At 650 K, the reaction MgCO₃(s) ⇌ MgO(s) + CO₂(g) has K_p = 0.026. A 10.0-L container at 650 K has 1.0 g of MgO(s) and CO₂ at P = 0.0260 atm. The container is then compressed to a volume of 0.100 L. Find the mass of MgCO₃ that is formed.

검증된 단계별 안내

Calculate the initial moles of CO2 using the ideal gas law equation: PV = nRT. Here, P is the initial pressure of CO2, V is the initial volume, R is the gas constant (0.0821 L atm K^{-1} mol^{-1}), and T is the temperature in Kelvin.

Determine the new pressure of CO2 after the volume is changed to 0.100 L using the equation P1V1 = P2V2, where P1 and V1 are the initial pressure and volume, and P2 and V2 are the final pressure and volume.

Use the expression for the equilibrium constant Kp = \(\frac{P_{CO2}\)}{1} to find the new equilibrium partial pressure of CO2. Rearrange the equation to solve for P_{CO2} at equilibrium.

Calculate the change in moles of CO2 from the initial state to the equilibrium state using the difference in initial moles of CO2 and moles of CO2 at equilibrium.

Convert the change in moles of CO2 to mass of MgCO3 formed using the molar mass of MgCO3. The stoichiometry of the reaction indicates that 1 mole of CO2 corresponds to 1 mole of MgCO3.

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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Equilibrium Constant (Kp)

The equilibrium constant (Kp) is a numerical value that expresses the ratio of the partial pressures of the products to the reactants at equilibrium for a given reaction at a specific temperature. In this case, Kp = 0.026 indicates that at 650 K, the reaction favors the formation of reactants over products. Understanding Kp is essential for predicting how changes in conditions, such as pressure and volume, will affect the position of equilibrium.

Le Chatelier's Principle

Le Chatelier's Principle states that if a dynamic equilibrium is disturbed by changing the conditions, the system will adjust itself to counteract the change and restore a new equilibrium. In this scenario, compressing the container decreases the volume, which increases the pressure. According to Le Chatelier's Principle, the system will shift towards the side with fewer moles of gas to reduce the pressure, influencing the formation of MgCO3.

Ideal Gas Law

The Ideal Gas Law (PV = nRT) relates the pressure (P), volume (V), number of moles (n), the ideal gas constant (R), and temperature (T) of a gas. This law is crucial for calculating the number of moles of CO2 present in the container before and after compression. By using the initial conditions and the new volume, one can determine how the concentration of gases changes, which is necessary for calculating the mass of MgCO3 formed.

At 650 K, the reaction MgCO3(s) ⇌ MgO(s) + CO2(g) has Kp = 0.026. A 10.0-L container at 650 K has 1.0 g of MgO(s) and CO2 at P = 0.0260 atm. The container is then compressed to a volume of 0.100 L. Find the mass of MgCO3 that is formed.