An equilibrium mixture of H2, I2, and HI at 458 _x001F_C contains 0.112 mol H2, 0.112 mol I2, and 0.775 mol HI in a 5.00-L vessel. What are the equilibrium partial pressures when equilibrium is reestablished following the addition of 0.200 mol of HI?

Verified step by step guidance

Step 1: Write the balanced chemical equation for the reaction. The reaction between hydrogen gas (H2) and iodine gas (I2) to form hydrogen iodide (HI) is: \[ \text{H}_2(g) + \text{I}_2(g) \rightleftharpoons 2\text{HI}(g) \]

Step 2: Calculate the initial concentrations of each species in the 5.00 L vessel. Use the formula \( \text{Concentration} = \frac{\text{moles}}{\text{volume}} \). For example, the concentration of H2 is \( \frac{0.112 \text{ mol}}{5.00 \text{ L}} \). Repeat for I2 and HI.

Step 3: Determine the change in concentration due to the addition of 0.200 mol of HI. Calculate the new concentration of HI by adding the moles of HI added to the initial moles and dividing by the volume of the vessel.

Step 4: Use the reaction quotient \( Q_c \) to determine the direction in which the reaction will shift to reestablish equilibrium. Compare \( Q_c \) with the equilibrium constant \( K_c \) calculated from the initial concentrations.

Step 5: Set up an ICE (Initial, Change, Equilibrium) table to calculate the changes in concentration for each species as the system returns to equilibrium. Use the stoichiometry of the balanced equation to express changes in terms of a single variable, and solve for the equilibrium concentrations.

Key Concepts

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

Equilibrium Constant (K)

The equilibrium constant (K) 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. It is crucial for understanding how changes in concentration affect the position of equilibrium and can be used to calculate the new equilibrium state after a disturbance, such as the addition of a reactant or product.

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. In equilibrium calculations, knowing the partial pressures allows for the determination of the equilibrium constant and the shifts in equilibrium position when concentrations change.

Le Chatelier's Principle

Le Chatelier's Principle states that if a dynamic equilibrium is disturbed by changing the conditions, the system will adjust to counteract the change and restore a new equilibrium. This principle is essential for predicting how the addition of a substance, such as HI in this case, will affect the concentrations of reactants and products in the equilibrium mixture.

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Le Chatelier's Principle

Related Practice

Textbook Question

The equilibrium constant constant 𝐾_𝑐 for C(𝑠) + CO₂(𝑔) ⇌ 2 CO(𝑔) is 1.9 at 1000 K and 0.133 at 298 K. (a) If excess C is allowed to react with 25.0 g of CO2 in a 3.00-L vessel at 1000 K, how many grams of CO are produced? (b) If excess C is allowed to react with 25.0 g of CO₂ in a 3.00-L vessel at 1000 K, how many grams of C are consumed?

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Textbook Question

At 700 K, the equilibrium constant for the reaction CCl₄(𝑔) ⇌ C(𝑠) + 2 Cl₂(𝑔) is 𝐾_𝑝= 0.76. A flask is charged with 2.00 atm of CCl₄, which then reaches equilibrium at 700 K. (a) What fraction of the CCl₄ is converted into C and Cl₂?

Textbook Question

At 700 K, the equilibrium constant for the reaction CCl₄(𝑔) ⇌ C(𝑠) + 2 Cl₂(𝑔) is 𝐾_𝑝= 0.76. A flask is charged with 2.00 atm of CCl₄, which then reaches equilibrium at 700 K. (b) What are the partial pressures of CCl₄ and Cl₂ at equilibrium?

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Textbook Question

Consider the hypothetical reaction A(𝑔) + 2 B(𝑔) ⇌ 2 C(𝑔), for which 𝐾_𝑐= 0.25 at a certain temperature. A 1.00-L reaction vessel is loaded with 1.00 mol of compound C, which is allowed to reach equilibrium. Let the variable x represent the number of mol/L of compound A present at equilibrium.

(d) The equation from part (c) is a cubic equation (one that has the form ax3 + bx2 + cx + d = 0). In general, cubic equations cannot be solved in closed form. However, you can estimate the solution by plotting the cubic equation in the allowed range of x that you specified in part (b). The point at which the cubic equation crosses the x-axis is the solution.

(e) From the plot in part (d), estimate the equilibrium concentrations of A, B, and C. (Hint: You can check the accuracy of your answer by substituting these concentrations into the equilibrium expression.)

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Textbook Question

At a temperature of 700 K, the forward and reverse rate constants for the reaction 2 HI(g) ⇌ H₂(g) + I₂(g) are k_f = 1.8×10⁻³⁰ M⁻¹s⁻¹ and k_r = 0.063 M⁻¹s⁻¹.

(a) What is the value of the equilibrium constant K_c at 700 K?

(b) Is the forward reaction endothermic or exothermic if the rate constants for the same reaction have values of k_f= 0.097M⁻¹s⁻¹ and k_r= 2.6 M⁻¹s⁻¹ at 800 K?