Question

Given the following descriptions of reversible reactions, write a balanced equation (simplest whole-number coefficients) and the equilibrium constant expression \((K)\) for each. (a) Nitrogen gas reacts with solid sodium carbonate and solid carbon to produce carbon monoxide gas and solid sodium cyanide. (b) Solid magnesium nitride reacts with water vapor to form magnesium hydroxide solid and ammonia gas. (c) Ammonium ion in aqueous solution reacts with a strong base at \(25^{\circ} \mathrm{C}\), giving aqueous ammonia and water. (c) Hydrogen sulfide gas \(\left(\mathrm{H}_{2} \mathrm{~S}\right)\) bubbled into an aqueous solution of lead(II) ions produces lead sulfide precipitate and hydrogen ions.

Short answer

#Answer# a) \(K = \frac{[\mathrm{CO}]^3}{[\mathrm{N}_2]}\) b) \(K = \frac{[\mathrm{NH}_3]^2}{[\mathrm{H}_2\mathrm{O}]^6}\) c) \(K = \frac{[\mathrm{NH}_3]}{[\mathrm{NH}_4^+][\mathrm{OH}^-]}\) d) \(K = \frac{[\mathrm{H}^+]^2}{[\mathrm{H}_2\mathrm{S}][\mathrm{Pb}^{2+}]}\)

Step-by-step solution

a) Nitrogen gas reacts with solid sodium carbonate and solid carbon

Write the balanced chemical equation for this reaction: $$ \mathrm{N}_2(g) + 2\mathrm{Na}_2\mathrm{CO}_3(s) + 3\mathrm{C}(s) \rightleftharpoons 2\mathrm{NaCN}(s) + 3\mathrm{CO}(g) $$ Now, write the equilibrium constant expression: $$ K = \frac{[\mathrm{CO}]^3}{[\mathrm{N}_2]} $$ Keep in mind that the concentrations of pure solids (like \(\mathrm{Na}_2\mathrm{CO}_3\), \(\mathrm{C}\), and \(\mathrm{NaCN}\)) are not included in the equilibrium expression.

b) Solid magnesium nitride reacts with water vapor

Write the balanced chemical equation for this reaction: $$ \mathrm{Mg}_3\mathrm{N}_2(s) + 6\mathrm{H}_2\mathrm{O}(g) \rightleftharpoons 3\mathrm{Mg(OH)}_2(s) + 2\mathrm{NH}_3(g) $$ Now, write the equilibrium constant expression: $$ K = \frac{[\mathrm{NH}_3]^2}{[\mathrm{H}_2\mathrm{O}]^6} $$ Again, the concentrations of pure solids (like \(\mathrm{Mg}_3\mathrm{N}_2\) and \(\mathrm{Mg(OH)}_2\)) are not included in the equilibrium expression.

c) Ammonium ion in aqueous solution reacts with a strong base

Write the balanced chemical equation for this reaction: $$ \mathrm{NH}_4^+(aq) + \mathrm{OH}^-(aq) \rightleftharpoons \mathrm{NH}_3(aq) + \mathrm{H}_2\mathrm{O}(l) $$ Now, write the equilibrium constant expression: $$ K = \frac{[\mathrm{NH}_3]}{[\mathrm{NH}_4^+][\mathrm{OH}^-]} $$ In this case, water is not included in the equilibrium expression because it is a pure liquid.

d) Hydrogen sulfide gas reacts with lead(II) ions in an aqueous solution

Write the balanced chemical equation for this reaction: $$ \mathrm{H}_2\mathrm{S}(g) + \mathrm{Pb}^{2+}(aq) \rightleftharpoons \mathrm{PbS}(s) + 2\mathrm{H}^+(aq) $$ Now, write the equilibrium constant expression: $$ K = \frac{[\mathrm{H}^+]^2}{[\mathrm{H}_2\mathrm{S}][\mathrm{Pb}^{2+}]} $$ In this case, the concentration of pure solid lead sulfide (PbS) is not included in the equilibrium expression.

Key concepts

Reversible Reactions

Reversible reactions are fascinating chemical processes. Unlike irreversible reactions, which only go in one direction, reversible reactions can proceed in both forward and backward directions. This means the products can revert to reactants under certain conditions.

These reactions reach a state of balance known as equilibrium, where the rates of the forward and backward reactions are equal. This doesn't mean the concentrations of reactants and products are equal, just that they remain constant over time.

In reversible reactions, it's essential to remember that while equilibrium can be disturbed by changing conditions like temperature and concentration, the system will always try to reestablish equilibrium by shifting the reaction accordingly.

Balanced Chemical Equation

To fully understand a chemical reaction, writing a balanced chemical equation is crucial.

In a balanced equation, the number of atoms for each element is the same on both sides of the equation. This balance reflects the conservation of mass, as atoms are neither created nor destroyed in chemical reactions.

For instance, in the reaction where nitrogen gas reacts with solid sodium carbonate and carbon to produce carbon monoxide and sodium cyanide, it is represented as \( \mathrm{N}_2(g) + 2\mathrm{Na}_2\mathrm{CO}_3(s) + 3\mathrm{C}(s) \rightleftharpoons 2\mathrm{NaCN}(s) + 3\mathrm{CO}(g) \).

Balancing involves adjusting the coefficients, the numbers before chemical formulas, to ensure that each atom type has the same total count on both sides of the equation.

Equilibrium Expression

An equilibrium expression is a mathematical expression used to describe the concentrations of reactants and products at equilibrium.

It's given by the expression \( K = \frac{[\text{Products}]}{[\text{Reactants}]} \). Here, \( K \) is the equilibrium constant, a numerical value that is specific to a given reaction at a particular temperature.

Importantly, only the concentrations of gases and aqueous species are included in the equilibrium expression. Solids and liquids are omitted because their concentrations remain relatively constant.

For example, for the reaction of solid magnesium nitride with water, the equilibrium expression would be \( K = \frac{[\mathrm{NH}_3]^2}{[\mathrm{H}_2\mathrm{O}]^6} \), highlighting only the gaseous components involved.

Reaction Coefficients

Reaction coefficients are the numbers placed before substances in a chemical equation that indicate the proportion of each substance involved.

They are crucial for balancing reactions, ensuring mass conservation across the equation. For example, in the reaction \( \mathrm{NH}_4^+(aq) + \mathrm{OH}^-(aq) \rightleftharpoons \mathrm{NH}_3(aq) + \mathrm{H}_2\mathrm{O}(l) \), the coefficients are 1 for each substance, showing equal amounts of reactants and products participate.

Reaction coefficients help determine the stoichiometry of the reaction, showing the exact relationships and proportions of reactants converting to products. They are essential for calculating reactant or product amounts in chemical calculations.

Remember, even though they are essential for balancing, these coefficients do not appear in equilibrium expressions, which rely strictly on concentration values.