Ammonia has been studied as an alternative \"clean\" fuel for internal combustio

Question

Ammonia has been studied as an alternative "clean" fuel for internal combustion engines, since its reaction with oxygen produces only nitrogen and water vapor, and in the liquid form it is easily transported. An industrial chemist studying this reaction fills a 100. L tank with 5.5 mol of ammonia gas and 23. mol of oxygen gas at 38. °C. He then raises the temperature, and when the mixture has come to equilibrium measures the amount of nitrogen gas to be 1.4 mol Calculate the concentration equilibrium constant for the combustion of ammonia at the final temperature of the mixture. Round your answer to 2 significant digits.

Explanation / Answer

the reation is given by

4NH3 (l) + 3 O2 (g) ---> 2N2 (g) + 6H2O (g)

Initially we have NH3 moles = 5.5 , O2 moles = 23 , N2 moles = H2O moles = 0

concentration = moles / volume

Initially [NH3] =5.5 / 100 = 0.055 M , [O2] = 23/100 = 0.23M , [N2] =[H2O] =0

at equilibrium [NH3] = 0.055-4X , [O2] = 0.23-3X , [N2] = 2X , [H2O] = 6X

given N2 equilibrium moles = 1.4 , hence equilibrium [N2] = moles / volume = 1.4 /100 = 0.0014

hence 2X = 0.0014 , X = 0.0007

now [NH3] = ( 0.055- 4(0.0007) = 0.0522 ,  

[O2] = 0.23 - 3( 0.0007) = 0.2279 M

[N2] = 0.0014 M

[H2O] = 6 x 0.0007M = 0.0042 M

Kc = [N2]^2 [H2O]^ 6 / [NH3]^4 [O2] ^ 3

= 1.2 x 10^ -13

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