Question

Write the reaction quotient \(Q\) for (a) \(2 \mathrm{BCl}_{3}\) (g) \(+2 \mathrm{Hg}(\mathrm{l}) \rightarrow \mathrm{B}_{2} \mathrm{Cl}_{4}\) (s) \(+\mathrm{Hg}_{2} \mathrm{Cl}_{2}\) (s) (b) \(\mathrm{P}_{4} \mathrm{~S}_{10}\) (s) \(+16 \mathrm{H}_{2} \mathrm{O}(\mathrm{l}) \longrightarrow 4 \mathrm{H}_{3} \mathrm{PO}_{4}(\mathrm{aq})+10 \mathrm{H}_{2} \mathrm{~S}(\mathrm{aq})\) (c) \(\mathrm{Br}_{2}(\mathrm{~g})+3 \mathrm{~F}_{2}(\mathrm{~g}) \longrightarrow 2 \mathrm{BrF}_{3}(\mathrm{~g})\)

Short answer

For reactions (a), (b) and (c), the reaction quotient expressions are Q = 1, Q = \( [H_{3}PO_{4}]^4 [H_{2}S]^{10} \), and Q = \( \frac{[BrF_{3}]^{2}}{[Br_{2}][F_{2}]^{3}} \), respectively.

Step-by-step solution

- Understanding Reaction Quotient

The reaction quotient, Q, is calculated in the same way as the equilibrium constant, K, but for a reaction that has not necessarily reached equilibrium. It is the ratio of the concentrations of the products raised to their stoichiometric coefficients divided by the concentrations of the reactants raised to their stoichiometric coefficients.

- Writing Q for Reaction (a)

For the reaction (a), since the products are solids, they do not appear in the expression for Q. The reactants are gases and liquids; however, the concentration of liquids is also not included in Q. Therefore, Q for reaction (a) is simply Q = 1, because there are no gaseous products or reactants in their expression.

- Writing Q for Reaction (b)

For reaction (b), the solid reactant does not appear in the expression for Q. The products are aqueous solutions, and their concentrations will appear in the expression for Q. The water is a liquid, so its concentration doesn't appear in Q. The expression for Q is given by Q = \( \frac{[H_{3}PO_{4}]^4 [H_{2}S]^{10}}{1} \).

- Writing Q for Reaction (c)

For reaction (c), all reactants and products are gases, so all will appear in the expression for Q. The expression for Q is given by Q = \( \frac{[BrF_{3}]^{2}}{[Br_{2}][F_{2}]^{3}} \).

Key concepts

Equilibrium Constant (K)

The equilibrium constant (K) is a fundamental concept in chemistry that characterizes the ratio of the concentrations of products to reactants of a reaction at chemical equilibrium. At equilibrium, the rates of the forward and reverse reactions are equal, resulting in no net change in the concentration of reactants and products over time.

Mathematically, for a general reaction like \(aA + bB \longleftrightarrow cC + dD\), where \(A\) and \(B\) are reactants and \(C\) and \(D\) are products with stoichiometric coefficients \(a\), \(b\), \(c\), and \(d\) respectively, the equilibrium constant \(K\) is given by: \[K = \frac{[C]^{c}[D]^{d}}{[A]^{a}[B]^{b}}\]
K values are dimensionless and provide insights into the extent of the reaction—high values suggest a product-favored reaction, while low values indicate a reactant-favored reaction. Different reactions have their unique \(K\) values under specific conditions like temperature and pressure, which remain constant unless these conditions change.

Chemical Equilibrium

When a chemical reaction reaches a state where the concentrations of reactants and products remain constant over time, it is said to be at chemical equilibrium. This does not mean the reactants and products are equal in concentration, but rather that their rates of formation are equal, leading to a dynamic balance.

To reach equilibrium, the reaction must be reversible, meaning it can proceed in both forward and reverse directions. At this point, a system's macroscopic properties, such as color, pressure, and concentration, will appear stable. It's important to understand that equilibrium is a dynamic state; particles continue to react, but there's a stable ratio between the concentrations of reactants and products, which is described by the equilibrium constant \(K\).

Stoichiometry

Stoichiometry is the area of chemistry that involves the calculation of the quantities of reactants and products in chemical reactions. It's based on the conservation of mass and the concept of a mole, which is Avogadro's number of particles (usually atoms or molecules).

Stoichiometry allows scientists to predict how much product will form from a given amount of reactant and vice versa. This is essential for the calculation of the reaction quotient \(Q\) or equilibrium constant \(K\), as stoichiometric coefficients from the balanced chemical equation are used as exponents in their formulas. Understanding the proportional relationships in reactions enables one to convert from mass to moles, calculate yields, and understand limiting reactants.

Chemical Concentration

The term chemical concentration refers to the amount of a substance within a certain volume of solution. It's an essential concept because reaction rates, as well as the reaction quotient \(Q\) and equilibrium constant \(K\), often depend on the concentrations of the reactants and products involved.

Concentration is typically expressed in molarity, which is moles of solute per liter of solution (\(mol/L\)), but can also be expressed in terms of mass per volume or percentage composition. When writing expressions for \(Q\) and \(K\), it's crucial to use the correct concentration units and only include the concentrations of reactants and products that are in the gaseous phase or are dissolved in solution. Substances in the solid phase are omitted because their concentrations do not change during the reaction.