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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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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Key Concepts

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

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.

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Ideal Gas Law Formula

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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

Nitric oxide (NO) reacts readily with chlorine gas as follows: 2 NO(𝑔) + Cl₂(𝑔) ⇌ 2 NOCl(𝑔) At 700 K, the equilibrium constant Kp for this reaction is 0.26. Predict the behavior of each of the following mixtures at this temperature and indicate whether or not the mixtures are at equilibrium. If not, state whether the mixture will need to produce more products or reactants to reach equilibrium.

(a) P_NO = 0.15 atm, P_Cl2 = 0.31 atm, P_NOCl = 0.11 atm

(b) P_NO = 0.12 atm, P_Cl2 = 0.10 atm, P_NOCl = 0.050 atm

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