# Gibbs free energy of phosphorus pentachloride decomposition reaction

The equilibrium constant at $$\pu{227 °C}$$ for the equation

$$\ce{PCl5(g) <=> PCl3(g) + Cl2(g)}$$

is $$K_p = \pu{4.50E3 bar}.$$ Calculate the value of $$Δ_\mathrm{rxn}G^\circ$$ at $$\pu{227 °C}$$.

With the temperature at $$\pu{227 °C}$$ and the partial pressures of the gases of $$p(\ce{PCl3}) = \pu{0.286 bar},$$ $$p(\ce{Cl2}) = \pu{0.713 bar},$$ and $$p(\ce{PCl5}) = \pu{3.06E-6 bar},$$ calculate the value of $$Δ_\mathrm{rxn}G.$$

I calculated $$Δ_\mathrm{rxn}G^\circ$$ to be $$\pu{-34.97 kJ mol-1}.$$ Wouldn't it just be

$$Δ_\mathrm{rxn}G^\circ = -\pu{0.0083145 kJ mol-1 K-1} × \pu{500 K} × \ln(\pu{4.5E3})?$$

For the second part of the question I got $$\pu{11.20 kJ mol-1},$$ but apparently this is also wrong, no doubt because I got the first part wrong.

Would someone care to explain to me?

• What makes you think the first answer is wrong? – andselisk Oct 20 '19 at 5:06
• The website we submit the answer to (Sapling) claims it is wrong. – Denise Oct 20 '19 at 15:42
• It's like a HW platform. I've tried different sig figs and units are already provided. They don't provide an answer unless you either solve it correctly or press "Give Up". – Denise Oct 20 '19 at 16:10
• So I ended up pressing "Give Up". Apparently it wanted only 1 Sig Fig, but no where in the question did it ask for it. – Denise Oct 20 '19 at 18:47
• Thank you!!!! :) – Denise Oct 20 '19 at 20:43