Question

Write the reaction quotient \(Q_{c}\) for (a) \(\mathrm{NCl}_{3}\) (g) \(+3 \mathrm{H}_{2} \mathrm{O}(\mathrm{l}) \longrightarrow \mathrm{NH}_{3}\) (g) \(+3 \mathrm{HOCl}(\mathrm{aq})\) (b) \(\mathrm{P}_{4}(\mathrm{~s})+3 \mathrm{KOH}(\mathrm{aq})+3 \mathrm{H}_{2} \mathrm{O}(\mathrm{l}) \rightarrow \mathrm{PH}_{3}(\mathrm{aq})+3 \mathrm{KH}_{2} \mathrm{PO}_{2}(\mathrm{aq}\) (c) \(\mathrm{CO}_{3}^{2-}(\mathrm{aq})+2 \mathrm{H}_{3} \mathrm{O}^{+}(\mathrm{aq}) \rightarrow \mathrm{CO}_{2}(\mathrm{~g})+3 \mathrm{H}_{2} \mathrm{O}(\mathrm{l})\)

Short answer

\(Q_{c(a)} = \frac{[\mathrm{NH}_{3}] \times [\mathrm{HOCl}]^3}{[\mathrm{NCl}_{3}]}, Q_{c(b)} = \frac{[\mathrm{PH}_{3}] \times [\mathrm{KH}_{2}PO_{2}]^3}{[\mathrm{KOH}]^3}, Q_{c(c)} = \frac{[\mathrm{CO}_{2}]}{[\mathrm{CO}_{3}^{2-}] \times [\mathrm{H}_{3}O^{+}]^2}\).

Step-by-step solution

Writing the Reaction Quotient for (a)

The reaction quotient, \(Q_c\), is the ratio of the concentrations of the products raised to the power of their coefficients to the concentrations of the reactants raised to the power of their coefficients. For the reaction \(\mathrm{NCl}_{3}(g) + 3 \mathrm{H}_{2}O(l) \longrightarrow \mathrm{NH}_{3}(g) + 3 \mathrm{HOCl}(aq)\), the reaction quotient is: \[Q_c = \frac{[\mathrm{NH}_{3}] \times [\mathrm{HOCl}]^3}{[\mathrm{NCl}_{3}]}\]. Since water is in its liquid form, it is not included in the expression.

Writing the Reaction Quotient for (b)

Again, the reaction quotient is based on the products over reactants. For the reaction \(\mathrm{P}_{4}(s) + 3 \mathrm{KOH}(aq) + 3 \mathrm{H}_{2}O(l) \rightarrow \mathrm{PH}_{3}(aq) + 3 \mathrm{KH}_{2}PO_{2}(aq)\), the reaction quotient is: \[Q_c = \frac{[\mathrm{PH}_{3}] \times [\mathrm{KH}_{2}PO_{2}]^3}{[\mathrm{KOH}]^3}\]. Because \(P_4\) is a solid and \(H_2O\) is a liquid, they are not included in \(Q_c\).

Writing the Reaction Quotient for (c)

This reaction's reaction quotient involves ions in solution and a gas. For the reaction \(\mathrm{CO}_{3}^{2-}(aq) + 2 \mathrm{H}_{3}O^{+}(aq) \rightarrow \mathrm{CO}_{2}(g) + 3 \mathrm{H}_{2}O(l)\), the reaction quotient is: \[Q_c = \frac{[\mathrm{CO}_{2}]}{[\mathrm{CO}_{3}^{2-}] \times [\mathrm{H}_{3}O^{+}]^2}\]. Liquid water is not included in \(Q_c\) since it is a pure substance in its liquid form.

Key concepts

Chemical Equilibrium

Chemical equilibrium refers to the state of a chemical reaction where the rates of the forward and reverse reactions are equal, leading to no net change in the concentrations of reactants and products over time. It is a dynamic process, which means that the reactions continue to occur, but since they are happening at the same rate, the system appears to be at rest.

At equilibrium, the reaction has reached a balance between the reactants turning into products and the products reverting to reactants. The exact concentrations of each species at this point are known as the equilibrium concentrations. Importantly, the equilibrium point does not necessarily mean that the reactants and products are present in equal amounts; rather, it depends on the particular reaction and conditions, such as temperature and pressure.

The concept of equilibrium is crucial for understanding how chemical systems behave, and it is particularly important in fields such as chemistry, biology, and environmental science.

Concentration of Reactants and Products

The concentration of reactants and products in a reaction mixture is a central factor in determining the reaction's behavior and yield. Concentrations are usually expressed in moles per liter (Molarity, M) for solutions, but can also be expressed in partial pressures (for gases) or as pure numbers, in the case of solid and liquid species that do not change volume significantly during a reaction.

In the context of chemical equilibrium, concentration plays a vital role because the reaction quotient, and eventually the equilibrium constant, are expressed in terms of the concentrations of the reacting species. For example, in the solution for (a), \[Q_c = \frac{[\mathrm{NH}_{3}] \times [\mathrm{HOCl}]^3}{[\mathrm{NCl}_{3}]}\] only includes the concentrations of ammonia gas and hypochlorous acid in aqueous solution but not the liquid water or gaseous nitrogen trichloride. This is because pure solids and liquids do not vary in concentration and thus do not affect the equilibrium state of a reaction.

The manipulation of reactant and product concentrations is commonly used to shift equilibria according to Le Châtelier's Principle, which can be exploited to increase the yield of a desired product.

Chemical Reaction Coefficients

Chemical reaction coefficients are the numbers written in front of the reactants and products in a chemical equation. They indicate the relative amounts of each substance involved in the reaction and are essential for balancing chemical equations to obey the Law of Conservation of Mass.

In the expression of the reaction quotient and the equilibrium constant, the coefficients become exponents for the corresponding concentrations of reactants and products. For instance, in solution (b), the coefficient '3' for \(\mathrm{KOH}\) and \(\mathrm{KH}_{2}PO_{2}\) in the balanced chemical equation influences the reaction quotient: \[Q_c = \frac{[\mathrm{PH}_{3}] \times [\mathrm{KH}_{2}PO_{2}]^3}{[\mathrm{KOH}]^3}\].

The accurate application of reaction coefficients is essential when calculating the reaction quotient and understanding how changes in the system might affect the position of equilibrium. For students, visualizing or even calculating with mole ratios can sometimes be more intuitive when considering these coefficients as part of a recipe; they dictate how much of each 'ingredient' (reactant) is required to produce a certain amount of 'product'.