Consider the decomposition of barium carbonate: BaCO₃(s) ⇌ BaO(s) + CO₂(g) Using data from Appendix C, calculate the equilibrium pressure of CO₂ at (a) 298 K.

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Identify the reaction: BaCO_3(s) \(\rightleftharpoons\) BaO(s) + CO_2(g).

Use the standard Gibbs free energy change (\(\Delta\) G^\(\circ\)) for the reaction to find the equilibrium constant (K) at 298 K. \(\Delta\) G^\(\circ\) = \(\sum\) \(\Delta\) G^\(\circ\)_{\(\text{products}\)} - \(\sum\) \(\Delta\) G^\(\circ\)_{\(\text{reactants}\)}.

Calculate \(\Delta\) G^\(\circ\) using the values from Appendix C for BaCO_3, BaO, and CO_2.

Relate \(\Delta\) G^\(\circ\) to the equilibrium constant using the equation \(\Delta\) G^\(\circ\) = -RT \(\ln\) K, where R is the gas constant (8.314 J/mol·K) and T is the temperature in Kelvin.

Solve for K, which is equal to the equilibrium pressure of CO_2, since the reaction involves only one gaseous product.

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주요 개념

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Chemical Equilibrium

Chemical equilibrium occurs when the rates of the forward and reverse reactions are equal, resulting in constant concentrations of reactants and products. In the context of the decomposition of barium carbonate, the system reaches equilibrium when the amount of BaCO3 decomposing into BaO and CO2 is balanced by the amount of CO2 reacting back to form BaCO3.

Equilibrium Constant (Kp)

The equilibrium constant (Kp) for a gaseous reaction is defined in terms of the partial pressures of the products and reactants at equilibrium. For the decomposition of BaCO3, Kp can be expressed as the ratio of the partial pressure of CO2 to the concentration of BaCO3 and BaO, allowing for the calculation of the equilibrium pressure of CO2 at a given temperature.

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 pressure of CO2 at equilibrium by rearranging the equation to solve for pressure (P) when the number of moles and temperature are known, providing a practical approach to finding the equilibrium pressure in the reaction.

Consider the decomposition of barium carbonate: BaCO3(s) ⇌ BaO(s) + CO2(g) Using data from Appendix C, calculate the equilibrium pressure of CO2 at (a) 298 K.