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?

검증된 단계별 안내

Calculate the number of moles of CO₂ initially present using its molar mass. The molar mass of CO₂ is approximately 44.01 g/mol.

Write the balanced chemical equation for the reaction: C(s) + CO₂(g) ⇌ 2 CO(g).

Use the equilibrium constant (K_c) value at 1000 K to set up the equilibrium expression: K_c = [CO]² / [CO₂].

Assume x moles of CO₂ react, then 2x moles of CO are produced at equilibrium. Substitute these values into the equilibrium expression and solve for x.

Calculate the mass of carbon consumed by converting the moles of reacted CO₂ (x) back to grams using the molar mass of carbon, which is approximately 12.01 g/mol.

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주요 개념

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Equilibrium Constant (Kc)

The equilibrium constant, Kc, quantifies 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 higher Kc value indicates a greater concentration of products at equilibrium, while a lower Kc suggests that reactants are favored.

Stoichiometry

Stoichiometry involves the calculation of reactants and products in chemical reactions based on balanced chemical equations. It allows us to determine the amount of substances consumed or produced in a reaction. In this case, stoichiometry will help relate the amount of CO2 reacted to the amount of solid carbon (C) consumed, using the coefficients from the balanced equation.

Ideal Gas Law

The Ideal Gas Law (PV = nRT) relates the pressure, volume, temperature, and number of moles of a gas. In this scenario, it can be used to determine the number of moles of CO2 present in the vessel, which is essential for calculating how much carbon is consumed during the reaction. Understanding this law is crucial for converting between grams and moles, facilitating stoichiometric calculations.