Equilibrium of stearic acid dimerization when dissolved in hexane

[ada0713]

Homework Statement

Stearic acid, nature's most common fatty acid, dimerizes when dissolved in hexane:
2C17H35COOH --> (C17H35COOH)2 H°rxn = -172 kJ
The equilibrium constant for this reaction at 28°C is 2900. Estimate the equilibrium constant at 38°C.

1) 4.7 *10^5
2) 1.9 * 10^3
3) 2.6 *10^4
4) 18
5) 3.2 *10^2

The Attempt at a Solution

The reaction is exothermic( since delta H is negative)
therefore the actual equation will look like:

2C17H35COOH --> (C17H35COOH)2 + heat

If the temperature chanages from 28C to 38C it means that
the heat is added to the system, thus, the equilibrium will shift towards left.
this will cause the reactant to increase
making Kc to decrease. (since Kc= product/reactant)

So I eliminated answer choices that are larger than 2900 (the Kc at 28C).
And I'm left with 2, 4, and 5.
The anwer choice 2 seems to be the most reasonable
since it decrease by 100, and the other answers seem to decrease too much.
But I'm not positive about my decision.
Is there any way to actually caculate Kc value, or is my method correct?

Help!

 

[ada0713]

Does anyone know how to slove this question?

 

[Blueshift5]

Your method is correct. The equilibrium constant at a higher temperature will be lower due to the shift towards the reactants. Choice 2, 1.9 * 10^3, is the most reasonable answer. However, if you wanted to calculate the exact value, you could use the Van't Hoff equation:

ln(K2/K1) = -(ΔH°/R)(1/T2 - 1/T1)

where K1 and K2 are the equilibrium constants at temperatures T1 and T2 respectively, ΔH° is the enthalpy change of the reaction, and R is the gas constant. Rearranging for K2, we get:

K2 = K1 * e^[(ΔH°/R)(1/T2 - 1/T1)]

Plugging in the values given in the problem, we get:

K2 = (2900) * e^[(172000/8.314)(1/311 - 1/301)] = 1914.9

which is closest to choice 2, 1.9 * 10^3.