A mixture of argon gas and hydrogen gas at 1 atm total pressure is passed throug

Question

A mixture of argon gas and hydrogen gas at 1 atm total pressure is passed through a reaction vessel containing a mixture of liquid Sn and liquid SnCl2 at 900K. The composition of the gas leaving the vessel is 50% H2, 7% HCl, and 43% Ar. Has equilibrium been obtained between the gas phase and the liquid phases in the vessel?

I've tried to work this out but I can't figure out where I went wrong. Please help me???

This question is 12.5 in Introduction to the Thermodynamics of Materials, 5th edition by David R. Gaskell

Explanation / Answer

Knowns:

T=900K

P=1atm

Components: Ar(g), H2(g), HCl(g), Sn(l), SnCl2(l)

The reactions you’ll need can be found in table A-1:

(a) Sn(l)+Cl2(g) <-> SnCl2(l)                        G°=-333000+118.4T J/mol

(b) H2(g)+Cl2(g) <-> 2HCl(g)                        G°= -188200-12.8T J/mol

Combine the reactions by subtracting a from b:

H2(g)+Cl2(g) <-> 2HCl(g)

-(Sn(l)+Cl2(g) <-> SnCl2(l))=

H2(g)+SnCl2(l) <-> 2HCl(g)+Sn(l)

Calculate G°rxn by subtracting G° of the Sn reaction from G° of the H2 reaction:

G°rxn=-188200-12.8T-(-333000+118.4T)= 144800-131.2T J/mol

At T=900 K, G°rxn=26720 J/mol

Kp=e-G°rxn/RT=e-(26720)/(8.3144*900)

Kp= 0.028134

In the gas phase leaving the reaction vessel,

50% H2, 7% HCl, 43% Ar

PTotal=1atm => Ppi=MFi                  (where Pp= partial pressure and MF=mole fraction)

                  H2                  HCl                  Ar

Ppi=MF .50                  .07                  .43

(The gases went in at 1atm and will come out at 1atm if equilibrium is obtained. The percentages allowed us to calculate the partial pressures of the gasses if the total pressure of the gas leaving the vessel is 1atm)

Now we need to calculate the Product quotient, Jp, and compare it to the value we got for Kp. If they’re equal, equilibrium was obtained.

Jp= ((PpHCl(g))2)/(PpH2(g)) = (.072)/(.50)

Jp= 9.8*10-3

Because KpJp, equilibrium wasn’t obtained.

Another way to figure out if equilibrium were obtained:

Grxn=G°rxn+R*T*ln(Kp)

Grxn=(26720J/mol)+(8.3144J/mol*K)(900K)ln(.028134)

Grxn=-7891 J/mol <- the reaction must proceed toward the products to reach equilibrium

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