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Dr. Ahmed Faiq Al-Alawy
Chapter 9
The Chemical Reaction Equation and Stoichiometry
9.1 Stoichiometry
The stoichiometric coefficients in the chemical reaction equation Is (1 for C 7 H 16 , 11 for O 2 and so on). Another way to use the chemical reaction equation is to indicate that 1 mole of CO 2 is formed from each (1/7) mole of C 7 H 16 , and 1 mole of H 2 O is formed with each (7/8) mole of CO 2. The latter ratios indicate the use of stoichiometric ratios in determining the relative proportions of products and reactants. For example how many kg of CO 2 will be produced as the product if 10 kg of C 7 H 16 react completely with the stoichiometric quantity of O 2? On the basis of 10 kg of C 7 H 6
Example 9. The primary energy source for cells is the aerobic catabolism (oxidation) of glucose (C 6 H 12 O 6 , a sugar). The overall oxidation of glucose produces CO 2 and H 2 O by the following reaction
Determine the values of a, b, and c that balance this chemical reaction equation. Solution Basis: The given reaction By inspection, the carbon balance gives b = 6, the hydrogen balance gives c = 6, and an oxygen balance 6 + 2a = 6 * 2 + 6 Gives a = 6. Therefore, the balanced equation is Example 9. In the combustion of heptane, CO 2 is produced. Assume that you want to produce 500 kg of dry ice per hour, and that 50% of the CO 2 can be converted into dry ice, as shown in Figure E9.2. How many kilograms of heptane must be burned per hour? (MW: CO 2 = 44 and C 7 H 16 = 100.1)
Dr. Ahmed Faiq Al-Alawy
Solution The chemical equation is Basis: 500 kg of dry ice (equivalent to 1 hr) The calculation of the amount of C 7 H 16 can be made in one sequence:
Example 9. A limestone analyses (weight %): CaCO 3 92.89%, MgCO 3 5.41% and Inert 1.70% By heating the limestone you recover oxides known as lime. (a) How many pounds of calcium oxide can be made from 1 ton of this limestone? (b) How many pounds of CO 2 can be recovered per pound of limestone? (c) How many pounds of limestone are needed to make 1 ton of lime? Mol. Wt.: CaCO 3 (100.1) MgCO 3 (84.32) CaO (56.08) MgO (40.32) CO 2 (44.0) Solution
Chemical Equation:
Basis: 100 lb of limestone
The quantities listed under Products are calculated from the chemical equations. For example, for the last column:
Dr. Ahmed Faiq Al-Alawy
Equation (9.1) can be rearranged to calculate the number of moles of component i from the value of the extent of reaction … 9. Example 9. Determine the extent of reaction for the following chemical reaction given the following analysis of feed and product: N 2 H 2 NH 3 Feed 100 g 50 g 5 g Product 90 g
Also, determine the g and g mol of N 2 and H 2 in the product. Solution The extent of reaction can be calculated by applying Equation 9.1 based on NH 3 :
Equation 9.2 can be used to determine the g mol of N 2 and H 2 in the products of the reaction
Note : If several independent reactions occur in the reactor, say k of them, ξ can be defined for each reaction, with vki being the stoichiometric coefficient of species i in the k th reaction, the total number of moles of species i is
nH mH
Dr. Ahmed Faiq Al-Alawy
Where R is the total number of independent reactions.
9.2.2 Limiting and Excess Reactants
The excess material comes out together with, or perhaps separately from, the product, and sometimes can be used again. The limiting reactant is the species in a chemical reaction that would theoretically run out first ( would be completely consumed ) if the reaction were to proceed to completion according to the chemical equation— even if the reaction does not proceed to completion! All the other reactants are called excess reactants.
amount oftheexcessreactantrequiredtoreact withthelimitingreactant 100
react withthelimitingreactant
amountoftheexcessreactantfed-amountoftheexcessreactantrequiredto % excessreactant
For example , using the chemical reaction equation in Example 9.2 ,
If 1 g mol of C 7 H 16 and 12 g mol of O 2 are mixed. As a straightforward way of determining the limiting reactant , you can determine the maximum extent of reaction , ξmax, for each reactant based on the complete reaction of the reactant. The reactant with the smallest maximum extent of reaction is the limiting reactant. For the example, for 1 g mol of C 7 H 16 plus 12 g mole of O 2 , you calculate
Therefore, heptane is the limiting reactant and oxygen is the excess reactant. As an alternate to determining the limiting reactant ,
Dr. Ahmed Faiq Al-Alawy
Given g: 10 10 0 MW: 28 2.016 17. Calculated g mol: 0.357 4.960 0
(b) N 2 is the limiting reactant, and that (c) H 2 is the excess reactant. The excess H 2 = 4.960 – 3(0.357) = 3.89 g mol. To answer question (a), the maximum amount of NH 3 that can be produced is based on assuming complete conversion of the limiting reactant
9.2.3 Conversion and degree of completion
Conversion is the fraction of the feed or some key material in the feed that is converted into products. Conversion is related to the degree of completion of a reaction namely the percentage or fraction of the limiting reactant converted into products. Thus, percent conversion is
% conversionmolesmoles(or(ormass)mass)ofoffeedfeed(or(oraacomponentcompoundin thein thefeed)feed)introducedthatreact 100
For example , for the reaction equation described in Example 9.2 , if 14.4 kg of CO 2 are formed in the reaction of 10 kg of C 7 H 16 , you can calculate what percent of the C 7 H 16 is converted to CO 2 (reacts) as follows:
C 7 H 16 equivalent to CO 2 in the product
C 7 H 16 in the reactants
Dr. Ahmed Faiq Al-Alawy
The conversion can also be calculated using the extent of reaction as follows: Conversion is equal to the extent of reaction based on CO 2 formation (i.e., the actual extent of reaction ) divided by the extent of reaction assuming complete reaction of C 7 H 16 (i.e., the maximum possible extent of reaction ).
extentofreaction that wouldoccurifcompletereaction tookplace Conversion extentofreaction thatactuallyoccurs
max
9.2.4 Selectivity
Selectivity is the ratio of the moles of a particular (usually the desired) product produced to the moles of another (usually undesired or by-product) product produced in a set of reactions. For example, methanol (CH 3 OH) can be converted into ethylene (C 2 H 4 ) or propylene (C 3 H 6 ) by the reactions
What is the selectivity of C 2 H 4 relative to the C 3 H 6 at 80% conversion of the CH 3 OH? At 80% conversion: C 2 H 4 19 mole % and for C 3 H 6 8 mole %. Because the basis for both values is the same, the selectivity = 19/8 = 2.4 mol C 2 H 4 per mol C 3 H 6.
9.2.5 Yield
No universally agreed-upon definitions exist for yield —in fact, quite the contrary. Here are three common ones: Yield (based on feed) —the amount (mass or moles) of desired product obtained divided by the amount of the key (frequently the limiting) reactant fed. Yield (based on reactant consumed) —the amount (mass or moles) of desired product obtained divided by amount of the key (frequently the limiting) reactant consumed. Yield (based on theoretical consumption of the limiting reactant) —the amount (mass or moles) of a product obtained divided by the theoretical (expected) amount of the product that would be obtained based on the limiting reactant in the chemical reaction equation if it were completely consumed.
Dr. Ahmed Faiq Al-Alawy
C 3 H 6 Cl 2 is propylene chloride (1,2—dichloropropane) (MW = 112.99) The species recovered after the reaction takes place for some time are listed in Table E9.8.
species Cl 2 C 3 H 6 C 3 H 5 C1^ C 3 H 6 Cl 2 HCl g mol 141 651 4.6 24.5 4. Based on the product distribution assuming that no allyl chlorides were present in the feed, calculate the following: a. How much Cl 2 and C 3 H 6 were fed to the reactor in g mol? b. What was the limiting reactant? c. What was the excess reactant? d. What was the fraction conversion of C 3 H 6 to C 3 H 5 C1? e. What was the selectivity of C 3 H 5 C1 relative to C 3 H 6 Cl 2? f. What was the yield of C 3 H 5 C1 expressed in g of C 3 H 5 C1 to the g of C 3 H 6 fed to the reactor? g. What was the extent of reaction of the first and second reactions? Solution Figure E9.8 illustrates the process as an open-flow system. A batch process could alternatively be used.
A convenient basis is what is given in the product list in Table E9.8. Reaction (a)
Reaction (b)
Total = 4.6 + 24.5 = 29.l g mol Cl 2 reacts Cl 2 in product = 141.0 from Table E9. (a) Total Cl 2 fed = 141.0 + 29.1 = 170.1 g mol Cl 2 Total C 3 H 6 fed = 651.0 + 29.1 = 680.1 g mol of C 3 H 6
Dr. Ahmed Faiq Al-Alawy
(b) and (c) Since both reactions involve the same value of the respective reaction stoichiometric coefficients , both reactions will have the same limiting and excess reactants
Thus, C 3 H 6 was the excess reactant and Cl 2 the limiting reactant.
(d) The fraction conversion of C 3 H 6 to C 3 H 5 C1 was
(e) The selectivity was
(f) The yield was
(g) Because C 3 H 5 C1 is produced only by the first reaction , the extent of reaction of the first reaction is
Because C 3 H 6 C 12 is produced only by the second reaction , the extent of reaction of the second reaction is
Example 9. Five pounds of bismuth (MW=209) is heated along with one pound of sulfur (MW=32) to form Bi 2 S 3 (MW=514). At the end of the reaction, the mass is extracted and the free sulfur recovered is 5% of the reaction mass. Determine 2 Bi + 3 S Bi 2 S 3
- The limiting reactant.
- The percent excess reactant.
- The percent conversion of sulfur to Bi 2 S 3
Dr. Ahmed Faiq Al-Alawy
Problems
- Write balanced reaction equations for the following reactions: a. C 9 H 18 and oxygen to form carbon dioxide and water. b. FeS 2 and oxygen to form Fe 2 O 3 and sulfur dioxide.
- If 1 kg of benzene (C 6 H 6 ) is oxidized with oxygen, how many kilograms of O 2 are needed to convert all the benzene to CO 2 and H 2 O?
- The electrolytic manufacture of chlorine gas from a sodium chloride solution is carried out by the following reaction:
How many kilograms of Cl 2 can be produced from 10 m^3 of brine solution containing 5% by weight of NaCl? The specific gravity of the solution relative to that of water at 4°C is 1.07.
- Can you balance the following chemical reaction equation?
- For the reaction in which stoichiometric quantities of the reactants are fed
and the reaction goes to completion, what is the maximum extent of reaction based on C 5 H 10? On O 2? Are the respective values different or the same? Explain the result.
- Calcium oxide (CaO) is formed by decomposing limestone (pure CaCO 3 ). In one kiln the reaction goes to 70% completion. a. What is the composition of the solid product withdrawn from the kiln? b. What is the yield in terms of pounds of CO 2 produced per pound of limestone fed into the process?
- Aluminum sulfate can be made by reacting crushed bauxite ore with sulfuric acid, according to the following chemical equation:
The bauxite ore contains 55.4% by weight of aluminum oxide, the remainder being impurities. The sulfuric acid solution contains 77.7% pure sulfuric acid, the remainder being water. To produce crude aluminum sulfate containing 1798 lb of pure aluminum sulfate, 1080 lb of bauxite ore and 2510 lb of sulfuric acid solution are reacted. a. Identify the excess reactant. b. What percentage of the excess reactant was consumed?
Dr. Ahmed Faiq Al-Alawy
c. What was the degree of completion of the reaction?
- Two well-known gas phase reactions take place in the dehydration of ethane:
Given the product distribution measured in the gas phase reaction of C 2 H 6 as follows C 2 H 6 27%, C 2 H 4 33%, H 2 13%, and CH 4 27%
a. What species was the limiting reactant? b. What species was the excess reactant? c. What was the conversion of C 2 H 6 to CH 4? d. What was the degree of completion of the reaction? e. What was the selectivity of C 2 H 4 relative to CH 4? f. What was the yield of C 2 H 4 expressed in kg mol of C 2 H 4 produced per kg mol of C 2 H 6? g. What was the extent of reaction of C 2 H 6?
Answers:
- (a) (b)
- 323
- No
- (a) 1, (b) 1, (c) The same, (d) The extent of reaction depends on the reaction equation as a whole and not on one species in the equation.
- CaCO 3 : 43.4%, CaO: 56.4%; (b) 0.
- (a) H 2 SO 4 (b) 79.2%; (c) 0.
- (a) C 2 H 6 (the hydrogen is from reaction No.2, not the feed); (b) None;
Dr. Ahmed Faiq Al-Alawy
Problem 2
Dr. Ahmed Faiq Al-Alawy
