Consider the reaction: CO(g) + 2 H2(g) ⇌ CH3OH(g). A reaction mixture in a 5.19-L flask at a certain temperature contains 26.9 g CO and 2.34 g H2. At equilibrium, the flask contains 8.65 g CH3OH. Calculate the equilibrium constant (Kc) for the reaction at this temperature.

Verified step by step guidance

Convert the masses of CO, H2, and CH3OH to moles using their respective molar masses: CO (28.01 g/mol), H2 (2.02 g/mol), and CH3OH (32.04 g/mol).

Determine the initial moles of CO and H2 in the 5.19-L flask using the converted moles from step 1.

Calculate the change in moles of CH3OH at equilibrium, which is equal to the moles of CH3OH formed, and use stoichiometry to find the change in moles of CO and H2.

Determine the equilibrium moles of CO and H2 by subtracting the change in moles from their initial moles.

Calculate the equilibrium concentrations of CO, H2, and CH3OH by dividing their equilibrium moles by the volume of the flask (5.19 L), and then use these concentrations to find the equilibrium constant Kc using the expression Kc = [CH3OH] / ([CO][H2]^2).

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. It is calculated using the formula Kc = [products]^[coefficients] / [reactants]^[coefficients]. A Kc value greater than 1 indicates that products are favored at equilibrium, while a value less than 1 suggests that reactants are favored.

Molar Mass and Conversion to Molarity

To calculate Kc, it is essential to convert the mass of each substance in the reaction to moles using their molar masses. Molarity, defined as moles of solute per liter of solution, is then determined by dividing the number of moles by the volume of the flask in liters. This conversion is crucial for accurately determining the concentrations of reactants and products at equilibrium.

Stoichiometry of the Reaction

Stoichiometry involves the quantitative relationships between the reactants and products in a chemical reaction. In the given reaction, the coefficients indicate that one mole of CO reacts with two moles of H2 to produce one mole of CH3OH. Understanding these ratios is vital for calculating the changes in concentrations as the system reaches equilibrium and for determining the equilibrium constant.

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Consider the reaction: NH₄HS(s) ⇌ NH₃(g) + H₂S(g) At a certain temperature, K_c = 8.5⨉10^-3. A reaction mixture at this temperature containing solid NH₄HS has [NH₃] = 0.166 M and [H₂S] = 0.166 M. Will more of the solid form or will some of the existing solid decompose as equilibrium is reached?

Textbook Question

Silver sulfate dissolves in water according to the reaction: Ag₂SO₄(s) ⇌ 2 Ag⁺(aq) + SO₄^2-(aq) K_c = 1.1⨉10^-5 at 298 K. A 1.5-L solution contains 6.55 g of dissolved silver sulfate. If additional solid silver sulfate is added to the solution, will it dissolve?