Sodium sulfate 10-hydrate, \(\mathrm{Na}_{2} \mathrm{SO}_{4} \cdot 10 \mathrm{H}_{2} \mathrm{O},\) dehydrates according to the equation \(\mathrm{Na}_{2} \mathrm{SO}_{4} \cdot 10 \mathrm{H}_{2} \mathrm{O}(s) \rightleftharpoons \mathrm{Na}_{2} \mathrm{SO}_{4}(s)+10 \mathrm{H}_{2} \mathrm{O}(g) \quad K_{P}=4.08 \times 10^{-25} \mathrm{at} 25^{\circ} \mathrm{C}\) What is the pressure of water vapor at equilibrium with a mixture of \(\mathrm{Na}_{2} \mathrm{SO}_{4} \cdot 10 \mathrm{H}_{2} \mathrm{O}\) and \(\mathrm{NaSO}_{4} ?\)

Chemical equilibrium is a state in a chemical reaction where the rate of the forward reaction equals the rate of the reverse reaction, meaning that the amounts of reactants and products remain constant over time. It's an essential concept in chemistry because it helps us understand how chemical reactions proceed and under what conditions they will favor the formation of either reactants or products.

Understanding the equilibrium of a reaction involves learning about the equilibrium constant, usually denoted as Keq or Kc for concentrations and Kp for partial pressures. These constants provide a quantitative measure of the reaction's position at equilibrium; high values suggest product-favorable conditions, while low values indicate reactant-favorable conditions.

When dealing with gases, we often use the equilibrium constant in terms of partial pressure (Kp), since gases mix homogeneously and their individual pressures can be related to the total pressure and mole fraction.

Sodium sulfate decahydrate, also known as Glauber's salt, is a hydrated ionic compound with the formula \(\mathrm{Na}_{2} \mathrm{SO}_{4} \cdot 10 \mathrm{H}_{2} \mathrm{O}\). It is often used in laboratories and industries for its properties as a drying agent and as part of the manufacturing process in detergents.

In its crystalline form, sodium sulfate decahydrate contains ten water molecules for every formula unit, which are integral to its structure and properties. Upon heating or exposure to dry conditions, it can lose these water molecules through a dehydration reaction, transforming into anhydrous sodium sulfate. This process is not only a physical change but also a chemical one as the state of the system changes and new substances form.

Partial pressure is a term used to describe the pressure exerted by a single gas within a mixture of gases. According to Dalton's Law of Partial Pressures, the total pressure in a gas mixture is the sum of the partial pressures of each individual gas. This concept is incredibly useful when dealing with chemical reactions involving gases, as it allows us to calculate the concentrations of individual gases at equilibrium.

The partial pressure of a gas can be found using the ideal gas law, given by the equation \( PV = nRT \), where P is the pressure, V is the volume, n is the number of moles of the gas, R is the universal gas constant, and T is the temperature. When considering chemical equilibrium involving gases, only the partial pressures of the gaseous substances appear in the equilibrium constant expression, not the pressures of any solids or liquids present.

A dehydration reaction is a chemical reaction in which a compound loses water molecules. In the context of sodium sulfate decahydrate (\(\rm{Na}_2SO_4 \times 10H_2O\)), the dehydration reaction involves the loss of water to form anhydrous sodium sulfate (\(\rm{Na}_2SO_4\) and water vapor (\(10H_2O\rm{(g)}\) at high temperatures.

This type of reaction is generally endothermic, meaning it absorbs heat from its surroundings, which is why heat is needed for sodium sulfate decahydrate to dehydrate. Dehydration reactions are also reversible. When humidity is high, the anhydrous salt can reabsorb water and convert back into the hydrate form, demonstrating a dynamic chemical equilibrium where the rates of hydration and dehydration are equal, and the amounts of the hydrate and anhydrous forms remain constant over time.