Question

With increase in temperature, equilibrium constant of a reaction (a) always decreases (b) always increases (c) may increase or decrease depending upon whether \(n_{p}n_{r}\).

Short answer

The equilibrium constant may increase or decrease with increasing temperature depending on whether the reaction is endothermic (\(n_{p}>n_{r}\)) or exothermic (\(n_{p}<n_{r}\)), hence the correct answer is (c).

Step-by-step solution

Interpreting the effect of temperature on equilibrium constant

According to the Van't Hoff equation, the equilibrium constant of a reaction is directly proportional to the changes in temperature for a reaction. When the temperature increases, if the reaction is exothermic (i.e., releases heat), the equilibrium shifts to the left (reactant side), meaning the equilibrium constant decreases, and hence option (a) is incorrect. Conversely, if the reaction is endothermic (i.e., absorbs heat), the equilibrium shifts to the right (product side), which leads to the increase of the equilibrium constant, and hence option (b) is also incorrect.

Connecting changes in moles with temperature on equilibrium constant

We need to connect this idea with whether \(n_{p}n_{r}\). In a chemical reaction, if there are more moles on the product side (\(n_{p} > n_{r}\)), the reaction is endothermic. Thereby, when the temperature increases, the equilibrium constant increases. On the contrary, when there are more moles on the reactants side (\(n_{p}<n_{r}\)), the reaction is exothermic. Thus, an increase in temperature results in a decrease in the equilibrium constant. This connects to the changes of the equilibrium constant with the number of moles of reactants and products under different temperature conditions.

Conclusion of the exercise

Hence, the equilibrium constant may increase or decrease with increasing temperature depending on whether the reaction is endothermic (\(n_{p}>n_{r}\)) or exothermic (\(n_{p}<n_{r}\)). This satisfies option (c) in the exercise.

Key concepts

Van't Hoff Equation

The Van't Hoff equation is a useful tool in understanding how temperature influences the equilibrium constant of a chemical reaction. It links these concepts through the equation: \[ \ln K_2 - \ln K_1 = -\frac{\Delta H^{\circ}}{R} \left(\frac{1}{T_2} - \frac{1}{T_1}\right) \]where \( K_1 \) and \( K_2 \) are equilibrium constants at temperatures \( T_1 \) and \( T_2 \), respectively, \( \Delta H^{\circ} \) is the standard enthalpy change, and \( R \) is the gas constant.

This equation tells us that the sign of \( \Delta H^{\circ} \) determines how the equilibrium constant \( K \) will shift with temperature. Specifically, the reaction's enthalpy change (whether it is exothermic or endothermic) dictates whether the equilibrium constant will increase or decrease as temperature changes.

So, understanding the Van't Hoff equation helps predict the behavior of chemical reactions under different thermal conditions. This can be particularly vital in chemical engineering and laboratory settings.

Equilibrium Constant

The equilibrium constant, often represented as \( K \), is a fundamental concept in chemistry that quantifies the balance between reactants and products in a chemical reaction at equilibrium. It is defined by the equation:\[ K = \frac{[C]^c [D]^d}{[A]^a [B]^b} \] where \([A]^a\), \([B]^b\), \([C]^c\), and \([D]^d\) refer to the molar concentrations of the reactants and products, with \(a\), \(b\), \(c\), and \(d\) as their stoichiometric coefficients.

The value of \( K \) provides insight into the extent of a reaction:

• If \( K \) is much greater than 1, products dominate at equilibrium.
• If \( K \) is much less than 1, reactants are more prevalent.
• If \( K \) is approximately equal to 1, there are comparable amounts of reactants and products.

Changes in temperature, as described by the Van't Hoff equation, can influence \( K \), leading to shifts in the position of equilibrium. However, \( K \) itself does not tell us whether a reaction is fast or slow; it only indicates the potential completion level under a specific set of conditions.

Exothermic and Endothermic Reactions

Chemical reactions can be classified based on their heat exchange as either exothermic or endothermic. These classifications have a significant impact on how a reaction's equilibrium constant responds to temperature changes.

• In an **exothermic reaction**, heat is released. For these reactions, as temperature increases, the equilibrium shifts towards the reactants (left), decreasing the equilibrium constant.
• In an **endothermic reaction**, heat is absorbed. Here, increasing temperature causes the equilibrium to shift towards the products (right), thus increasing the equilibrium constant.

Understanding whether a reaction is exothermic or endothermic is crucial for predicting how equilibrium will respond to temperature changes using the Van't Hoff equation. It also aids in the design of chemical processes, ensuring conditions are optimized for either maximizing product yield or minimizing undesired by-products.