Question

In the experiment, a probe was used to measure the conductivities in each solution. The probe generates a potential difference between two electrodes and reads the current that is produced as a voltage. The computer then outputs the conductivity. If several different solutions were all heated from room temperature to \(75^{\circ}\) Celsius, how would the conductivity of the solutions change and how would the \(\mathrm{K}_{\mathrm{sp}}\) be affected? A. The conductivity would increase and the \(\mathrm{K}_{\mathrm{sp}}\) would increase. B. The conductivity would decrease and the change in \(\mathrm{K}_{\text {sp }}\) would increase. C. The conductivity would increase and the change in \(\mathrm{K}_{\mathrm{sp}}\) cannot be determined. D. The conductivity would decrease and the change in \(\mathrm{K}_{\text {sp }}\) cannot be determined.

Short answer

A. The conductivity would increase and the \(K_{sp}\) would increase.

Step-by-step solution

Understand Conductivity

Conductivity refers to the ability of a solution to conduct electric current. As the temperature increases, the ions in the solution move more rapidly, which generally increases conductivity.

Determine Effect on Conductivity

Since higher temperatures increase the movement of ions, the conductivity of solutions typically increases when heated from room temperature to 75°C.

Understand \(\text{K}_{\text{sp}}\)

\(K_{sp}\) represents the solubility product constant, which is dependent on temperature. When temperature increases, the solubility of most salts in water increases, thus increasing the \(K_{sp}\).

Analyze Answer Choices

Based on the previous steps, we know that both the conductivity and \(K_{sp}\) increase with temperature. Therefore, the correct answer is: \(K_{sp}\) increases and conductivity increases.

Key concepts

conductivity of solutions

Conductivity is a measure of how well a solution can carry an electric current. This ability depends largely on the ions present in the solution. More ions mean higher conductivity. When a salt dissolves in water, it splits into positive and negative ions, which enable the solution to conduct electricity.

Different solutions have different conductivities based on the type and number of ions they contain. A solution of table salt (NaCl) will have different conductivity than a solution of sugar, as sugar does not dissociate into ions.

To measure conductivity, a probe with two electrodes is used. The probe applies a potential difference (voltage) and measures the resulting current. The computer then interprets this signal as conductivity. By understanding conductivity, we can infer the concentration and mobility of ions in the solution.

temperature effects on ion movement

Temperature has a significant impact on ion movement in a solution. As temperature rises, the kinetic energy of ions increases. This means ions move faster at higher temperatures.

When a solution is heated from room temperature to 75°C, the increased kinetic energy causes ions to collide more frequently and move more rapidly. This results in higher conductivity because the ions are more active and facilitate better movement of electric current.

It's important to note, however, that excessive temperatures can sometimes lead to the breakdown of the solvent or solute, which might affect the overall conductivity adversely. But within moderate temperature ranges, an increase generally leads to higher ion movement and thus higher conductivity.

solubility product constant (Ksp)

The solubility product constant, denoted as \(K_{sp}\), reflects a salt's solubility in water. \(K_{sp}\) is defined for a saturated solution in equilibrium, where the salt dissociates into its constituent ions.

For example, if a salt \(AB\) dissolves in water, it splits into \(A^+\) and \(B^-\) ions. The \(K_{sp}\) expression would be \[K_{sp} = [A^+][B^-]\].

Temperature affects \(K_{sp}\) since higher temperatures typically increase the solubility of salts in water. This means more \(A^+\) and \(B^-\) ions are present in the solution, increasing the \(K_{sp}\) value. However, this effect can vary with different salts. In the provided exercise, as the temperature increases from room temperature to 75°C, the \(K_{sp}\) will increase, facilitating more ion dissociation and better conductivity, as described in the step-by-step solution.