Chemistry · General chemistry II · Worked example
Predict how temperature changes K
A reaction has ΔH° = −100. kJ and ΔS° = −200. J/K, both taken as constant with temperature. Find K at 298 K and at 400. K, and explain the change with Le Châtelier’s principle.
ΔG° at each temperature
Use ΔG° = ΔH° − TΔS°, with ΔS° in kJ/K.
K from ΔG°
ln K = −ΔG°/RT, with ΔG° in J. So ln K = 16.3 at 298 K and 6.01 at 400. K, which gives K = 1.2 × 10⁷ and K = 4.1 × 10².
Explain with Le Châtelier
The forward reaction is exothermic, so heat acts as a product. Raising the temperature is like adding heat, and the equilibrium shifts toward reactants: K falls by a factor of about 30,000.
The rule behind it
The sign of ΔH° decides the direction: on heating, K falls for an exothermic reaction and rises for an endothermic one. Concentration, pressure and catalysts never change K.
Result
K = 1.2 × 10⁷ at 298 K and 4.1 × 10² at 400. K: heating shifts this exothermic reaction toward reactants.
Your turn
An endothermic reaction has ΔH° = +50.0 kJ and ΔS° = +100. J/K. How does K change between 300. K and 600. K?
Show the answer and explanation
It rises, from 3.3 × 10⁻⁴ to 7.4.
ΔG° is +20.0 kJ at 300. K and −10.0 kJ at 600. K, so ln K goes from −8.02 to +2.00. Heating favors the endothermic direction.
Keep exploring
Hess law & thermodynamics opens at 298 K and gives K = 1.2 × 10⁷. Change the temperature to 400 K to see K fall to about 409.
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