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.

Verified step by step guidance

Step 1: Write down the balanced chemical equation. In this case, it is 2 NO(g) + Cl2(g) ⇌ 2 NOCl(g).

Step 2: Identify the equilibrium concentrations of the reactants and products. In this case, the partial pressures of NO, Cl2, and NOCl are given, which can be converted to concentrations using the ideal gas law (PV=nRT). The concentrations are calculated by dividing the partial pressure by the gas constant R (0.0821 L·atm/K·mol) and the temperature in Kelvin (500.0 K).

Step 3: Write down the expression for the equilibrium constant Kc. For the given reaction, it is Kc = [NOCl]^2 / ([NO]^2 * [Cl2]).

Step 4: Substitute the equilibrium concentrations into the Kc expression and solve for Kc. Remember that the concentrations should be in moles per liter (M).

Step 5: The value you get is the equilibrium constant Kc at 500.0 K.

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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 equilibrium constants and the behavior of reactions under varying conditions.

Equilibrium Constant (Kc)

The equilibrium constant, Kc, quantifies 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 NO(g) + Cl2(g) ⇌ 2 NOCl(g), Kc is calculated using the formula Kc = [NOCl]^2 / ([NO]^2 * [Cl2]). This constant is temperature-dependent and provides insight into the position of equilibrium.

Partial Pressure and Concentration Relationship

In gas-phase reactions, the partial pressure of a gas is directly related to its concentration through the ideal gas law, where P = (n/V)RT. At equilibrium, the concentrations of the gases can be derived from their partial pressures, allowing for the calculation of Kc. This relationship is essential for converting the given partial pressures into concentrations for the equilibrium constant calculation.

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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?