Question

Write the equilibrium expression for each of the following reactions. a. \(\mathrm{CO}(g)+2 \mathrm{H}_{2}(g) \rightleftharpoons \mathrm{CH}_{3} \mathrm{OH}(g)\) b. \(2 \mathrm{NO}_{2}(g) \rightleftharpoons 2 \mathrm{NO}(g)+\mathrm{O}_{2}(g)\) c. \(\mathrm{P}_{4}(g)+6 \mathrm{Br}_{2}(g) \rightleftharpoons 4 \mathrm{PBr}_{3}(g)\)

Short answer

a. \( K_\textrm{c} = \frac{[\textrm{CH}_3\textrm{OH}]}{[\textrm{CO}] [\textrm{H}_2]^2} \) b. \( K_\textrm{c} = \frac{[\textrm{NO}]^2 [\textrm{O}_2]}{[\textrm{NO}_2]^2} \) c. \( K_\textrm{c} = \frac{[\textrm{PBr}_3]^4}{[\textrm{P}_4] [\textrm{Br}_2]^6} \)

Step-by-step solution

Reaction 1: CO(g) + 2 H2(g) CH3OH(g)

To derive the equilibrium expression for this reaction, we start by writing the equilibrium constant expression (Kc) as follows: \[ K_\textrm{c} = \frac{[\textrm{CH}_3\textrm{OH}]}{[\textrm{CO}] [\textrm{H}_2]^2} \] Here, [CH3OH], [CO], and [H2] represent the equilibrium concentrations of CH3OH, CO, and H2, respectively.

Reaction 2: 2 NO2(g) 2 NO(g) + O2(g)

Similarly, for this reaction, we write the equilibrium constant expression (Kc) as: \[ K_\textrm{c} = \frac{[\textrm{NO}]^2 [\textrm{O}_2]}{[\textrm{NO}_2]^2} \] Here, [NO], [O2], and [NO2] represent the equilibrium concentrations of NO, O2, and NO2, respectively.

Reaction 3: P4(g) + 6 Br2(g) 4 PBr3(g)

For this reaction, we write the equilibrium constant expression (Kc) as: \[ K_\textrm{c} = \frac{[\textrm{PBr}_3]^4}{[\textrm{P}_4] [\textrm{Br}_2]^6} \] Here, [PBr3], [P4], and [Br2] represent the equilibrium concentrations of PBr3, P4, and Br2, respectively.

Key concepts

Equilibrium Expressions

In chemistry, reacting substances in a closed system tend to reach a balance point called equilibrium. An equilibrium expression describes the ratio of products to reactants when a reaction reaches this point. It reflects how the concentrations of molecules relate to each other. Simple enough, it's a mathematical way to remind us that every little molecule counts.

To write these expressions, we need to look at the chemical equation of the reaction. This equation shows us which reactants form which products. The equilibrium expression is then derived using:

• Products: These are the substances formed by the reaction. In the expression, their concentrations are placed in the numerator (on top).
• Reactants: These are the starting materials of the reaction. Placed in the denominator (bottom) of the expression.
• Coefficients: These are the numbers in front of the chemical formulae in the balanced equation. They become exponents in the equilibrium expression.

This forms a powerful formula that allows us to calculate important characteristics of the reaction at equilibrium.

Equilibrium Constant (Kc)

The equilibrium constant, represented as \( K_\textrm{c} \), is a treasured number for chemists. It tells us how much of each substance is present at equilibrium. So, when we say chemical reactions are in equilibrium, they don't just "pause." Instead, they keep going, with a constant flow back and forth. The \( K_\textrm{c} \) value shows which direction is favored.

• A large \( K_\textrm{c} \) means products are favored, indicating the forward reaction is stronger or more complete.
• A small \( K_\textrm{c} \) means reactants win the balancing game, hinting at a stronger reverse reaction.

Calculating \( K_\textrm{c} \) using concentrations from each side of the reaction gives a numerical expression of this balance. Remember, it's constant only at a specific temperature, and changes in temperature can shift this balance, altering the \( K_\textrm{c} \). Equilibrium is like a seesaw—changing the balance point shifts everything.

Reaction Stoichiometry

Reaction stoichiometry is the silent rulebook that reactions follow. It dictates how much of each reactant is consumed and how much product is formed. This concept is crucial in all chemical equations, including equilibrium reactions, where the exact amounts dictate the components of the equilibrium expression. The balanced chemical equation provides the stoichiometry of a reaction. For instance, if the equation shows that one molecule of A reacts with two molecules of B to form three molecules of C, this stoichiometry reflects in the equilibrium expression too. For example, products and reactants will be raised to the power of their coefficients:

• Reaction formula: The balanced equation helps clarify proportions and relationships among different substances.
• Mole Ratios: Establishing the correct proportions, retrieving molecular ratios helps define where concentrations stand at equilibrium.
• Predicting Outcomes: By understanding the stoichiometry, we can predict or calculate concentrations of other substances in the reaction using stoichiometric coefficients.

In essence, stoichiometry is the mathematics that supports chemistry—it lets us know that two buns and a patty make a burger, a delightful analogy for balancing equations.