Question

Hydrogen chloride can be made from the reaction of chlorine and hydrogen: $$ \mathrm{Cl}_{2}(g)+\mathrm{H}_{2}(g) \longrightarrow 2 \mathrm{HCl}(g) $$ For this reaction, \(K=26 \times 10^{33}\) and \(\Delta H=-184 \mathrm{~kJ} / \mathrm{mol}\) at \(298 \mathrm{~K}\). (a) Is the reaction endothermic or exothermic? (b) Are the reactants or the products favored at equilibrium? (c) Explain the effect on the equilibrium of (1) Increasing pressure by decreasing volume (2) Increasing the concentration of \(\mathrm{HCl}(g)\) (3) Decreasing the concentration of \(\mathrm{Cl}_{2}(g)\) (4) Increasing the concentration of \(\mathrm{H}_{2}(g)\) (5) Adding a catalyst

Short answer

(a) Exothermic. (b) Products favored. (c) (1) No effect, (2) shift left, (3) shift left, (4) shift right, (5) no effect.

Step-by-step solution

Determine if the reaction is endothermic or exothermic

The sign of \( \Delta H \) indicates whether the reaction is exothermic or endothermic. In this case, \( \Delta H = -184 \,\mathrm{kJ/mol}\). Since \( \Delta H \) is negative, the reaction releases heat and is exothermic.

Determine equilibrium favorability

Evaluate the given equilibrium constant \( K = 26 \times 10^{33} \). This extraordinarily large value of \( K \) suggests that the concentration of products (\( \mathrm{HCl} \)) is much greater than that of the reactants (\( \mathrm{Cl_2} \) and \( \mathrm{H_2} \)) at equilibrium. Therefore, the products are heavily favored at equilibrium.

Consider equilibrium changes with pressure

Analyze the effect of increasing pressure by decreasing volume. According to Le Chatelier's Principle, the equilibrium will shift to favor the side of the reaction with fewer moles of gas to counteract the pressure increase. The reaction: \( \mathrm{Cl}_2(g) + \mathrm{H}_2(g) \rightarrow 2 \mathrm{HCl}(g) \) has 2 moles of gas on both sides. Thus, pressure changes will not shift the equilibrium.

Effect of increasing \( \mathrm{HCl}(g) \) concentration

Increasing the concentration of \( \mathrm{HCl}(g) \) will cause the equilibrium to shift to the left, towards the reactants, to counter the change and decrease the concentration of \( \mathrm{HCl}(g) \).

Effect of decreasing \( \mathrm{Cl}_2(g) \) concentration

Decreasing the concentration of \( \mathrm{Cl}_2(g) \) will shift the equilibrium to the left as well, towards the reactants, as the system attempts to increase the concentration of \( \mathrm{Cl}_2(g) \).

Effect of increasing \( \mathrm{H}_2(g) \) concentration

Increasing the concentration of \( \mathrm{H}_2(g) \) will shift the equilibrium to the right, toward the products, since the system will attempt to consume more \( \mathrm{H}_2(g) \).

Effect of adding a catalyst

Adding a catalyst speeds up both the forward and reverse reactions equally, so it does not affect the position of equilibrium. It only helps the system reach equilibrium more quickly.

Key concepts

Exothermic Reaction

An exothermic reaction is a chemical process that releases heat into the surroundings. This is identified by a negative change in enthalpy (\( \Delta H \)). In our specific reaction, the value of \( \Delta H \) is \(-184 \, \mathrm{kJ/mol}\). The negative sign indicates that heat is being released as the reaction proceeds, making it exothermic.
This release of energy is often felt as heat and can also result in light or other forms of energy, depending on the context of the reaction. The release of heat indicates that the products formed are more stable, having lower energy than the reactants.
In exothermic reactions like the one given, the surrounding environment may experience an increase in temperature. An everyday example is the combustion of fuels, which releases significant amounts of heat energy.

Le Chatelier's Principle

Le Chatelier's Principle is a fundamental concept in chemical equilibrium. It helps us understand how a system at equilibrium reacts to external changes. This principle states that if a dynamic chemical equilibrium is disturbed by changing the conditions, the position of equilibrium shifts to counteract the change and re-establish equilibrium.
For example, in our reaction, if we increase the concentration of \(\mathrm{HCl}(g)\), Le Chatelier's Principle predicts that the equilibrium will shift. It will move towards the reactants' side to reduce \(\mathrm{HCl}(g)\) concentration. Conversely, decreasing the concentration of \(\mathrm{Cl}_2(g)\) will shift the equilibrium towards the reactants to increase \(\mathrm{Cl}_2(g)\) concentration.
Additionally, according to this principle, changing the pressure by decreasing the volume can affect reactions with differing moles of gas on each side. In our exercise, because both sides have the same number of moles of gas, changing pressure does not shift the equilibrium.
This principle provides a predictive basis for understanding how equilibrium systems respond to changes, though it does not explain why these shifts happen at a molecular level.

Equilibrium Constant

The equilibrium constant \(K\) gives insight into the position of the equilibrium in a chemical reaction. It reflects the ratio of the concentrations of products to reactants at equilibrium, with each concentration raised to the power of its stoichiometric coefficient. For our reaction which produces hydrogen chloride, the equilibrium constant \(K\) is given as \(26 \times 10^{33}\).
This is an incredibly large value, indicating the concentration of products is much higher than that of the reactants at equilibrium. Hence, the reaction heavily favors the formation of products. The equilibrium constant is affected by temperature, and changes to the system or modifications at a different temperature would result in a different value.
Calculating \(K\) for other reactions allows chemists to grasp whether a reaction will proceed further to form products or reactants at equilibrium, guiding decisions in industrial and laboratory scenarios.

Catalysis

Catalysis involves using a catalyst to change the rate of a chemical reaction. Catalysts do not affect the position of equilibrium; instead, they allow the system to reach equilibrium faster by providing a different pathway for the reaction with a lower activation energy.
The activation energy is the energy required for reactants to be converted into products. By lowering this energy barrier, a catalyst increases the reaction rate without being consumed in the process.
In the given reaction, adding a catalyst would speed up both the forward and reverse reactions equally. As a result, the equilibrium is reached more quickly, but the ratio of products to reactants at equilibrium remains unchanged.
Catalysts play a critical role in many industrial processes, effectively reducing the time and energy required to produce certain products. This concept is widely utilized, from manufacturing to biological systems where enzymes act as biological catalysts.