Question

Sodium chloride is added to water (at \(25^{\circ} \mathrm{C}\) ) until it is saturated. Calculate the \(\mathrm{Cl}^{-}\) concentration in such a solution.

Short answer

The concentration of \(\mathrm{Cl}^{-}\) ions in a saturated sodium chloride solution at \(25^{\circ} \mathrm{C}\) is approximately 6.01 mol/L.

Step-by-step solution

Write the dissolution equation for sodium chloride

Write the balanced equation for the dissolution process of sodium chloride: \(NaCl \rightleftharpoons Na^+ + Cl^-\)

Find the solubility product constant (Ksp) for sodium chloride at 25°C

The Ksp value for sodium chloride at 25°C is 36.1. This value can be found in reference tables or online.

Write the expression for the solubility product constant (Ksp)

Write the expression for Ksp based on the equation from Step 1: \(K_{sp} = [Na^+][Cl^-]\)

Determine the relationship between the concentrations of ions

Based on the stoichiometry of the dissolution equation, the concentration of Na⁺ and Cl⁻ ions will be equal at saturation. Let's use 'x' to represent the concentration of both ions at saturation: \([Na^+] = [Cl^-] = x\)

Substitute the values into the Ksp expression

Use the relationship from Step 4 to substitute the concentrations of Na⁺ and Cl⁻ in the Ksp expression from Step 3: \(K_{sp} = (x)(x) = x^2\)

Calculate the concentration of Cl⁻ ions at saturation

Substitute the Ksp value from Step 2 into the equation from Step 5 and solve for 'x': \(x^2 = 36.1\) \(x = \sqrt{36.1} \approx 6.01\) Thus, the concentration of Cl⁻ ions in the saturated sodium chloride solution at 25°C is approximately 6.01 mol/L.

Key concepts

Sodium Chloride

Sodium chloride, commonly known as table salt, is a compound composed of sodium (Na) and chloride (Cl) ions. It forms when sodium donates an electron to chlorine, resulting in an ionic bond.

When sodium chloride is added to water, it dissociates into its constituent ions. This is a reversible process depicted by the equation: \(NaCl \rightleftharpoons Na^+ + Cl^-\).

In a saturated solution, the amount of sodium chloride dissolving in water is balanced by the amount recrystallizing from the solution. Understanding how sodium chloride behaves in a solution helps us to grasp the concept of solubility effectively.

Ksp

The solubility product constant, abbreviated as \(K_{sp}\), is a vital concept in understanding solubility.
For a sparingly soluble salt like sodium chloride, \(K_{sp}\) reflects the product of the concentrations of the ions at equilibrium.

Mathematically, this is described as:

• \(K_{sp} = [Na^+][Cl^-]\)

At a given temperature, \(K_{sp}\) remains constant for a given salt. In the case of sodium chloride at 25°C, \(K_{sp}\) is 36.1. This means that the concentrations of \(Na^+\) and \(Cl^-\) ions in a saturated solution will adjust until their product equals 36.1.

Concentration

Concentration refers to the amount of solute present in a given volume of solution. For sodium chloride in water, it's crucial to determine the concentration of the dissolved ions.

In a saturated solution of sodium chloride, the concentrations of \(Na^+\) and \(Cl^-\) ions are equal due to the 1:1 ratio in which they dissociate.

We can express this mathematically using the variable 'x', where \([Na^+] = [Cl^-] = x\).

By substituting into \(K_{sp}\), we find \([Cl^-] = x = \sqrt{36.1} \approx 6.01 \text{ mol/L}\). Thus, the concentration of chloride ions in a saturated solution at a given temperature can be easily calculated once \(K_{sp}\) is known.

Saturated Solution

A saturated solution contains the maximum concentration of solute that can dissolve at a particular temperature.

In this state, any added solute will not dissolve, but remain as solid precipitate unless the conditions (such as temperature) change.

Considering sodium chloride, in a saturated solution, the rates of dissolution and precipitation are equal, maintaining a dynamic equilibrium. The chloride ion concentration reaches a point where adding more salt doesn't increase its concentration in the solution, maintaining the equilibrium as dictated by its \(K_{sp}\) value.

Understanding saturated solutions helps predict how substances behave when they are added to solvents and aids in practical applications like chemical manufacturing and cooking.