# How to determine the temperature dependence of equilibrium constants?

Given $K_c=2.8\times10^2$ at $727~^\circ\mathrm{C}$ for $$\ce{ 2SO2 + O2 <=> 2SO3},$$ calculate $K_c$ and $K_p$ when 8 grams of $\ce{SO2}$ result in 0.32 grams of $\ce{O2}$ forming at equilibrium (temperature is not $727~^\circ\mathrm{C}$).

Now at first I thought this was straightforward :

• determine $K_c$ at this temperature from the equilibrium conditions
• apply Van 't Hoff equation to determine the temperature
• calculate $K_p$ from $K_c$ and the temperature

However right after that part of the question the next part asks

Is the new temperature higher or lower than $727~^\circ\mathrm{C}$?

This implies that it is possible to calculate $K_p$ without calculating the temperature? With the new $K$ values then provide a qualitative argument for the temperature increasing or decreasing without having to calculate it?

• Are you certain there isn't a typo in transcribing the original question? – electronpusher Jan 18 '17 at 5:47