At 100 _x001F_C, Kc = 0.078 for the reaction SO2Cl2(g) ⇌ SO2(g) + Cl2(g). In an equilibrium mixture of the three gases, the concentrations of SO2Cl2 and SO2 are 0.108 M and 0.052 M, respectively. What is the partial pressure of Cl2 in the equilibrium mixture?

Verified step by step guidance

Identify the equilibrium expression for the reaction: SO2Cl2(g) ⇌ SO2(g) + Cl2(g). The equilibrium constant expression (Kc) is given by Kc = [SO2][Cl2]/[SO2Cl2].

Substitute the known values into the equilibrium expression. You have [SO2Cl2] = 0.108 M and [SO2] = 0.052 M. The equilibrium constant Kc is 0.078.

Rearrange the equilibrium expression to solve for the unknown concentration of Cl2. This gives [Cl2] = Kc * [SO2Cl2] / [SO2].

Substitute the known values into the rearranged equation to find the concentration of Cl2. This involves multiplying Kc by [SO2Cl2] and then dividing by [SO2].

The concentration of Cl2 obtained from the calculation is the same as its partial pressure in the equilibrium mixture, assuming ideal gas behavior.

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Equilibrium Constant (Kc)

The equilibrium constant (Kc) is a numerical value that expresses the ratio of the concentrations of products to reactants at equilibrium for a given reaction at a specific temperature. For the reaction SO2Cl2(g) ⇌ SO2(g) + Cl2(g), Kc = [SO2][Cl2]/[SO2Cl2]. A Kc value less than 1 indicates that at equilibrium, the concentration of reactants is greater than that of products.

Partial Pressure

Partial pressure is the pressure exerted by a single component of a gas mixture. According to Dalton's Law, the total pressure of a gas mixture is the sum of the partial pressures of each individual gas. The partial pressure of a gas can be calculated using the ideal gas law, where P = (n/V)RT, or by using the concentration of the gas in the mixture and the total pressure.

Ideal Gas Law

The ideal gas law is a fundamental equation in chemistry that relates the pressure, volume, temperature, and number of moles of an ideal gas. It is expressed as PV = nRT, where P is pressure, V is volume, n is the number of moles, R is the ideal gas constant, and T is temperature in Kelvin. This law allows for the calculation of gas properties under various conditions, including determining partial pressures in equilibrium systems.

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Related Practice

Textbook Question

Indicate whether each of the following statements about the reaction quotient Q is true or false: (b) If 𝑄_𝑐< 𝐾_𝑐, the reaction needs to proceed to the right to reach equilibrium.

Textbook Question

At 100°C, the equilibrium constant for the reaction COCl₂(𝑔) ⇌ CO(𝑔) + Cl₂(𝑔) has the value 𝐾_𝑐= 2.19×10⁻¹⁰. Are the following mixtures of COCl₂, CO, and Cl₂ at 100°C at equilibrium? If not, indicate the direction that the reaction must proceed to achieve equilibrium.

(a) [COCl₂] = 2.00×10⁻³M, [CO] = 3.3×10⁻⁶M, [Cl₂] = 6.62×10⁻⁶ M

(b) [COCl₂] = 4.50×10⁻²M, [CO] = 1.1×10⁻⁷M, [Cl₂] = 2.25×10⁻⁶ M

Textbook Question

At 900 K, the following reaction has 𝐾_𝑝 = 0.345: 2 SO₂(𝑔) + O₂(𝑔) ⇌ 2 SO₃(𝑔) In an equilibrium mixture the partial pressures of SO₂ and O₂ are 0.135 atm and 0.455 atm, respectively. What is the equilibrium partial pressure of SO₃ in the mixture?