Question

Consider the reaction \(\mathrm{SnO}_{2}(s)+2 \mathrm{H}_{2}(g) \rightleftarrows \mathrm{Sn}(s)+2 \mathrm{H}_{2} \mathrm{O}(l)\) run in an explosion-proof sealed vessel. (a) Running the reaction in a sealed vessel allows equilibrium to be established. Explain why. (b) Express the concentration of \(\mathrm{H}_{2}(g)\) in terms of \(K_{\text {eq }}\) (c) The equilibrium constant for this reaction decreases as the reaction mixture is heated. Which way does the equilibrium shift? (d) Is the reaction exothermic or endothermic? Explain. (e) A new employee at a chemical company adds additional \(\mathrm{SnO}_{2}(s)\) to the reaction in order to drive its position of equilibrium further to the right. Will this get her a promotion or get her fired? Explain.

Short answer

(a) In a sealed vessel, equilibrium is established because the reaction proceeds in both forward and reverse directions, and the rates of these reactions become equal over time, resulting in constant concentrations of reactants and products. (b) The concentration of H₂ can be expressed as: \([\text{H}_{2}] = \sqrt{\frac{[\text{H}_{2}\text{O}]^2}{K_{eq}}}\) (c) When the equilibrium constant decreases with increasing temperature, the equilibrium shifts to the left, towards the reactants. (d) The reaction is endothermic since it absorbs heat as the equilibrium shifts towards the reactants with increasing temperature. (e) Adding more SnO₂(s) will not affect the position of the equilibrium since it is a solid and not included in the equilibrium expression. The employee will neither get a promotion nor be fired for this action, but it may indicate a lack of understanding of chemical equilibria.

Step-by-step solution

(a) Understanding Equilibrium

In a closed system like a sealed vessel, all of the substances involved in the reaction exist and interact as a whole. The reaction proceeds both in the forward and reverse direction, and, over time, the rates of the forward and reverse reactions become equal. This equilibrium state is established, where the concentrations of reactants and products no longer change.

(b) Concentration of H₂ in terms of K_eq

The equilibrium constant, \(K_{eq}\), for the reaction is given by the expression: \(K_{eq} = \frac{[\text{Sn}][\text{H}_{2}\text{O}]^2}{[\text{SnO}_{2}][\text{H}_{2}]^2}\) Since solids like Sn and SnO₂ do not have concentrations, they're treated as constants in the equilibrium expression. The equilibrium constant then simplifies to: \(K_{eq} = \frac{[\text{H}_{2}\text{O}]^2}{[\text{H}_{2}]^2}\) Now, we can solve for the concentration of H₂: \([\text{H}_{2}] = \sqrt{\frac{[\text{H}_{2}\text{O}]^2}{K_{eq}}}\)

(c) Equilibrium shift with decreasing K_eq

If the equilibrium constant, \(K_{eq}\), decreases as the reaction mixture is heated, it means that the reaction tends to favor the reactants more than the products at higher temperatures. Therefore, the equilibrium will shift to the left, towards the reactants.

(d) Reaction Endothermic/Exothermic nature

Since the equilibrium shifts to the left (favoring the reactants) as the temperature increases, it implies that the reaction absorbs heat. Thus, the reaction is endothermic.

(e) Workplace consequences of adding SnO₂

Adding more SnO₂(s) to the system will not affect the position of the equilibrium because SnO₂(s) is a solid, and its concentration is not included in the equilibrium expression. Since there's no significant positive or negative consequence of adding more SnO₂(s) to the reaction, the new employee will neither get a promotion nor be fired for this specific action. It might, however, indicate a lack of understanding of chemical equilibria, which could have implications for future tasks.

Key concepts

Equilibrium Constant

The equilibrium constant, denoted as \(K_{eq}\), is a crucial concept in chemical equilibrium and represents the balance between products and reactants in a reversible reaction. When a reaction reaches a state where the rates of the forward and reverse reactions are equal, we say it has reached equilibrium. The concentrations of the reactants and products remain constant at this point, although the reactions continue to occur.

The equation for the equilibrium constant for a reaction \(aA + bB \rightleftarrows cC + dD\) is given as:\[K_{eq} = \frac{[C]^c[D]^d}{[A]^a[B]^b}\]In this expression, the brackets signify the concentration of each species, while \(a\), \(b\), \(c\), and \(d\) represent the respective stoichiometric coefficients of the reactants and products. It's crucial to note that solids and pure liquids are not included in the equilibrium expression, as their concentration doesn't change in a closed system.

In the context of our textbook problem, \(K_{eq}\) for the reaction between tin oxide and hydrogen can be simplified because solids and liquids are not included, leaving us with the concentrations of gases only in the expression. Knowing \(K_{eq}\) allows us to predict the direction of the reaction under different conditions and calculate the concentrations of reactants and products at equilibrium.

Le Chatelier's Principle

Le Chatelier's principle is like nature's way of maintaining balance. Whenever an external condition is applied to a reaction at equilibrium, the reaction adjusts itself to counteract the change and re-establish equilibrium.

This principle can be applied to various scenarios, including changes in concentration, temperature, and pressure. For instance, increasing the concentration of a reactant will cause the reaction to shift towards the products to lower the concentration of that reactant. In contrast, increasing the temperature of an exothermic reaction will shift the equilibrium towards the reactants because the reaction releases heat as a product.

When the new employee in the exercise added more \(SnO_2(s)\), they might have thought it would drive the reaction toward producing more \(Sn(s)\) and \(H_2O(l)\). According to Le Chatelier's principle, because \(SnO_2(s)\) is a solid, its addition doesn't influence the equilibrium, leading to no significant shift in balance. This highlights how crucial it is to understand the intricacies of equilibrium and the principles governing it.

Reaction Quotient

While the equilibrium constant \(K_{eq}\) describes the concentrations at equilibrium, the reaction quotient, \(Q\), is a snapshot of the ratio of products to reactants at any point before the system has reached equilibrium. \(Q\) is calculated with the same formula as \(K_{eq}\) but using the current concentrations.

If we're given a reaction \(aA + bB \rightleftarrows cC + dD\), the reaction quotient \(Q\) is:\[Q = \frac{[C]^c[D]^d}{[A]^a[B]^b}\]Comparing \(Q\) with \(K_{eq}\) allows us to predict which direction the reaction will proceed to reach equilibrium. If \(Q < K_{eq}\), the reaction will move forward, increasing the concentration of products. Conversely, if \(Q > K_{eq}\), the reaction will move backward, increasing the concentration of reactants. When \(Q = K_{eq}\), the reaction is at equilibrium, and no net change is observed.

Understanding the reaction quotient is important for students as it provides immediate insight into the position of any reaction relative to its equilibrium state.

Endothermic and Exothermic Reactions

The terms 'endothermic' and 'exothermic' describe whether a chemical reaction absorbs or releases energy, particularly in the form of heat. In an exothermic reaction, energy is released into the surroundings, typically making it feel warmer. In contrast, an endothermic reaction absorbs energy, which cools down the surroundings.

The differential heating effects can be explained by the basic principle that breaking bonds requires energy (endothermic process) and forming bonds releases energy (exothermic process).

Returning to our sealed vessel scenario, if heating the mixture causes the equilibrium constant to decrease and the reaction shifts towards the reactants, this indicates that the reaction must absorb heat—you’re looking at an endothermic process. This ability to correlate temperature changes and equilibrium shifts is an essential skill for students, as it deepens their understanding of how energy changes accompany chemical reactions.