Question

How will the value of \(K_{\mathrm{P}}\) for the following reactions be affected by an increase in temperature? (a) \(\mathrm{CO}(g)+2 \mathrm{H}_{2}(g) \rightleftharpoons \mathrm{CH}_{3} \mathrm{OH}(g)\) $$ \Delta H^{\circ}=-18 \mathrm{~kJ} $$ (b) \(\mathrm{N}_{2} \mathrm{O}(g)+\mathrm{NO}_{2}(g) \rightleftharpoons 3 \mathrm{NO}(g)\) $$ \Delta H^{\circ}=+155.7 \mathrm{~kJ} $$ (c) \(2 \mathrm{NO}(g)+\mathrm{Cl}_{2}(g) \rightleftharpoons 2 \mathrm{NOCl}(g)\) \(\Delta H^{\circ}=-77.07 \mathrm{~kJ}\)

Short answer

The value of \(K_{\mathrm{P}}\) will decrease for reactions (a) and (c) as they are exothermic and increase for reaction (b) since it is endothermic.

Step-by-step solution

Analyze Reaction (a)

Identify if the reaction (a) \(\mathrm{CO}(g) + 2 \mathrm{H}_{2}(g) \rightleftharpoons \mathrm{CH}_{3}\mathrm{OH}(g)\) is exothermic or endothermic. The given enthalpy change \(\Delta H^{\circ}\) is -18 kJ, meaning the reaction releases heat and is exothermic.

Apply Le Chatelier’s Principle to Reaction (a)

According to Le Chatelier's Principle, increasing the temperature for an exothermic reaction shifts the equilibrium to the left, decreasing the product concentration and thus, lowering the value of \(K_{\mathrm{P}}\).

Analyze Reaction (b)

Determine if reaction (b) \(\mathrm{N}_{2}\mathrm{O}(g) + \mathrm{NO}_{2}(g) \rightleftharpoons 3 \mathrm{NO}(g)\) is exothermic or endothermic. The enthalpy change \(\Delta H^{\circ}\) is +155.7 kJ, indicating the reaction absorbs heat and is endothermic.

Apply Le Chatelier’s Principle to Reaction (b)

Increasing temperature for an endothermic reaction will shift the equilibrium to the right, increasing the product concentration and thus, increasing the value of \(K_{\mathrm{P}}\).

Analyze Reaction (c)

Assess if reaction (c) \(2 \mathrm{NO}(g) + \mathrm{Cl}_{2}(g) \rightleftharpoons 2 \mathrm{NOCl}(g)\) is exothermic or endothermic. The enthalpy change \(\Delta H^{\circ}\) is -77.07 kJ, which means the reaction is exothermic.

Apply Le Chatelier’s Principle to Reaction (c)

For an exothermic reaction, increasing the temperature will shift the equilibrium toward the reactants. This results in a decrease in the concentration of products and a lower value of \(K_{\mathrm{P}}\).

Key concepts

Equilibrium Constant

Understanding the equilibrium constant is pivotal in grasping the nuances of chemical reactions that are reversible. At a fixed temperature, this constant, symbolized as K or K_P when referring to pressures, is a measure of the relative concentrations (or pressures for gases) of products to reactants at equilibrium.

Imagine a busy downtown where traffic flows both ways; the equilibrium constant would be like having a snapshot of the number of cars in each direction when traffic is perfectly balanced. If the reaction favors products, K is large; if it favors reactants, K is small.

So, when temperature changes, it's like changing the traffic rules: the balance is affected, and the value of K shifts to find a new normal.

Effect of Temperature Change on K

With an increase in temperature, for endothermic reactions, K increases as more products are favored (like turning up the heat encourages more cars to move towards the products' side). Conversely, for exothermic reactions, K decreases with higher temperatures, favoring reactants (as if making it harder for the cars to leave the reactants' side).

Enthalpy Change

The concept of enthalpy change, denoted as ΔH, is akin to the heat content of a system. Think of it as a bank account for energy: deposits and withdrawals represent energy going in or out of the reaction. Positive ΔH (endothermic) means the reaction is 'depositing' heat from the surroundings; it feels cold to the touch because it 'withdraws' warmth from your hand.

Negative ΔH (exothermic), on the other hand, is like an 'energy withdrawal', releasing heat into the surroundings and feeling hot as a cozy fireplace. This energy change is a crucial factor in predicting the effect of temperature changes on the position of equilibrium in a reaction, as per Le Chatelier's Principle.

Role of Enthalpy Change in Equilibrium

When external conditions, such as temperature, change, the enthalpy change indicates in which direction the balance will tip. An increase in temperature supplies additional energy to the system, influencing the direction in which the reaction will shift to re-establish equilibrium.

Endothermic and Exothermic Reactions

Every chemical reaction involves a transfer of energy. In endothermic reactions, energy is absorbed from the environment. Picture a sponge soaking up water; these reactions need external energy to proceed, so when you heat them, they absorb that energy eagerly, like someone wrapping themselves in a warm blanket. This makes the products of an endothermic reaction more stable at higher temperatures.

Exothermic reactions, meanwhile, release energy to the surroundings. Imagine popping a heat pack; they give off energy in the form of heat, making the reactants more stable when the temperature rises.

Application to Daily Life

Whether it's the cooling sensation of an endothermic sports injury pack or the warmth from an exothermic combustion in a car engine, these concepts are essential to understanding everyday physical sensations and the various technologies that power our world.