# Thermochemistry, calculating T given Q

I have the reaction $\ce{2COCl2(g) -> CCl4(l) + CO2(g)}$

And I want to calculate $T$ (temperature) when $Q = 10^{-4}$ at equilibrium.

I tried simply putting $$T = -\frac{\Delta G^{0}}{\Delta S^{0}-R \ln Q}$$

Anyway, since $\Delta G^{0}$ for the reaction ($\pu{42000J/mol}$) is the value at standard condition (25 degrees celsius) I use that $\Delta G = \Delta H^{0} - T\times\Delta S^{0} + RT\ln Q$ where $\Delta G = 0$ since we're at equilibrium.

From this I obtain that $$T = \frac{\Delta H^{0}}{\Delta S^{0}-R\ln Q}$$

But which $\Delta H^{0}$ and $\Delta S^{0}$ values do I use here? I can calculate them from the standard conditions at 25 degrees celsius using SI, but that wouldnt be correct, would it? I'm rather confused by this task, which seems simple at first sight. Hope someone can clarify.

(The answer should be $\pu{476K}$)

• Are you familiar with the Van't Hoff equation? – Chet Miller Oct 31 '17 at 11:37
• No, not yet. Is this required here? – novo Oct 31 '17 at 11:39
• Your $\LaTeX$ skills are fine, as far as $\Delta{}G^0$ goes. There was another thing that needed correction, but it is specific to this site. – Ivan Neretin Oct 31 '17 at 12:05
• Look it up online and see. – Chet Miller Oct 31 '17 at 12:39
• This question was taken from an earlier test I'm practising on, van't Hoff shouldn't be required. Is there a way around it without using van't Hoff? – novo Oct 31 '17 at 14:10

We know that, at temperature T, $$\Delta G^0(T)=\Delta H^0(T)-T\Delta S^0(T)$$ From Hess's Law, we also know that $$\Delta H^0(T)=\Delta H^0(298)+???$$ and $$\Delta S^0(T)=\Delta S^0(298)+???$$