Question

Balance each of the following examples of heterogeneous equilibria and write each reaction quotient, \(Q_{\mathrm{c}}\) : (a) \(\mathrm{Na}_{2} \mathrm{O}_{2}(s)+\mathrm{CO}_{2}(g) \rightleftharpoons \mathrm{Na}_{2} \mathrm{CO}_{3}(s)+\mathrm{O}_{2}(g)\) (b) \(\mathrm{H}_{2} \mathrm{O}(l) \rightleftharpoons \mathrm{H}_{2} \mathrm{O}(g)\) (c) \(\mathrm{NH}_{4} \mathrm{Cl}(s) \rightleftharpoons \mathrm{NH}_{3}(g)+\mathrm{HCl}(g)\)

Short answer

(a) \[\begin{equation}Q_{\text{c}} = \frac{[\text{O}_{2}]}{[\text{CO}_{2}]}d{\text{c}} = [\text{H}_{2} \text{O}(g)](c)Q_{\text{c}}= \text{NH}_{3}][\text{HCl}]end{equation}

Step-by-step solution

Balance the Reaction

For each reaction, ensure that the number of atoms for each element is the same on both sides of the reaction equation.

Write the Reaction Quotient, Qc

For each reaction equilibrium, write the expression for the reaction quotient, which involves the concentrations of the gaseous and aqueous species (solids and liquids are omitted).

Balancing Equation (a)

The given reaction is \[\begin{equation}\text{\(\mathrm{Na}_{2} \mathrm{O}_{2}(s) + \mathrm{CO}_{2}(g) \rightleftharpoons \mathrm{Na}_{2} \mathrm{CO}_{3}(s) + \mathrm{O}_{2}(g)\)}\end{equation}\]It is already balanced because the number of Na, O, and C atoms are the same on both sides of the equation.

Write Qc for (a)

Since only gases and aqueous species are included in the expression:\[\begin{equation}Q_\mathrm{c} = \frac{[\mathrm{O}_{2}]}{[\mathrm{CO}_{2}]}\end{equation}\]Note that the concentrations of solids (\( \mathrm{Na}_{2} \mathrm{O}_{2}\) and \( \mathrm{Na}_{2} \mathrm{CO}_{3} \)) are not included.

Balancing Equation (b)

The given reaction is \[\begin{equation}\text{\( \mathrm{H}_{2} \mathrm{O}(l) \rightleftharpoons \mathrm{H}_{2} \mathrm{O}(g) \)}\end{equation}\]It is already balanced because the number of H and O atoms are the same on both sides of the equation.

Write Qc for (b)

Since only gases and aqueous species are included in the expression:\[\begin{equation}Q_\mathrm{c} = [\mathrm{H}_{2} \mathrm{O}(g)]\end{equation}\]The concentration of liquid water \( (\mathrm{H}_{2} \mathrm{O}(l)) \) is not included.

Balancing Equation (c)

The given reaction is \[\begin{equation}\text{\( \mathrm{NH}_{4} \mathrm{Cl}(s) \rightleftharpoons \mathrm{NH}_{3}(g) + \mathrm{HCl}(g) \)}\end{equation}\]It is already balanced because the number of N, H, and Cl atoms are the same on both sides of the equation.

Write Qc for (c)

Since only gases and aqueous species are included in the expression:\[\begin{equation}Q_\mathrm{c} = [\mathrm{NH}_{3}][\mathrm{HCl}]\end{equation}\]The concentration of solid ammonium chloride \( (\mathrm{NH}_{4} \mathrm{Cl}) \) is not included.

Key concepts

Reaction Balancing

Balancing reactions is a fundamental step in chemical equilibrium. You balance a reaction to ensure that there are the same number of each type of atom on both sides of the equation. This means the law of conservation of mass is satisfied.

For example, consider the reaction \text{\[ \mathrm{NH_3} + \mathrm{O_2} \rightarrow \mathrm{NO} + \mathrm{H_2O} \]}. To balance it, you equalize the number of nitrogen, oxygen, and hydrogen atoms on both sides. Start by balancing the more complex molecule first, often balancing elements (other than hydrogen and oxygen) followed by hydrogen atoms, and then oxygen atoms.

• In heterogeneous equilibria, include states of matter (s, l, g, aq) to identify phases.
• For the reaction in the exercise, all three given reactions are already balanced.

Balancing these reactions provide the baseline to determine the reaction quotient and further predict the direction of the shift in equilibrium.

Reaction Quotient (Qc)

The reaction quotient, denoted as \(Q_c\), is an expression that allows you to predict the direction of a reaction at any given point in time. It is derived from the balanced chemical equation.

\(Q_c\) is calculated similarly to the equilibrium constant (\(K_c\)), but pertains to non-equilibrium conditions.

• For gases, concentrations are in terms of partial pressures or molarity.
• Solids and pure liquids are excluded because their concentrations don't change much.

For example, for the reaction
\text{\[ \mathrm{NH_4Cl(s)} \rightleftharpoons \text{\(\mathrm{NH_3(g)} + \mathrm{HCl(g)}\)},\]} \(Q_c\) can be expressed as:
\text{\[ Q_c = \text{\( [\mathrm{NH_3}][\mathrm{HCl}] \)} \]}

Only the gaseous species are included. Understanding \(Q_c\) helps in predicting whether the system will favor the formation of products or reactants to reach equilibrium.

Chemistry Education

Understanding heterogeneous equilibria is an essential part of chemistry education. Students learn how substances in different phases interact and reach equilibrium.

The basic steps in solving these problems are:

• Identify and balance the reaction.
• Write the equilibrium expression.
• Understand which concentrations to include.

Grasping these concepts builds a strong foundation for more complex chemical analysis.

Teachers can utilize visual aids and real-life examples to illustrate these processes. Hands-on experiments also help solidify understanding by allowing students to manipulate variables and observe changes in equilibrium.

Chemical Equilibrium

Chemical equilibrium occurs when the rate of the forward reaction equals the rate of the reverse reaction. The concentrations of all reactants and products remain constant over time.

• In heterogeneous equilibria, different phases like solids, liquids, and gases are involved.
• Equilibrium constants (\(K_c\) and \(K_p\)) are derived from balanced reactions showing the relationship between reactants and products.

For the reaction \text{\[\mathrm{H_2O(l)} \rightleftharpoons \text{\(\mathrm{H_2O(g)}\)}\]}, the equilibrium expression \(Q_c = [\mathrm{H_2O(g)}]\) includes only the gas phase component since the liquid water's concentration remains essentially constant in the reaction. By understanding chemical equilibrium, predictions can be made on how changes in concentration, pressure, or temperature affect a system at equilibrium.