Problem 72 - Chemistry The Science in Context

Question

In which of the following equilibria does an increase in temperature produce a shift toward the formation of more product? a. \(\mathrm{N}_{2}(g)+3 \mathrm{H}_{2}(g) \rightleftharpoons 2 \mathrm{NH}_{3}(g) \quad \Delta H^{\circ}<0\) b. \(2 \mathrm{NO}_{2}(g) \rightleftharpoons 2 \mathrm{NO}(g)+\mathrm{O}_{2}(g) \quad \Delta H^{\circ}>0\) c. \(\mathrm{C}_{2} \mathrm{H}_{4}(g)+\mathrm{H}_{2}(g) \rightleftharpoons \mathrm{C}_{2} \mathrm{H}_{6}(g) \quad \Delta H^{\circ}<0\)

Step-by-Step Solution

Answer

a) N2(g) + 3 H2(g) ↔ 2 NH3(g) ΔH° < 0 b) 2 NO2(g) ↔ 2 NO(g) + O2(g) ΔH° > 0 c) C2H4(g) + H2(g) ↔ C2H6(g) ΔH° < 0 Answer: b) 2 NO2(g) ↔ 2 NO(g) + O2(g) ΔH° > 0

Step 1: Case (a) N2(g) + 3 H2(g) ↔ 2 NH3(g) ΔH° < 0

The given enthalpy change is negative, which means that the forward reaction is exothermic. According to Le Chatelier's principle, an increase in temperature will shift the equilibrium towards the reverse reaction, i.e., the formation of more reactants (N2 and H2). Therefore, the equilibrium will not shift toward the formation of more products in this case.

Step 2: Case (b) 2 NO2(g) ↔ 2 NO(g) + O2(g) ΔH° > 0

The given enthalpy change is positive, which means that the forward reaction is endothermic. According to Le Chatelier's principle, an increase in temperature will shift the equilibrium towards the forward reaction, i.e., the formation of more products (2 NO and O2). Therefore, the equilibrium will shift toward the formation of more products in this case.

Step 3: Case (c) C2H4(g) + H2(g) ↔ C2H6(g) ΔH° < 0

The given enthalpy change is negative, which means that the forward reaction is exothermic. According to Le Chatelier's principle, an increase in temperature will shift the equilibrium towards the reverse reaction, i.e., the formation of more reactants (C2H4 and H2). Therefore, the equilibrium will not shift toward the formation of more products in this case. In conclusion, an increase in temperature will produce a shift towards the formation of more products only in case (b) 2 NO2(g) ↔ 2 NO(g) + O2(g) ΔH° > 0.

Key Concepts

Chemical Equilibrium

Understanding the concept of chemical equilibrium is crucial for students studying chemistry. Equilibrium is the state where the rate of the forward reaction equals the rate of the reverse reaction. At this point, the concentrations of reactants and products remain constant over time, not because the reactions have stopped, but because they occur at an equal rate.

In a balanced chemical equation, for example, when A and B react to form C and D (\(A + B \rightleftharpoons C + D\)), chemical equilibrium is reached when the amount of A and B converting into C and D equals the amount of C and D reverting back into A and B. However, this does not mean the quantities of reactants and products are equal; it simply implies their conversion rates are the same.

Understanding Equilibrium Constant (K)

Consider the equilibrium expression for the reaction mentioned above, defined as the concentration of products over the concentration of reactants raised to the power of their coefficients: \[ K = \frac{{[C]^c[D]^d}}{{[A]^a[B]^b}} \]If K is greater than 1, the products are favored at equilibrium; if K is less than 1, the reactants are favored. Remember that K is temperature-dependent and that changes in temperature will alter the value of K, shifting the position of equilibrium, as explained by Le Chatelier's principle.

Exothermic and Endothermic Reactions

In the realm of chemistry, reactions are categorized as either exothermic or endothermic based on their heat exchange with the surroundings. Exothermic reactions release heat, thus increasing the temperature of the surroundings, and are typically associated with a negative change in enthalpy (\( \text{Δ}H˚ < 0\text{, meaning the system loses heat}\)). Common examples include combustion reactions and respiration.

On the other hand, endothermic reactions absorb heat, resulting in a decrease in temperature of the surroundings. They exhibit a positive change in enthalpy (\( \text{Δ}H˚ > 0 \text{, indicating heat is taken in by the system}\)). Examples include photosynthesis and the melting of ice.

Implications on Equilibrium

The enthalpy change during a reaction affects equilibrium. For exothermic reactions, the products are favored at lower temperatures since heat is a product of the reaction. Conversely, endothermic reactions favor the formation of products at higher temperatures because they require heat as a reactant.

Temperature Effect on Equilibrium

Le Chatelier's principle provides insight into how systems at equilibrium respond to changes in conditions, such as temperature. If a system at equilibrium is disturbed, it will adjust itself to counteract the disturbance and re-establish equilibrium.

When the temperature of a system is increased, Le Chatelier's principle predicts that the system will shift the equilibrium to consume the excess heat. In an exothermic reaction, this means favoring the reverse reaction to absorb heat and produce more reactants. Conversely, in an endothermic reaction, increasing temperature shifts the equilibrium toward the forward reaction, thus producing more products as the reaction absorbs heat.

Temperature and Equilibrium Constant

Temperature changes not only shift the equilibrium position but also alter the equilibrium constant (K). For exothermic reactions, an increase in temperature will decrease K since the products are less favored. In contrast, for endothermic reactions, increasing temperature raises K, indicating that the products are more favored at higher temperatures. This knowledge is important for industrial processes and can be applied when predicting the outcome of a chemical reaction under different thermal conditions.