Problem 75 - Introductory Chemistry Atoms First

Question

One way of preparing hydrogen is by decomposition of water: \(2 \mathrm{H}_{2} \mathrm{O}(g) \rightleftarrows 2 \mathrm{H}_{2}(g)+\mathrm{O}_{2}(g) \quad \Delta E_{\mathrm{rxn}}=484 \mathrm{~kJ}\) (a) Would you expect the decomposition to be more complete at equilibrium when it is run at high temperature or when it is run at low temperature? Explain. (b) According to your answer to (a), would the reaction speed up, slow down, or occur at the same rate as before the temperature was changed? Explain.

Step-by-Step Solution

Answer

(a) The decomposition of water will be more complete at equilibrium at high temperatures, as it is an endothermic reaction and the system favors the endothermic reaction to absorb the additional heat. (b) The reaction will speed up at higher temperatures, as the increased kinetic energy of reactant molecules leads to more frequent and energetic collisions, resulting in an increased likelihood of forming product molecules.

Step 1: (a) Identifying equilibrium shift

For an endothermic reaction, heat can be considered as a reactant. According to Le Chatelier's principle, if a stress is applied to a system at equilibrium, the system will adjust to counteract the applied stress. In this case, if the temperature increases, the system will respond by favoring the endothermic reaction to absorb this additional heat. In the given decomposition reaction, since it is endothermic (\( \Delta E_{\mathrm{rxn}}=484 \mathrm{~kJ}\)), an increase in temperature will shift the equilibrium towards the products side. Therefore, at high temperatures, the decomposition of water will be more complete at equilibrium.

Step 2: (b) Effect of temperature on reaction speed

The rate of a chemical reaction depends on the temperature of the system, according to the collision theory and Arrhenius equation. As the temperature increases, the kinetic energy of reactant molecules increases, leading to more frequent and energetic collisions between them. This results in an increased likelihood of forming product molecules. Therefore, as we increase the temperature, the decomposition reaction will speed up.

Key Concepts

Le Chatelier's Principle

Le Chatelier's Principle helps us understand how a system at equilibrium responds to changes. If a system at equilibrium experiences a change in temperature, pressure, or concentration of one of the components, it will adjust to minimize that change and re-establish equilibrium. For endothermic reactions like the decomposition of water, heat functions as a reactant. When we increase the temperature, the system compensates by favoring the endothermic process, shifting the equilibrium toward more hydrogen and oxygen production. Thus, manipulating temperature can influence the equilibrium position, allowing us to predict the direction a reaction will shift under certain conditions.

Endothermic Reactions

Endothermic reactions absorb heat from their surroundings. In the context of the water decomposition reaction, written as \(2 \mathrm{H}_{2} \mathrm{O}(g) \rightleftarrows 2 \mathrm{H}_{2}(g) + \mathrm{O}_{2}(g)\), the reaction requires and absorbs energy, which is evident from the positive value of \(\Delta E_{\mathrm{rxn}} = 484 \mathrm{~kJ}\). As temperature increases, these reactions receive more heat energy, thus proceeding more readily. The absorption of this extra energy by the system enables it to break bonds more efficiently in water molecules, resulting in a greater yield of hydrogen and oxygen gas at equilibrium. Knowing that heat is a reactant helps us predict how the system will behave with temperature changes.

Reaction Rate

The rate of a chemical reaction describes how fast the reactants are converted into products. For the decomposition of water, the reaction rate is influenced by temperature. As temperature increases, the kinetic energy of molecules also increases. This heightened energy leads to more frequent and more forceful collisions between molecules. According to the Arrhenius equation, an increase in temperature results in an exponential increase in the reaction rate. Thus, a higher temperature not only shifts the equilibrium position as per Le Chatelier's Principle but also speeds up the rate at which the equilibrium is reached. Reactant molecules collide more often and with greater energy, breaking bonds more quickly to form products like hydrogen and oxygen gases.

Temperature Effects on Equilibrium

Temperature changes impact chemical equilibrium significantly, as illustrated in an endothermic reaction like the decomposition of water to hydrogen and oxygen. When temperature rises, the system absorbs additional heat energy and shifts the equilibrium towards the product side, making the reaction more complete. In contrast, cooler temperatures would slow down the reaction, favoring the endothermic reverse reaction where the system shifts towards the reactants. By controlling the temperature, we can influence not only the rate of the reaction but also the position of equilibrium. This control is crucial in industrial and laboratory settings where maximizing product yield is a priority. Understanding the role temperature plays allows chemists to optimize conditions for desired reaction outcomes.