Question

Write the equilibrium constant expressions for the following reactions: (a) \(2 \mathrm{CO}(g)+\mathrm{O}_{2}(g) \rightleftarrows 2 \mathrm{CO}_{2}(g)\) (b) \(\mathrm{Mg}(s)+\mathrm{HCl}(a q) \rightleftarrows \mathrm{MgCl}_{2}(a q)+\mathrm{H}_{2}(g)\) (c) \(\mathrm{HF}(a q)+\mathrm{H}_{2} \mathrm{O}(l) \rightleftarrows \mathrm{H}_{3} \mathrm{O}^{+}(a q)+\mathrm{F}^{-}(a q)\) (d) \(\mathrm{S}(s)+\mathrm{O}_{2}(g) \rightleftarrows \mathrm{SO}_{2}(g)\)

Short answer

(a) \(K_c = \frac{[\mathrm{CO}_2]^2}{[\mathrm{CO}]^2[\mathrm{O}_2]}\) (b) \(K_c = \frac{[\mathrm{MgCl}_2][\mathrm{H}_2]}{[\mathrm{HCl}]^2}\) (c) \(K_c = \frac{[\mathrm{H}_3\mathrm{O}^+][\mathrm{F}^-]}{[\mathrm{HF}]}\) (d) \(K_c = \frac{[\mathrm{SO}_2]}{[\mathrm{O}_2]}\)

Step-by-step solution

Understanding Equilibrium Constant Expression

The equilibrium constant expression, denoted as \( K_c \), is determined by the ratio of the concentrations of products to reactants, each raised to the power of their respective coefficients in the balanced chemical equation. Solids and liquids are excluded from the expression.

Solving Part (a)

For the reaction \( 2 \mathrm{CO}(g)+\mathrm{O}_{2}(g) \rightleftharpoons 2 \mathrm{CO}_{2}(g) \), the equilibrium constant expression \( K_c \) is written as:\[K_c = \frac{[\mathrm{CO}_2]^2}{[\mathrm{CO}]^2[\mathrm{O}_2]}\]

Solving Part (b)

For the reaction \( \mathrm{Mg}(s)+\mathrm{HCl}(aq) \rightleftharpoons \mathrm{MgCl}_2(aq)+\mathrm{H}_2(g) \), note that \( \mathrm{Mg} \) is a solid and should not appear in the expression. Thus, the expression is:\[K_c = \frac{[\mathrm{MgCl}_2][\mathrm{H}_2]}{[\mathrm{HCl}]^2}\]

Solving Part (c)

For the reaction \( \mathrm{HF}(aq)+\mathrm{H}_2 \mathrm{O}(l) \rightleftharpoons \mathrm{H}_3 \mathrm{O}^+(aq)+\mathrm{F}^-(aq) \), water is a liquid and should be excluded from the expression. Thus, the equilibrium constant expression is:\[K_c = \frac{[\mathrm{H}_3\mathrm{O}^+][\mathrm{F}^-]}{[\mathrm{HF}]}\]

Solving Part (d)

For the reaction \( \mathrm{S}(s)+\mathrm{O}_2(g) \rightleftharpoons \mathrm{SO}_2(g) \), \( \mathrm{S} \) is excluded because it's a solid. The expression is:\[K_c = \frac{[\mathrm{SO}_2]}{[\mathrm{O}_2]}\]

Key concepts

Chemical Reactions

Chemical reactions involve the transformation of substances through the breaking and forming of bonds. The given reactions showcase how reactants convert into products, often changing their chemical properties. Understanding these transformations helps predict product formation and reaction conditions.

In the chemical reactions,

• Reactants are the starting materials, like \( \mathrm{CO} \) and \( \mathrm{O}_2 \) in the first reaction.
• Products are the substances formed from the reaction, such as \( \mathrm{CO}_2 \).

The type and nature of these reactions provide insights into the rate and extent to which they occur. For example, gaseous reactions can often reach equilibrium more readily compared to those involving only solids. Recognizing these forms, such as reversible reactions indicated by \( \rightleftharpoons \), is crucial for understanding how products and reactants interact.

Equilibrium Expressions

Equilibrium expressions are mathematical representations of the concentrations of products and reactants at equilibrium. These expressions, like \( K_c \), quantify the relationship between product concentration and reactant concentration. For each reaction, it is essential to:

• Identify the gaseous and aqueous substances, since solids and liquids do not appear in the equilibrium expressions.
• Raise each concentration term to the power of its stoichiometric coefficient from the balanced equation.

For instance, in the reaction \( 2 \mathrm{CO}(g)+\mathrm{O}_{2}(g) \rightleftharpoons 2 \mathrm{CO}_{2}(g) \), the expression is: \[ K_c = \frac{[\mathrm{CO}_2]^2}{[\mathrm{CO}]^2[\mathrm{O}_2]} \]This expression illustrates the balance between the formation and decomposition of \( \mathrm{CO}_2 \). Understanding and constructing such expressions is vital in predicting the direction and position of equilibrium.

Chemical Equilibrium

Chemical equilibrium occurs when the rate of the forward reaction equals the rate of the backward reaction in a reversible process. This state of balance means that the concentrations of reactants and products remain constant over time, although dynamic molecular processes continue.

At equilibrium:

• Reactants and products coexist in a fixed ratio, steady even though molecules are continually reacting.
• The equilibrium constant, such as \( K_c \), plays a key role in determining the position of equilibrium.

For example, in reactions involving \( \mathrm{HF}(aq)+\mathrm{H}_2\mathrm{O}(l) \rightleftharpoons \mathrm{H}_3\mathrm{O}^+(aq)+\mathrm{F}^-(aq) \), the constant \( K_c = \frac{[\mathrm{H}_3\mathrm{O}^+][\mathrm{F}^-]}{[\mathrm{HF}]} \) helps understand if products or reactants are favored at equilibrium. Identifying these conditions in various systems aids in controlling chemical processes accurately.