What is the relationship between temperature and the equilibrium constant k? Is it a direct or indirect relationship? And why?
A + B + heat = C
Keq = (C)/(A)(B)
For endothermic reactions increased T will mean the rxn shifts to the right which makes C larger, A and B smaller so K is larger. For exothermic rxns
A + B = C + heat
K = (C)/(A)(B)
For increase in T rxn shifts to left, C becomes smaller, A and B larger so K decreases.
The relationship between temperature and the equilibrium constant (K) is usually described by the Van't Hoff equation, which states that the natural logarithm of the equilibrium constant is directly proportional to the temperature. Mathematically, it can be expressed as:
ln(K2/K1) = ΔH/R * (1/T1 - 1/T2)
where K1 and K2 are the equilibrium constants at temperatures T1 and T2 respectively, ΔH is the enthalpy change of the reaction, R is the ideal gas constant, and T1 and T2 are the absolute temperatures in Kelvin.
From this equation, we can deduce that the relationship between temperature and the equilibrium constant is indirect. As the temperature increases, the value of K increases if the reaction is endothermic (ΔH > 0), while it decreases if the reaction is exothermic (ΔH < 0).
This indirect relationship between temperature and equilibrium constant can be explained by the principle of Le Chatelier. According to Le Chatelier's principle, when temperature is increased, the system tends to shift in the direction that consumes or absorbs heat to counteract the increase in temperature. In an endothermic reaction, heat is consumed during the forward reaction, so increasing the temperature promotes the forward reaction, leading to an increase in K. Conversely, in an exothermic reaction, heat is released during the forward reaction, so increasing the temperature favors the reverse reaction, causing a decrease in K.
In summary, the relationship between temperature and equilibrium constant is indirect, and it is governed by the sign of the enthalpy change (ΔH) of the reaction.