Question

Consider the general reaction $$ 2 \mathrm{~A}(g)+\mathrm{B}(s) \rightleftharpoons \mathrm{C}(g)+3 \mathrm{D}(g) \quad \Delta H=+115 \mathrm{~kJ} / \mathrm{mol} $$ which has already come to equilibrium. Predict whether the equilibrium will shift to the left, will shift to the right, or will not be affected if the changes indicated below are made to the system. a. Additional \(\mathrm{B}(s)\) is added to the system. b. \(\mathrm{C}(g)\) is removed from the system as it forms. c. The volume of the system is decreased by a factor of 2 . d. The temperature is increased.

Short answer

a. The equilibrium position will not be affected. b. The equilibrium will shift to the right. c. The equilibrium will shift to the left. d. The equilibrium will shift to the right.

Step-by-step solution

(a) Additional B(s) is added to the system

: Since B is a solid, adding more B(s) would not change its concentration. Therefore, according to Le Chatelier's principle, the equilibrium position will not be affected.

(b) C(g) is removed from the system as it forms

: According to Le Chatelier's principle, when a product (C) is removed from the system, the equilibrium shifts to the right to replace the removed product. Thus, more A(g) and B(s) will react to form C(g) and D(g), and the equilibrium will shift to the right.

(c) The volume of the system is decreased by a factor of 2

: When the volume of the system is decreased, the partial pressures of the gases (A, C, and D) increase. According to Le Chatelier's principle, the system will counteract the change by shifting the equilibrium position to the side with fewer gas moles. In this case, there are 2 moles of A(g) on the left side and 4 moles of gaseous products (C and D) on the right side. Hence, the equilibrium will shift to the left to decrease the pressure.

(d) The temperature is increased

: Since the given reaction is endothermic (\(\Delta H = +115 \ \text{kJ/mol}\)), increasing the temperature will lead to an increase in the rate of the forward reaction (favoring endothermic reactions). According to Le Chatelier's principle, when the temperature is increased for an endothermic reaction, the equilibrium will shift to the right to absorb the added heat. Thus, more A(g) and B(s) will react to form C(g) and D(g), and the equilibrium will shift to the right.

Key concepts

Le Chatelier's Principle

Le Chatelier's principle is a fundamental tool for predicting how a change in conditions can affect a chemical system at equilibrium. It states that if a change is applied to a system at equilibrium, the system will adjust itself to counteract that change and restore a new state of equilibrium.

For example, if you increase the concentration of a reactant in a reversible reaction, the system will tend to produce more products to reduce the increased concentration of the reactant. Conversely, if you remove a product, the system will try to produce more of that product to replace what was removed.

In the context of our exercise, when the reactant B(s) is added to the system, there is no effect on the equilibrium as B is a solid and its concentration remains constant. When product C(g) is removed, the system shifts to the right to produce more C(g). Lowering the system volume causes a pressure increase, shifting the equilibrium to the side with fewer gas moles to reduce pressure. Increasing the temperature of an endothermic reaction shifts the equilibrium to the right to absorb the added heat.

Endothermic Reactions

Endothermic reactions are chemical reactions that absorb energy from their surroundings, usually in the form of heat. This is indicated by a positive \( \Delta H \), which signifies a gain in enthalpy.

In the provided exercise, the reaction absorbing heat (\( +115 \text{kJ/mol} \) is given) is endothermic. Increasing the temperature supplies more heat to the system, thus promoting the endothermic process. For such reactions, Le Chatelier's principle predicts that adding heat will shift the equilibrium to the side that absorbs heat—the side of the reaction that requires energy input. Therefore, for the reaction in the exercise, an increase in temperature will drive the reaction to produce more products C(g) and D(g).

Equilibrium Shifts

Equilibrium shifts occur when a system at equilibrium is disturbed by a change in concentration, pressure, volume, or temperature. The reaction shifts in a direction that counteracts the change, as described by Le Chatelier's principle.

When analyzing how equilibrium will shift, it's important to consider all changes. For instance, adding or removing substances shifts the equilibrium towards products or reactants, respectively. Changing the volume affects pressure—reducing volume increases pressure, so the system shifts towards the side with fewer gas particles to reduce pressure. As for temperature changes, the direction of shift depends on whether the reaction is endothermic or exothermic. The exercise illustrates how these different types of changes can result in shifts to the left or right in an attempt to reestablish equilibrium.

Reaction Quotient

The reaction quotient, \( Q \), is a measure that compares the concentrations of reactants and products at any point during a reaction. It is calculated in the same way as the equilibrium constant \( K \) but is not limited to equilibrium conditions.

\( Q \) helps us determine the direction in which a reaction will need to shift to reach equilibrium. If \( Q < K \) for a chemical reaction, the system will shift to the right, favoring product formation to reach equilibrium. If \( Q > K \) the system will shift to the left, favoring the formation of reactants. This concept is not directly addressed in the exercise but is crucial for understanding how systems at equilibrium respond to changes in the reaction conditions.