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Homework Statement
At 2600 K, ΔG° = 775 kJ for the vaporization of boron carbide:
[itex]B_{4}C (s) ⇔ 4 B (g) + C (s)[/itex]
Find ΔG and determine if the process is spontaneous if the reaction vessel contains 4.00 mol of [itex]B_{4}C (s)[/itex], 0.400 mol of [itex]C (s)[/itex], and [itex] B (g)[/itex] 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?