Gaseous hydrogen iodide is placed in a closed container at 425 °C, where it partially decomposes to hydrogen and iodine: 2 HI(g) ⇌ H2(g) + I2(g). At equilibrium, it is found that [HI] = 3.53 × 10⁻³ M, [H2] = 4.79 × 10⁻⁴ M, and [I2] = 4.79 × 10⁻⁴ M. What is the value of Kc at this temperature?

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Identify the balanced chemical equation for the reaction: 2 HI(g) ⇌ H2(g) + I2(g).

Write the expression for the equilibrium constant Kc for the reaction: Kc = \( \frac{[H_2][I_2]}{[HI]^2} \).

Substitute the given equilibrium concentrations into the Kc expression: [HI] = 3.53 × 10⁻³ M, [H2] = 4.79 × 10⁻⁴ M, and [I2] = 4.79 × 10⁻⁴ M.

Calculate the numerator of the Kc expression: [H2] × [I2].

Calculate the denominator of the Kc expression: [HI]^2.

Key Concepts

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

Chemical Equilibrium

Chemical equilibrium occurs when the rates of the forward and reverse reactions are equal, resulting in constant concentrations of reactants and products. In this state, the system is dynamic, meaning that reactions continue to occur, but there is no net change in the concentrations. Understanding this concept is crucial for analyzing reactions like the decomposition of hydrogen iodide.

Equilibrium Constant (Kc)

The equilibrium constant, Kc, is a numerical value that expresses the ratio of the concentrations of products to reactants at equilibrium, each raised to the power of their coefficients in the balanced equation. For the reaction 2 HI(g) ⇌ H2(g) + I2(g), Kc is calculated using the formula Kc = [H2][I2]/[HI]². This constant provides insight into the extent of the reaction and the position of equilibrium.

Concentration Units

Concentration is a measure of the amount of a substance in a given volume and is typically expressed in molarity (M), which is moles of solute per liter of solution. In this question, the concentrations of HI, H2, and I2 are provided in molarity, which is essential for calculating Kc. Understanding how to manipulate and interpret these units is vital for solving equilibrium problems.

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Related Practice

Textbook Question

Consider the equilibrium N₂(𝑔) + O₂(𝑔) + Br₂(𝑔) ⇌ 2 NOBr(𝑔) Calculate the equilibrium constant 𝐾𝑝 for this reaction, given the following information at 298 K:

2 NO(𝑔) + Br₂(𝑔) ⇌ 2 NOBr(𝑔) 𝐾_𝑐= 2.02

NO(𝑔) ⇌ N₂(𝑔) + O₂(𝑔) 𝐾_𝑐= 2.1×10³⁰

Textbook Question

The equilibrium 2 NO(𝑔) + Cl₂(𝑔) ⇌ 2 NOCl(𝑔) is established at 500.0 K. An equilibrium mixture of the three gases has partial pressures of 0.095 atm, 0.171 atm, and 0.28 atm for NO, Cl₂, and NOCl, respectively. (a) Calculate 𝐾_𝑝 for this reaction at 500.0 K.

Textbook Question

The equilibrium 2 NO(𝑔) + Cl₂(𝑔) ⇌ 2 NOCl(𝑔) is established at 500.0 K. An equilibrium mixture of the three gases has partial pressures of 0.095 atm, 0.171 atm, and 0.28 atm for NO, Cl₂, and NOCl, respectively. (b) If the vessel has a volume of 5.00 L, calculate Kc at this temperature.

Textbook Question

Phosphorus trichloride gas and chlorine gas react to form phosphorus pentachloride gas: PCl₃(𝑔) + Cl₂(𝑔) ⇌ PCl₅(𝑔). A 7.5-L gas vessel is charged with a mixture of PCl₃(𝑔) and Cl₂(𝑔), which is allowed to equilibrate at 450 K. At equilibrium the partial pressures of the three gases are 𝑃_PCl3= 0.124 atm, 𝑃_Cl2= 0.157 atm, and 𝑃_PCl5= 1.30 atm. (a) What is the value of 𝐾_𝑝 at this temperature?