Question

For the reaction \(2 \mathrm{CO}(g)+\mathrm{O}_{2}(g) \rightleftarrows 2 \mathrm{CO}_{2}(g),\) the equilibrium concentrations at a certain temperature are \(\left[\mathrm{CO}_{2}\right]=0.11 \mathrm{~mol} / \mathrm{L},\left[\mathrm{O}_{2}\right]=0.015 \mathrm{~mol} / \mathrm{L},\) and \([\mathrm{CO}]=0.025 \mathrm{~mol} / \mathrm{L}\). (a) Write the equilibrium constant expression for the reaction. (b) What is the value of \(K\) at this temperature? Are reactants or products favored?

Short answer

(a) \(K_c = \frac{[\mathrm{CO}_2]^2}{[\mathrm{CO}]^2[\mathrm{O}_2]}\). (b) \(K_c \approx 1290.67\), products are favored.

Step-by-step solution

Write the Equilibrium Expression

For the given reaction \(2 \mathrm{CO}(g) + \mathrm{O}_{2}(g) \rightleftarrows 2 \mathrm{CO}_{2}(g)\), the equilibrium constant expression, \(K_c\), is written as \[K_c = \frac{[\mathrm{CO}_2]^2}{[\mathrm{CO}]^2 [\mathrm{O}_2]}\]. This expression is constructed by placing the concentrations of the products raised to the power of their coefficients in the balanced equation over the concentrations of the reactants raised to the power of their coefficients.

Substitute Equilibrium Concentrations

Substitute the given equilibrium concentrations into the expression: \([\mathrm{CO}_2] = 0.11\), \([\mathrm{O}_2] = 0.015\), and \([\mathrm{CO}] = 0.025\). The equilibrium constant expression becomes \[K_c = \frac{(0.11)^2}{(0.025)^2 \times 0.015}\].

Perform the Calculations

Calculate each part: first, \((0.11)^2 = 0.0121\) and \((0.025)^2 = 0.000625\). Then calculate the denominator \(0.000625 \times 0.015 = 0.000009375\). Finally, divide \(0.0121\) by \(0.000009375\) to find \(K_c = 1290.67\).

Analyze the Equilibrium Constant

The calculated equilibrium constant \(K_c \approx 1290.67\) is much greater than 1, which indicates that at equilibrium the concentration of products is much higher than that of reactants. This suggests that products are favored in this reaction at the given temperature.

Key concepts

Chemical Equilibrium

Chemical equilibrium describes the point in a reversible chemical reaction where the rate of the forward reaction equals the rate of the backward reaction.
This means that the amounts of reactants and products remain constant over time, even though the reactions still proceed.
At equilibrium, the system looks static macroscopically, yet dynamically, the individual molecules continue to react and form products and reactants. Several factors can shift the equilibrium in a chemical reaction, such as changes in concentration, pressure, and temperature.
The principle governing these shifts is Le Chatelier's Principle, which states that a system at equilibrium will adjust to counteract changes imposed on it. Chemical equilibrium is crucial in understanding how reactions proceed in closed systems, allowing chemists to predict the concentrations of various substances at equilibrium based on initial conditions.

Reaction Quotient

The reaction quotient, represented as \( Q \), is an expression similar to the equilibrium constant \( K \), but it is used to determine the direction a reaction must shift to reach equilibrium.
By calculating \( Q \), we can compare it to \( K \) to predict whether the reactants or products are favored at a given time.

• If \( Q < K \), the reaction will shift to the right, forming more products to achieve equilibrium.
• If \( Q > K \), the reaction will shift to the left, creating more reactants to reach equilibrium.
• When \( Q = K \), the system is already at equilibrium.

The concept of the reaction quotient is valuable because it offers insight into the progress of a reaction at any point before it reaches equilibrium.

Equilibrium Concentration

Equilibrium concentration refers to the concentration of reactants and products in a reaction mixture when the system is at equilibrium.
Calculating these concentrations is essential to understand the position of equilibrium for any chemical reaction.To determine equilibrium concentrations, one can use the equilibrium constant expression for the reaction, and plug in the equilibrium concentrations provided or calculated through stoichiometric relationships.
This is illustrated in the expression used for the reaction \( 2\text{CO}(g)+\text{O}_2(g) \rightleftharpoons 2\text{CO}_2(g) \), which is \( K_c = \frac{[\text{CO}_2]^2}{[\text{CO}]^2 [\text{O}_2]} \).Equilibrium concentrations are crucial in determining the value of the equilibrium constant and for predicting how a system will respond to changes in conditions.

Product-Favored Reaction

A product-favored reaction is one where, at equilibrium, a greater concentration of products exists relative to the reactants.
This inclination towards product formation can often be gauged by evaluating the value of the equilibrium constant \( K_c \). If \( K_c \) is significantly greater than 1, as in the given exercise example where \( K_c = 1290.67 \), it indicates that the reaction heavily favors the formation of products.
This means that, under the given conditions, more products than reactants are present when the reaction reaches equilibrium.Understanding whether a reaction is product-favored helps in predicting the outcome and extent of a reaction, guiding industrial chemical processes and laboratory experiments alike.
It is fundamental in developing an efficient design for chemical manufacturing and ensuring the maximum yield of desired products.