Question

For which reaction does the cquilibrium constant depend on the units of concentration? (1) \(\mathrm{NO}(\mathrm{g}) \rightleftharpoons \frac{1}{2} \mathrm{~N}_{2}(\mathrm{~g})+\frac{1}{2} \mathrm{O}_{2}(\mathrm{~g})\) (2) \(\mathrm{Zn}(\mathrm{s})+\mathrm{Cu}^{2+}(\mathrm{aq}) \rightleftharpoons \mathrm{Cu}(\mathrm{s})+\mathrm{Zn}^{2+}(\mathrm{aq})\) (3) \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}(\mathrm{l})+\mathrm{CH}_{3} \mathrm{COOH}(1) \rightleftharpoons\) \(\mathrm{CH}_{3} \mathrm{COOC}_{2} \mathrm{H}_{5}(1)+\mathrm{H}_{2} \mathrm{O}(\mathrm{l})\) (4) \(\mathrm{COCl}_{2}(\mathrm{~g}) \rightleftharpoons \mathrm{CO}(\mathrm{g})+\mathrm{Cl}_{2}(\mathrm{~g})\)

Short answer

The equilibrium constant depends on the concentration units for reactions (1), (2), and (4).

Step-by-step solution

- Identify phases of reactants and products

Examine the phases of all reactants and products in each reaction. Equilibrium constants can have dependencies on the concentration units if they involve gases or aqueous solutions, but not for pure solids and liquids.

- Analyze reaction (1)

In reaction (1), \(\text{NO(g)} \rightleftharpoons \frac{1}{2} \text{N}_{2}\text{(g)} + \frac{1}{2} \text{O}_{2}\text{(g)}\), all species are in the gaseous state. The equilibrium constant depends on the concentration units for gases.

- Analyze reaction (2)

In reaction (2), \(\text{Zn(s)} + \text{Cu}^{2+}\text{(aq)} \rightleftharpoons \text{Cu(s)} + \text{Zn}^{2+}\text{(aq)}\), the solid species (Zn and Cu) do not affect the equilibrium constant units, while the aqueous ions (\text{Cu}^{2+} and \text{Zn}^{2+}) do. The equilibrium constant will have concentration units due to the aqueous species.

- Analyze reaction (3)

In reaction (3), \(\text{C}_{2}\text{H}_{5}\text{OH(l)} + \text{CH}_{3}\text{COOH(l)} \rightleftharpoons \text{CH}_{3}\text{COOC}_{2}\text{H}_{5}(l) + \text{H}_{2}\text{O(l)}\), all species are in the liquid state. The equilibrium constant will not depend on the concentration units for liquids.

- Analyze reaction (4)

In reaction (4), \(\text{COCl}_{2}\text{(g)} \rightleftharpoons \text{CO(g)} + \text{Cl}_{2}\text{(g)}\), all species are in the gaseous state. The equilibrium constant depends on the concentration units for gases.

- Conclusion

Reactions (1), (2), and (4) involve gaseous or aqueous species, meaning their equilibrium constants depend on the concentration units. Reaction (3) involves only liquids, so its equilibrium constant does not depend on the concentration units.

Key concepts

chemical equilibrium

When a chemical reaction reaches a point where the concentrations of reactants and products no longer change with time, we say it has reached a state of chemical equilibrium.
This occurs because the rates of the forward and reverse reactions are equal.
At this stage, the reaction has not stopped, but the rate at which reactants are converted to products and vice versa is the same.
The equilibrium constant, denoted as \( K \), is a value that indicates the ratio of the concentrations of products to reactants at equilibrium.
This ratio provides insight into the extent to which a reaction proceeds.

concentration units

Concentration refers to the amount of a substance in a given volume and is typically expressed in units such as molarity (M), which is moles per liter.
For gaseous reactions, the equilibrium constant often uses partial pressures with units of atmospheres (atm).
When analyzing equilibrium, it's crucial to note that the concentration units can affect the value of the equilibrium constant.
Reactions involving gases or aqueous solutions will have equilibrium constants dependent on these units.
This is due to the variable nature of gases and ions in solution compared to solids and pure liquids, which have fixed concentrations.

reaction phases

The phases of reactants and products play a significant role in defining the equilibrium constant.
Reactions can involve different phases including gases (g), liquids (l), solids (s), and aqueous solutions (aq).
For pure solids and liquids, their activities are considered to be 1, meaning they do not affect the equilibrium constant units.
However, gases and aqueous solutions do influence the equilibrium constant because their concentrations can vary with pressure and temperature.
Analyzing the phase of each component allows us to determine if and how the equilibrium constant will be dependent on concentration units.

gaseous state

Gaseous reactions can have equilibrium constants expressed in terms of concentrations or partial pressures.
For example, in reaction \( NO(g) \rightleftharpoons \frac{1}{2} N_{2}(g) + \frac{1}{2} O_{2}(g) \), the equilibrium constant, \( K_{p} \), is based on the partial pressures of the gases involved.
Since gases can expand and compress, their concentrations or partial pressures can vary significantly with changes in volume or pressure.
This variability causes the equilibrium constant for gaseous reactions to be dependent on these units.
Understanding this aspect is essential in predicting how changes in conditions will affect the equilibrium state.

aqueous solutions

In reactions involving aqueous solutions, the equilibrium constant can also depend on the concentration units.
Aqueous solutions involve solutes dissolved in water, often measured in molarity (M).
For instance, in the reaction \( Zn(s) + Cu^{2+}(aq) \rightleftharpoons Cu(s) + Zn^{2+}(aq) \), the equilibrium constants depend on the concentrations of the \( Cu^{2+} \) and \( Zn^{2+} \) ions in solution.
Concentration changes in these ions directly impact the equilibrium position.
Knowing how to calculate and interpret these concentration units helps in understanding and controlling chemical processes in solutions.