Problem 58 - General Chemistry: Principles and Modern Applications

Question

In the gas phase, iodine reacts with cyclopentene \(\left(\mathrm{C}_{5} \mathrm{H}_{8}\right)\) by a free radical mechanism to produce cyclopentadiene \(\left(\mathrm{C}_{5} \mathrm{H}_{6}\right)\) and hydrogen iodide. Explain how each of the following affects the amount of \(\mathrm{HI}(\mathrm{g})\) present in the equilibrium mixture in the reaction \begin{array}{r} \mathrm{I}_{2}(\mathrm{g})+\mathrm{C}_{5} \mathrm{H}_{8}(\mathrm{g}) \rightleftharpoons \mathrm{C}_{5} \mathrm{H}_{6}(\mathrm{g})+2 \mathrm{HI}(\mathrm{g}) \\ \Delta H^{\circ}=92.5 \mathrm{kJ} \end{array} (a) Raising the temperature of the mixture; (b) introducing more \(\mathrm{C}_{5} \mathrm{H}_{6}(\mathrm{g}) ;\) (c) doubling the volume of the container holding the mixture; (d) adding an appropriate catalyst; (e) adding an inert gas such as He to a constant-volume reaction mixture.

Step-by-Step Solution

Answer

(a) The amount of HI(g) will decrease. (b) The amount of HI(g) will decrease. (c) The amount of HI(g) will increase. (d) The amount of HI(g) will not change. (e) The amount of HI(g) will not change.

Step 1: Analyze the effect of changing temperature

In general, an increase in temperature favors the endothermic reaction, and a decrease in temperature favors the exothermic reaction. Given that the reaction is exothermic (\(\Delta H^{\circ}=92.5 \mathrm{kJ}\)), raising the temperature will shift the equilibrium to the left, decreasing the amount of HI(g).

Step 2: Analyze the effect of adding more C5H6(g)

Adding more of a product (C5H6(g) in our case) to an equilibrium mixture will shift the equilibrium to the left according to Le Chatelier’s principle. This means more reactants will be formed at the expense of products, hence the amount of HI(g) will decrease.

Step 3: Analyze the effect of doubling the volume of the container

An increase in volume decreases the pressure and favors the side of the reaction with more moles of gas. In our case, the right side of the reaction has more moles of gas (3 moles: 2 moles of HI and 1 mole of C5H6) than the left side (2 moles: 1 mole each of I2 and C5H8). So, doubling the volume of the container will shift the equilibrium to the right, increasing the amount of HI(g).

Step 4: Analyze the effect of adding a catalyst

Adding a catalyst does not shift the equilibrium position. A catalyst only changes the rate at which equilibrium is achieved. It does this by reducing the activation energy of both the forward and the reverse reactions equally. Therefore, adding an appropriate catalyst does not affect the amount of HI(g).

Step 5: Analyze the effect of adding an inert gas

Adding an inert gas at constant volume does not affect the equilibrium position because it doesn't change the partial pressures of the reaction components. The total pressure of the system increases, but the reaction quotient remains unaffected. Hence, the addition of an inert gas like He to the reaction mixture at constant volume doesn't change the amount of HI(g).

Key Concepts

Le Chatelier's Principle

Le Chatelier's principle is a fundamental concept used to predict the behavior of a chemical system at equilibrium when it is subjected to an external change. According to this principle, if a dynamic equilibrium is disturbed by changing the conditions, the system adjusts its position to partially counteract the change.

For example, in the gas-phase reaction between iodine and cyclopentene, adding more product cyclopentadiene would result in the system shifting its equilibrium position to the left to decrease the concentration of this newly added product and produce more reactants. Similarly, changes in temperature and pressure also induce shifts in the system's equilibrium according to Le Chatelier's principle, aiming to restore balance.

Reaction Quotient

The reaction quotient (Q) is a measure that tells us whether a system is at equilibrium or which direction it has to shift to reach equilibrium. It is calculated just like the equilibrium constant (K), but with the concentrations (or partial pressures) of the reactants and products at any point in time rather than at equilibrium.

If QK, the reaction will shift to the left to form more reactants. In our exercise, by adding more cyclopentadiene (a product), Q would be greater than K, indicating that the reaction would shift to the left to reduce the amount of cyclopentadiene and HI and to increase the amount of iodine and cyclopentene.

Catalyst Effect on Equilibrium

A catalyst affects the rate at which chemical equilibrium is achieved but does not alter the position of the equilibrium itself. It achieves this by providing an alternative reaction pathway with a lower activation energy, which increases the rate of both the forward and reverse reactions equally.

In the given exercise, introducing an appropriate catalyst would hasten the attainment of equilibrium but wouldn't change the equilibrium concentrations of the reactants or products, including hydrogen iodide (HI). Therefore, the amount of HI(g) present in the equilibrium mixture remains constant regardless of the presence of a catalyst.

Equilibrium and Temperature

Temperature changes affect the equilibrium position of endothermic and exothermic reactions differently. Raising the temperature of an exothermic reaction (like our HI-forming reaction, which releases heat) shifts the equilibrium to favor the reactants, as per Le Chatelier's principle. This shift counteracts the temperature change by absorbing the added heat. Conversely, lowering the temperature would favor the formation of products in an exothermic reaction.

Applying this to our scenario, raising the temperature of the mixture would result in a decrease in the concentration of HI(g) due to the equilibrium shift towards the reactants, thus reducing the amount of hydrogen iodide produced.

Equilibrium Shift with Volume Change

Changing the volume of a container affects the equilibrium position of reactions involving gases, because it changes the partial pressures of the reactants and products. According to Le Chatelier's principle, reducing the volume increases pressure and shifts the equilibrium toward the side with fewer moles of gas, and vice versa.

In the case of the iodine-cyclopentene reaction, doubling the volume of the container decreases the pressure and favors the formation of more products, as the right side of the reaction has more moles of gas. This shift increases the amount of hydrogen iodide (HI) in the equilibrium mixture, as the system tries to restore equilibrium by moving toward the side with more moles of gas.