Sodium chloride is added to water (at 25^∘ C ) until it is saturated. Calculate the Cl - concent

step 1 First we need to write out an equilibrium reaction for the dissolution of sodium chloride in wat

Sodium chloride is added to water (at 25^∘ C ) until it is...

Sodium chloride is added to water (at $25^{\circ} \mathrm{C}$ ) until it is saturated. Calculate the Cl - concentration in such a solution. $$\begin{array}{lc}\text { Species } & \left.\Delta G^{\circ}(\mathrm{k}] / \mathrm{mol}\right) \\\hline \mathrm{NaCl}(s) & -384 \\\mathrm{Na}^{+}(a q) & -262 \\\mathrm{Cl}^{-}(a q) & -131\end{array}$$

Key Concepts

Solubility Equilibrium

This concept refers to the state where a solid salt in contact with its saturated solution reaches an equilibrium between the dissolving ions and the undissolved solid. In such systems, the product of the concentration of the ions is constant at a given temperature, known as the solubility product (Ksp). This equilibrium framework is essential for understanding and quantifying the concentration of ions in a saturated solution.

Gibbs Free Energy and Equilibrium Constant Relationship

This principle establishes the link between the standard Gibbs free energy change (?G°) of a reaction and its equilibrium constant (K) through the equation ?G° = -RT ln K. It allows one to calculate the equilibrium constant from thermodynamic data, which is crucial for predicting the extent of a dissolution process in solution.

Dissolution Reaction Thermodynamics

This concept involves understanding the energetics of dissolving a solid salt into its constituent ions in water. The dissolution process is treated as a chemical reaction with a certain ?G° value. By using the free energy changes of the products and reactants, one can compute the overall ?G° for dissolution, which then relates to the equilibrium constant governing the ion concentrations in a saturated solution.

Calculation of Ion Concentration in Saturated Solutions

When a salt dissolves completely into its component ions, assuming complete dissociation, the equilibrium concentrations of these ions can be determined from the solubility product relation. Typically, for a salt that dissociates into one cation and one anion, the concentration of each ion is the square root of the calculated Ksp. This approach is fundamental in quantifying the concentration of individual ions in saturated solutions.

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