Consider a system that initially consists of the gases inside two closed contain

Question

Consider a system that initially consists of the gases inside two closed containers. Container 1 initially contains 1 mole pure gas A at 25 ºC and 1 atm, whereas container 2 initially contains 1 mole pure gas B at 25 ºC and 1 atm. Under these conditions, the molar gibbs free energy of the pure A is 2 KJ/mole, and the molar gibbs free energy of the pure B is 3.714 KJ/mole. Suppose that the contents of container 1 are mixed with the contents of container 2 in a gas phase reactor, and that the following gas phase reaction occurs:

A + B = C + D

In the final state, the contents of the reactor reach equilibrium at 25 ºC and 1 atm. At 25 ºC and 1 atm, the molar gibbs free energy value of pure C is 2 KJ/mole, and the molar gibbs free energy of pure D is 2 KJ/mole. What will be the equilibrium composition in the reactor? Justify your answer.

Explanation / Answer

A + B <-------> C + D

delta G0rkn = delta G0f C + delta G0f D - delta G0f A - delta G0f B = 2+2 - 2 - 3.714 = -1.714 kJ

Now, delta G0rkn = -R*T*lnKeqb

or, Keqb = 2.019

Now, Keqb = {[C]*[D]}/{[A]*[B]}

or, 2.019 = (x*x)/{(1-x)*(1-x)}

or, 2.019 = {x/(1-x)}2

or, 1.421 = x/(1-x)

or, x = 0.587 = moles of C = moles of D

moles of A = moles of B = 1-x = 0.413

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