle 20.75 71 1473.2 = ×= 5 g = 1.473 kg % = f chlorine in recycle 100 w/w chlorine in recycle mass o = × total mass of rec + = 1 473 . . . % 26 2 . 4 15 1 473 ycle 100 % en in recycle = = 100 26 2 73 8 – . .% w/w hydrog If the purge is z kg h–1 of hydrogen, then chlorine removed will be 26 2 × = z . . . 73 8 0 355 z z hence ( ) + 17 68 3 55 . . 1000 17 68 3 55 355 + = . . 351 45 17 68 = 0 355 z . z z z = . . z 0 05 . – kg h 1 = (We could have estimated this answer as we started with 0.01% chlorine and end up with 1%, a factor of hundred. Since the recycled amount is similar to the feed amount, the amount removed will be about 1/100 of the feed entering. This will not be the case if the recycle was much greater or less than the feed). (vi) Thus the amount of hydrogen recycled to the reactor = 4.15 – 0.05 = 4.10 kg h–1. Teesside University Open Learning (Engineering) © Teesside University 2011 52 (vii) Fresh hydrogen 4.98 0.05 5.03 kg h 1 =+= – . As a check if 0.05 kg h–1 of hydrogen is removed in the purge then chlorine removed kg h = × = 0 05 26 2 0 0178 . . 73 8 g h 17 8. – = . . –1 1 hydrogen entering 5.03 kg h 1 – = 5 03 . × = 2 2515 moles = 1000 so chlorine entering 0.01% of 2515 = 0.0001 moles = × 0.2515 moles = 2515 mount of chlorine in grams moles = ×= Mr 0 2515 . × a 71 17 8. g = A balance! So even with very little information, by breaking down the process into individual steps the problem can be solved. It is very important to look at the question and the diagram of the system to get clues as to where to start on a problem. Teesside University Open Learning (Engineering) © Teesside University 2011 53 ________________________________________________________________________________________ SUMMARY ________________________________________________________________________________________ In this lesson we have looked at how we can do balances when the materials taking part in the process are changed by chemical reaction. It is important that the right concentration units are used throughout, whether moles or mass, and you know the way to change from one to the other, covered in the early lessons. The actual answer will not change, whichever method is used, but experience often tells us which the simplest method is. There are no hard and fast rules as to where you start and how you get the answer, once again this tends to come from experience. For those only involved in the educational side, a good clue as to the method to use is given by the order in which you are asked to calculate values in a problem but out in industry you haven't got the luxury of someone else doing the calculation first!! The most important things in doing mass balances are: • always break down the process into simple stages • use a block diagram to visualise what is going on • put all existing information onto the diagram and update when new values are obtained • keep the units consistent • use all types of mass balance if necessary; – overall – over items of equipment – over junctions/splits of flows – over all materials Teesside University Open Learning (Engineering) © Teesside University 2011 54 – over individual materials – over elements – over reactions • check your answers by making sure that all materials balance not just the one you are asked to calculate. We will be doing some more materials balances later in this module when we look at energy balances, so be certain you understand how to do them. Teesside University Open Learning (Engineering) © Teesside University 2011