Problem 91 - Chemistry: An Atoms-Focused Approach

Question

The \(K_{\text {sp }}\) of strontium sulfate increases from \(2.8 \times 10^{-7}\) at \(37^{\circ} \mathrm{C}\) to \(3.8 \times 10^{-7}\) at \(77^{\circ} \mathrm{C} .\) Is the dissolution of strontium sulfate endothermic or exothermic?

Step-by-Step Solution

Answer

Answer: The dissolution of strontium sulfate is endothermic.

Step 1: Identify the given Ksp values and temperatures

We are given the Ksp values at two different temperatures: - At 37°C: \(K_{sp} = 2.8 \times 10^{-7}\) - At 77°C: \(K_{sp} = 3.8 \times 10^{-7}\)

Step 2: Comparing the Ksp values at different temperatures

Now we will compare the two values of Ksp at different temperatures: - At 37°C: \(K_{sp} = 2.8 \times 10^{-7}\) - At 77°C: \(K_{sp} = 3.8 \times 10^{-7}\) Observe that when the temperature is increased from 37°C to 77°C, Ksp value increases from \(2.8 \times 10^{-7}\) to \(3.8 \times 10^{-7}\).

Step 3: Determine if the dissolution is endothermic or exothermic

Since the solubility product constant (Ksp) increases with increasing temperature, it indicates that the dissolution process requires more energy to take place at higher temperatures. Therefore, the dissolution of strontium sulfate is endothermic.

Key Concepts

Solubility Product Constant (Ksp)

The solubility product constant, known as Ksp, is a value that helps us understand how a compound dissolves in water. Specifically, it measures how much of a compound can dissolve before the solution becomes saturated.
Where no more solute can dissolve and is in equilibrium between the dissolved ions and the undissolved solute. For any given compound that dissolves in water, an equilibrium is established between the solid compound and the ions in the solution. The Ksp is calculated using the concentrations of these ions when the solution is at equilibrium.

• When the value of Ksp is small, the compound is less soluble in water.
• If Ksp is large, the compound is more soluble and can dissolve easily.

Using the numbers from the example, at 37°C, the Ksp of strontium sulfate is \(2.8 \times 10^{-7}\). At 77°C, it increases to \(3.8 \times 10^{-7}\). This increase tells us that more of the compound can dissolve in water at higher temperatures. This concept plays a key role in determining whether a reaction is endothermic or exothermic.

Endothermic Process

An endothermic process is one where the system absorbs energy from the surroundings, often in the form of heat. This means it requires energy input to proceed.
When thinking about dissolution, if a process is endothermic, it means the solubility of the substance increases with a rise in temperature. For strontium sulfate, as we noted in the previous section, the increase in the Ksp value with temperature shows that more solute dissolves at higher temperatures. This is a hallmark of an endothermic process.

• The system needs energy to break bonds in the solid.
• This energy comes from the heat energy around it, making the reaction more favorable at higher temperatures.

As a general rule:
- If solubility increases with temperature, the process is likely endothermic. - Conversely, if solubility decreases with temperature, the process is typically exothermic. In the case of strontium sulfate, as the temperature climbs from 37°C to 77°C, Ksp climbs, indicating that dissolution is more efficient at higher temperatures due to the endothermic nature of the process.

Temperature Effects on Solubility

Temperature can have a significant impact on the solubility of substances. It influences not just physical states but also chemical equilibria like solubility.
When temperature increases:

• The kinetic energy of molecules also increases.
• This often helps solutes dissolve more by providing the energy needed to break bonding forces in solids.

However, the effect of temperature on solubility isn't uniform:

• For endothermic processes, solubility increases with temperature.
• For exothermic processes, it decreases.

This is because, in an endothermic process, additional heat provides the energy needed to dissolve more solute. In the case of strontium sulfate, we observed that when the temperature was increased from 37°C to 77°C, the Ksp rose, indicating enhanced solubility due to the endothermic nature of its dissolution. Understanding how temperature affects solubility is important in many areas, such as in designing industrial applications and processes where controlling the solubility of compounds is essential.