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Steam reforming of methane (CH) produces "synthesis gas," a mixture of carbon monoxide gas and hydrogen gas, which is the starting point for many important industrial chemical syntheses. An industrial chemist studying this reaction fills a 125. L tank with 7.0 mol of methane gas and 45. mol of water vapor, and when the mixture has come to equilibrium measures the amount of carbon monoxide gas to be 4.9 mol. Calculate the concentration equilibrium constant for the steam reforming of methane at the final temperature of the mixture. Round your answer to 2 significant digits. K = []

Steam reforming of methane (CH) produces "synthesis gas," a mixture of carbon monoxide gas and hydrogen gas, which is the starting point for many important industrial chemical syntheses. An industrial chemist studying this reaction fills a 125. L tank with 7.0 mol of methane gas and 45. mol of water vapor, and when the mixture has come to equilibrium measures the amount of carbon monoxide gas to be 4.9 mol. Calculate the concentration equilibrium constant for the steam reforming of methane at the final temperature of the mixture. Round your answer to 2 significant digits. K = []

Chemistry
Chemistry
10th Edition
ISBN:9781305957404
Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Publisher:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Chapter1: Chemical Foundations
Section: Chapter Questions
Problem 1RQ: Define and explain the differences between the following terms. a. law and theory b. theory and...
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You could write down the concentration equilibrium constant expression from the balanced chemical equation -- but you're not given that. You are, however, given a description of the reaction, and you can use that to construct the chemical equation, provided you remember how to go from the names of binary chemical compounds to their chemical formulae, and how to balance a chemical equation: 4NH₂(g) + 30₂ (g) 2N₂(g) + 6H₂O(g) With the chemical equation you can construct the concentration equilibrium constant expression: [N₂] [H₂o] [NH.] [9₂] The next step is to find the equilibrium molarities to put into this expression, and here there may seem to be a snag: you're only given the equilibrium moles of the N₂. What about the rest of the reactants and products? What's important here is not to forget your skills in stoichiometry when you're focused on solving equilibrium problems. Remember that if you know the change in amount of any one reactant or product, you can solve for the change in the amounts of any other reactant or product by using the chemical equation. For example, the rise in moles of H₂O is equal to the rise in moles of N, multiplied by the ratio of their stoichiometric coefficients: 6 6 change in H₂O = ( change in N₂) = (3.0) = 9.000... mol You can use relationships like this to solve for all the equilibrium moles, and then divide by the volume of the tank to get equilibrium molarities. Another approach is to write an ICE table, even though you're not going to use it to solve a quadratic equation. Let's see what the ICE table for this reaction looks like when you let stand for the rise in molarity of ₂ initial change equilibrium [NH₂] 0.3280 -2x 0.3280 -2x EANSWER [%] 0.06000 [NH,]= 0.3280-2 (0.02400) = 0.2800... [0₂] = 0.06000-(0.02400) = 0.02400... [¹₂] = 0.02400... [H₂0]=3(0.02400) = 0.07200... (0.02400)²-(0.07200) (0.2800)*- (0.02400) X = 9.4 x 10-4 3 0.06000-x What's useful about this ICE table is that you already know *: you're told the equilibrium moles of N₂ is 3.0 mol, and dividing by the volume of the tank gives you its equilibrium molarity x = 0.02400 mol/L. So if you substitute 0.02400 for x in all the expressions on the "equilibrium" line of the ICE table -- why, there are your equilibrium molarities, ready to put into the equilibrium constant expression. Don't forget to round your final answer to 2 significant digits. [N] [H₂0] 0 0 9.444 x 10-4 3x Now you're ready to substitute the equilibrium molarities into the equilibrium constant expression to find 3x Remember you'll need to convert moles to mol/L by dividing each initial amount by the volume of the tank. Keep a few extra digits for now, and only round your final answer to the requested number of significant digits. Ar à 28
Transcribed Image Text:You could write down the concentration equilibrium constant expression from the balanced chemical equation -- but you're not given that. You are, however, given a description of the reaction, and you can use that to construct the chemical equation, provided you remember how to go from the names of binary chemical compounds to their chemical formulae, and how to balance a chemical equation: 4NH₂(g) + 30₂ (g) 2N₂(g) + 6H₂O(g) With the chemical equation you can construct the concentration equilibrium constant expression: [N₂] [H₂o] [NH.] [9₂] The next step is to find the equilibrium molarities to put into this expression, and here there may seem to be a snag: you're only given the equilibrium moles of the N₂. What about the rest of the reactants and products? What's important here is not to forget your skills in stoichiometry when you're focused on solving equilibrium problems. Remember that if you know the change in amount of any one reactant or product, you can solve for the change in the amounts of any other reactant or product by using the chemical equation. For example, the rise in moles of H₂O is equal to the rise in moles of N, multiplied by the ratio of their stoichiometric coefficients: 6 6 change in H₂O = ( change in N₂) = (3.0) = 9.000... mol You can use relationships like this to solve for all the equilibrium moles, and then divide by the volume of the tank to get equilibrium molarities. Another approach is to write an ICE table, even though you're not going to use it to solve a quadratic equation. Let's see what the ICE table for this reaction looks like when you let stand for the rise in molarity of ₂ initial change equilibrium [NH₂] 0.3280 -2x 0.3280 -2x EANSWER [%] 0.06000 [NH,]= 0.3280-2 (0.02400) = 0.2800... [0₂] = 0.06000-(0.02400) = 0.02400... [¹₂] = 0.02400... [H₂0]=3(0.02400) = 0.07200... (0.02400)²-(0.07200) (0.2800)*- (0.02400) X = 9.4 x 10-4 3 0.06000-x What's useful about this ICE table is that you already know *: you're told the equilibrium moles of N₂ is 3.0 mol, and dividing by the volume of the tank gives you its equilibrium molarity x = 0.02400 mol/L. So if you substitute 0.02400 for x in all the expressions on the "equilibrium" line of the ICE table -- why, there are your equilibrium molarities, ready to put into the equilibrium constant expression. Don't forget to round your final answer to 2 significant digits. [N] [H₂0] 0 0 9.444 x 10-4 3x Now you're ready to substitute the equilibrium molarities into the equilibrium constant expression to find 3x Remember you'll need to convert moles to mol/L by dividing each initial amount by the volume of the tank. Keep a few extra digits for now, and only round your final answer to the requested number of significant digits. Ar à 28
Steam reforming of methane (CH) produces "synthesis gas," a mixture of carbon monoxide gas and hydrogen gas, which is the starting point for many important industrial chemical syntheses. An industrial chemist studying this reaction fills a 125. L tank with 7.0 mol of methane gas and 45. mol of water vapor, and when the mixture has come to equilibrium measures the amount of carbon monoxide gas to be 4.9 mol. Calculate the concentration equilibrium constant for the steam reforming of methane at the final temperature of the mixture. Round your answer to 2 significant digits. K = [] x10 Xx
Transcribed Image Text:Steam reforming of methane (CH) produces "synthesis gas," a mixture of carbon monoxide gas and hydrogen gas, which is the starting point for many important industrial chemical syntheses. An industrial chemist studying this reaction fills a 125. L tank with 7.0 mol of methane gas and 45. mol of water vapor, and when the mixture has come to equilibrium measures the amount of carbon monoxide gas to be 4.9 mol. Calculate the concentration equilibrium constant for the steam reforming of methane at the final temperature of the mixture. Round your answer to 2 significant digits. K = [] x10 Xx
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