Use the data in Appendix B to calculate the equilibrium pressure of CO2 in a closed 1 L vessel that contains each of the following samples: (a) 15 g of MgCO3 and 1.0 g of MgO at 25 °C (b) 15 g of MgCO3 and 1.0 g of MgO at 280 °C . Assume that ∆H° and ∆S° are independent of temperature.
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Identify the chemical reaction involved. In this case, the decomposition of magnesium carbonate (MgCO3) to magnesium oxide (MgO) and carbon dioxide (CO2) can be represented by the equation: MgCO3(s) → MgO(s) + CO2(g).
Calculate the number of moles of MgCO3 using its molar mass. The molar mass of MgCO3 can be found in a periodic table or chemical database.
Use the stoichiometry of the reaction to determine the moles of CO2 produced. Since the reaction shows that 1 mole of MgCO3 produces 1 mole of CO2, the moles of CO2 will be equal to the moles of MgCO3 initially present.
Apply the ideal gas law, PV = nRT, to find the pressure of CO2. Here, P is the pressure of CO2, V is the volume of the vessel (1 L), n is the moles of CO2, R is the ideal gas constant (0.0821 L·atm/mol·K), and T is the temperature in Kelvin (298 K for 25 °C).
Consider any changes in pressure due to other gases or vapor pressures in the vessel, if applicable. Since only MgCO3 and MgO are present and MgO does not contribute to the gas phase, the total pressure in the vessel will be the pressure of CO2.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Equilibrium Constant (Kp)
The equilibrium constant for gases, Kp, relates the partial pressures of the products and reactants at equilibrium. It is derived from the balanced chemical equation and is crucial for calculating the equilibrium state of a reaction. In this case, understanding Kp will help determine the pressure of CO2 produced from the decomposition of MgCO3.
Gibbs Free Energy is a thermodynamic potential that indicates the spontaneity of a reaction at constant temperature and pressure. The relationship between ΔG, enthalpy (ΔH), and entropy (ΔS) is given by the equation ΔG = ΔH - TΔS. For the reaction in question, calculating ΔG will help assess whether the formation of CO2 is favorable under the given conditions.
The Ideal Gas Law (PV=nRT) relates the pressure, volume, temperature, and number of moles of a gas. In this scenario, it will be essential to use this law to convert the amount of CO2 produced into pressure within the 1 L vessel. Understanding this relationship allows for the calculation of the equilibrium pressure of CO2 based on the moles generated from the decomposition of MgCO3.