WBJEE 2024 Physics & Chemistry Paper

To understand the relationship between the equilibrium constant and the rate constant with temperature for a single-step chemical reaction, we need to consider the following concepts:Rate Constant $(k)$ :The rate constant of a reaction is influenced by temperature according to the Arrhenius equation:$k=A e^{-\frac{E_a}{R T}}$where $A$ is the pre-exponential factor, $E_a$ is the activation energy, $R$ is the gas constant, and $T$ is the temperature in Kelvin. From this equation, it's clear that the rate constant $k$ generally increases with an increase in temperature. Equilibrium Constant $(K_{\text{eq}})$ :The equilibrium constant is related to the Gibbs free energy change $(\Delta G^{\circ})$ of the reaction:$\Delta G^{\circ} = -R T \ln K_{\text{eq}}$If the reaction's $\Delta H$ is positive (endothermic), an increase in temperature results in an increase in $K_{\text{eq}}$. Conversely, for an exothermic reaction ( $\Delta H$ is negative), an increase in temperature results in a decrease in $K_{\text{eq}}$. This is described by the van 't Hoff equation:$\left( \frac{d \ln K_{\text{eq}}}{d T} \right) = \frac{\Delta H^{\circ}}{R T^2}$ Thus, the behavior of the equilibrium constant with temperature depends on the nature of the reaction (whether it is endothermic or exothermic).Given the above explanation, the correct answer is:Option A: Equilibrium constant may increase or decrease but the rate constant always increases with temperature.