When 1.50 mol CO2 and 1.50 mol H2 are placed in a 3.00-L container at 395 _x001F_C, the following reaction occurs: CO2(g) + H2(g) ⇌ CO(g) + H2O(g). If Kc = 0.802, what are the concentrations of each substance in the equilibrium mixture?

Verified step by step guidance

Step 1: Write the balanced chemical equation for the reaction: CO_2(g) + H_2(g) ⇌ CO(g) + H_2O(g).

Step 2: Set up an ICE (Initial, Change, Equilibrium) table to track the concentrations of each species. Initially, [CO_2] = [H_2] = 1.50 mol / 3.00 L, and [CO] = [H_2O] = 0 mol/L.

Step 3: Define the change in concentration for the reactants and products in terms of x, where x is the amount of CO_2 and H_2 that react. The changes are: [CO_2] = [H_2] = -x, [CO] = [H_2O] = +x.

Step 4: Express the equilibrium concentrations in terms of x: [CO_2] = [H_2] = (1.50/3.00) - x, [CO] = [H_2O] = x.

Step 5: Substitute the equilibrium concentrations into the expression for the equilibrium constant K_c = ([CO][H_2O])/([CO_2][H_2]) and solve for x using K_c = 0.802.

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 CO2(g) + H2(g) ⇌ CO(g) + H2O(g), Kc = [CO][H2O] / [CO2][H2]. A Kc value greater than 1 indicates that products are favored at equilibrium, while a value less than 1 suggests that reactants are favored.

Concentration Calculations

Concentration is defined as the amount of a substance per unit volume of solution, typically expressed in moles per liter (M). To find the equilibrium concentrations of each substance, one must first determine the initial concentrations by dividing the number of moles by the volume of the container. Changes in concentration due to the reaction must then be accounted for using an ICE (Initial, Change, Equilibrium) table.

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. In the context of the given reaction, if the concentration of reactants or products is altered, the system will shift in the direction that reduces the effect of that change, which is crucial for predicting how concentrations will adjust at equilibrium.

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Related Practice

Textbook Question

A 0.831-g sample of SO₃ is placed in a 1.00-L container and heated to 1100 K. The SO₃ decomposes to SO₂ and O₂: 2SO₃(𝑔) ⇌ 2 SO₂(𝑔) + O₂(𝑔) At equilibrium, the total pressure in the container is 1.300 atm. Find the values of 𝐾_𝑝 and 𝐾_𝑐 for this reaction at 1100 K.

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Textbook Question

Nitric oxide (NO) reacts readily with chlorine gas as follows: 2 NO(𝑔) + Cl₂(𝑔) ⇌ 2 NOCl(𝑔) At 700 K, the equilibrium constant 𝐾_𝑝 for this reaction is 0.26. For each of the following mixtures at this temperature, indicate whether the mixture is at equilibrium, or, if not, whether it needs to produce more products or reactants to reach equilibrium. (b) 𝑃_NO= 0.12atm, 𝑃_Cl2= 0.10atm, 𝑃_NOCl= 0.050atm

Textbook Question

At 900 °C, 𝐾_𝑐= 0.0108 for the reaction

CaCO₃(𝑠) ⇌ CaO(𝑠) + CO₂(𝑔)

A mixture of CaCO₃, CaO, and CO₂ is placed in a 10.0-L vessel at 900°C. For the following mixtures, will the amount of CaCO3 increase, decrease, or remain the same as the system approaches equilibrium?

(a) 15.0 g CaCO3, 15.0 g CaO, and 4.25 g CO2

(b) 2.50 g CaCO3, 25.0 g CaO, and 5.66 g CO2

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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