# Calculating Equilibrium Constant from Cell Potential at Nonstandard Temperature

I'm currently working on a problem for a general chemistry class.
This is the voltaic cell given in the problem: $$\ce{Sn^4+(aq) + Cu(s) -> Sn^2+(aq) + Cu^2+(aq)}$$
$$E^\circ_{cell} = \pu{-0.21 V}$$ What is the value of the equilibrium constant at $$\pu{115 ^\circ C}$$?

For this I'm using this equation $$-nFE^\circ_{cell} = RT\log(K)$$ Plugging this into the equation:
$$(\pu{2 mol e^-})(\pu{96500 C}/\pu{mol e^-})(\pu{-0.21 V}) = (\pu{8.314 J/molK})(\pu{388 K})\log(K)$$ I get a value of $$K = 3.49 \times 10^{-6}$$ However, my instructor's solution is using this equation $$- E^\circ_{cell} = (0.0592/n)\log(K)$$ and gets a value of $$8.04276 \times 10^{-8}$$.

I thought you could only use that equation if the temperature is $$T = \pu{298 K}$$ (standard state conditions). Not sure whether I'm right or wrong about this, any insight is appreciated.

• You'd want to use the van't Hoff equation. – Buck Thorn Jul 24 at 8:49
• What @Buck Thorn said is correct and works fine: I just did the calculation quick and dirty (neglecting entropy, so enthalpy is approximated as the free energy at 298.15K) and got about $1.6 x 10^{-5}$ for the equilibrium constant at 115°C. What your instructor got for the equilibrium constant is fine at 298.15K. – Ed V Jul 24 at 23:21