Solving Spontaneous Reactions Homework: ΔG -270 kJ

[τheory]

Homework Statement

At 2600 K, ΔG° = 775 kJ for the vaporization of boron carbide:
$B_{4}C (s) ⇔ 4 B (g) + C (s)$

Find ΔG and determine if the process is spontaneous if the reaction vessel contains 4.00 mol of $B_{4}C (s)$, 0.400 mol of $C (s)$, and $B (g)$ at a partial pressure of 1.0 x 10^-5 atm. At this temperature, R T = 21.6 kJ

2. The attempt at a solution

I first tried to find the reaction quotient but quickly realized that they did not give me the volume for this vessel. Thus, I just plugged everything into the reaction quotient (products/reactants) and got Q = 1*10^-21.

Then I plugged that into the ΔG = -RT*ln(Q) equation:

ΔG = -RT*ln(Q)
ΔG = -(21.6 J * 1000)*ln(1*10^-21)
ΔG = 1.044*10^6 J = 1044 kJ

The answer on the back of the book says that ΔG is in fact -270 kJ; how is this the answer? What mistake did I do in my calculations?

 

[Borek]

Please write the reaction quotient.

 

[τheory]

$Q=\frac{(pB)^4*[C]}{[B_{4}C]}$

 

[Borek]

What do you know about solids in this context?

 

[τheory]

Um all I can figure out is that the solids are within a closed vessel and that the temperature also appears to be 2600 K since 21.6kJ/8.314 = 2600. The only issue regarding the solid is that I don't know what the volume is, which is prohibiting me from finding the concentration mol/L.

The only other thing is that maybe I have the wrong idea of how concentration of a solid works?

 

[Borek]

Activity of solids is assumed to be 1, so they are not present in the reaction quotient.