If wet silver carbonate is dried in a stream of hot air, the...

If wet silver carbonate is dried in a stream of hot air, the air must have a certain concentration level of carbon dioxide to prevent silver carbonate from decomposing by the reaction $$\mathrm{Ag}_{2} \mathrm{CO}_{3}(s) \rightleftharpoons \mathrm{Ag}_{2} \mathrm{O}(s)+\mathrm{CO}_{2}(g)$$ $\Delta H^{\circ}$ for this reaction is $79.14 \mathrm{~kJ} / \mathrm{mol}$ in the temperature range of 25 to $125^{\circ} \mathrm{C}$. Given that the partial pressure of carbon dioxide in equilibrium with pure solid silver carbonate is $6.23 \times 10^{-3}$ torr at $25^{\circ} \mathrm{C}$, calculate the partial pressure of $\mathrm{CO}_{2}$ necessary to prevent decomposition of $\mathrm{Ag}_{2} \mathrm{CO}_{3}$ at $110 .{ }^{\circ} \mathrm{C}$. (Hint: Manipulate the equation in Exercise 71 .)

If wet silver carbonate is dried in a stream of hot air, the air must have a certain concentration level of carbon dioxide to prevent silver carbonate from decomposing by the reaction
$$\mathrm{Ag}_{2} \mathrm{CO}_{3}(s) \rightleftharpoons \mathrm{Ag}_{2} \mathrm{O}(s)+\mathrm{CO}_{2}(g)$$
$\Delta H^{\circ}$ for this reaction is $79.14 \mathrm{~kJ} / \mathrm{mol}$ in the temperature range of 25 to $125^{\circ} \mathrm{C}$. Given that the partial pressure of carbon dioxide in equilibrium with pure solid silver carbonate is $6.23 \times 10^{-3}$ torr at $25^{\circ} \mathrm{C}$, calculate the partial pressure of $\mathrm{CO}_{2}$ necessary to prevent decomposition of $\mathrm{Ag}_{2} \mathrm{CO}_{3}$ at $110 .{ }^{\circ} \mathrm{C}$. (Hint: Manipulate the equation in Exercise 71 .)

Key Concepts

Chemical Equilibrium

This concept refers to the state in a chemical reaction where the rates of the forward and reverse reactions are equal, resulting in constant concentrations or pressures of reactants and products. In heterogeneous systems, such as those involving solids and gases, equilibrium conditions are governed by the activity or partial pressures of the components that are in the reactive phase.

Heterogeneous Equilibria

Heterogeneous equilibria occur in reactions involving different phases (e.g., solids, liquids, and gases). In these systems, the equilibrium constant expression is simplified because the activities of pure solids and liquids are taken as unity, leaving gaseous components such as CO2 to determine the position of equilibrium.

Equilibrium Constant Expression for Gaseous Phases

For reactions involving gases, the equilibrium constant is often expressed in terms of partial pressures. This allows the prediction of how a change in conditions, such as the concentration or pressure of a gas, impacts the overall equilibrium of the reaction.

Temperature Dependence and the van't Hoff Equation

The van't Hoff equation relates the change in the equilibrium constant to the change in temperature and the reaction enthalpy. It is used to understand and predict how equilibrium positions shift when the system is heated or cooled. An endothermic reaction will generally have an increased equilibrium constant with rising temperature, whereas an exothermic reaction shows the opposite behavior.

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