Question

A gaseous solute dissolves in water. The solution process has \(\Delta H=-15 \mathrm{~kJ} .\) Its solubility at \(22^{\circ} \mathrm{C}\) and \(6.00 \mathrm{~atm}\) is \(0.0300 \mathrm{M}\). Would you expect the solubility to be greater or less at (a) \(22^{\circ} \mathrm{C}\) and \(1 \mathrm{~atm}\) ? (b) \(18^{\circ} \mathrm{C}\) and 6 atm? (c) \(15^{\circ} \mathrm{C}\) and \(10 \mathrm{~atm}\) ? (d) \(35^{\circ} \mathrm{C}\) and 3 atm?

Short answer

Answer: (a) The solubility at 22°C and 1 atm is expected to be less than that at 22°C and 6.00 atm due to the decrease in pressure. (b) The solubility at 18°C and 6 atm is expected to be greater than that at 22°C and 6.00 atm due to the decrease in temperature. (c) The solubility at 15°C and 10 atm is expected to be greater than that at 22°C and 6.00 atm due to the decrease in temperature and increase in pressure. (d) The solubility at 35°C and 3 atm is expected to be less than that at 22°C and 6.00 atm due to the increase in temperature and decrease in pressure.

Step-by-step solution

(a) Solubility at 22°C and 1 atm

(First, we will analyze the effect of changing the pressure from 6.00 atm to 1 atm while keeping the temperature constant at 22°C. Since the pressure is decreasing, we can apply Henry's Law which states that the solubility of a gas in a liquid is directly proportional to the pressure of the gas above the liquid. In this case, the solubility will decrease proportionally to the decrease in pressure. So, the solubility at 22°C and 1 atm is expected to be less than that at 22°C and 6.00 atm.

(b) Solubility at 18°C and 6 atm

(Now, we will analyze the effect of changing the temperature from 22°C to 18°C while keeping the pressure constant at 6.00 atm. Since the enthalpy change is negative, the solution process is exothermic, meaning that it releases heat. According to Le Chatelier's Principle, a decrease in temperature will cause the equilibrium to shift in the direction of the exothermic process. Therefore, the solubility at 18°C and 6 atm is expected to be greater than that at 22°C and 6.00 atm.

(c) Solubility at 15°C and 10 atm

(In this case, we have a change in both temperature and pressure. First, let us analyze the effect of decreasing the temperature from 22°C to 15°C. As discussed earlier, the solubility will increase with a decrease in temperature due to the exothermic nature of the solution process. Secondly, we need to analyze the effect of increasing the pressure from 6.00 atm to 10 atm. Based on Henry's Law, increasing the pressure will increase the solubility. Since both the factors are favoring an increase in solubility, we expect the solubility at 15°C and 10 atm to be greater than that at 22°C and 6.00 atm.

(d) Solubility at 35°C and 3 atm

(In this case, we have a change in both temperature and pressure. First, let us analyze the effect of increasing the temperature from 22°C to 35°C. Since the solution process is exothermic, increasing the temperature will decrease the solubility. Secondly, we need to analyze the effect of decreasing the pressure from 6.00 atm to 3 atm. Based on Henry's Law, decreasing the pressure will decrease the solubility. Since both the factors are favoring a decrease in solubility, we expect the solubility at 35°C and 3 atm to be less than that at 22°C and 6.00 atm.

Key concepts

Henry's Law

Henry's Law is a principle that plays a crucial role in predicting the solubility of gases in liquids. It articulates a direct relationship between the pressure of a gas above a liquid and the solubility of that gas within the liquid. Specifically, it states that at a constant temperature, the solubility of a gas in a liquid is directly proportional to the partial pressure of the gas above the liquid.

This relationship can be expressed through the equation: \[ S = kH \times P \] where \(S\) is the solubility of the gas in the liquid, \(kH\) is Henry's Law constant (specific for each gas), and \(P\) is the partial pressure of the gas. From a practical standpoint, this means that increasing the pressure will increase the gas's solubility, and vice versa. For example, carbonated beverages utilize Henry's Law; the high pressure inside a sealed bottle ensures a higher CO2 solubility, keeping the drink fizzy until opened.

Le Chatelier's Principle

Le Chatelier's Principle helps us understand how a system at equilibrium responds to changes in concentration, temperature, or pressure. It states that if any of these factors change, the equilibrium will shift to counteract the change and establish a new balance. For solubility, this principle implies that factors which remove solute from the solution will shift equilibrium toward dissolving more solute, and factors that add more solute to the solution will shift equilibrium toward depositing solute out of the solution.

In the context of temperature, if the dissolution of the gas is an exothermic process (heat is released), reducing the temperature will increase the solubility because the equilibrium will shift to release more heat by dissolving more gas. Conversely, if the process is endothermic (heat is absorbed), decreasing the temperature will decrease solubility. Understanding this principle is fundamental for manipulating and predicting the behavior of solutions in various chemical processes and environmental conditions.

Enthalpy Change

Enthalpy change (\( \triangle H \)) is a measure of the heat absorbed or released during a chemical process. In solutions, the enthalpy change indicates whether the process is exothermic (negative \( \triangle H \)) or endothermic (positive \( \triangle H \)). An exothermic solution process, as in the given exercise, means that heat is released when the solute dissolves in the solvent, which can influence solubility according to Le Chatelier's Principle.

In scenarios where the temperature changes, it's crucial to consider the enthalpy of the solution process. If the enthalpy change is negative (exothermic), lowering the external temperature will generally increase the solubility of a solute, as the system can release more heat into its surroundings. Conversely, with a positive enthalpy change (endothermic), lowering the temperature will decrease solubility, as the system cannot absorb enough heat from the cooler surroundings to dissolve more solute.

Temperature and Pressure Effects on Solubility

Temperature and pressure significantly affect the solubility of substances. For gases in liquids, as we previously discussed, Henry's Law tells us that at a higher pressure, more gas will dissolve in the liquid. This is observed in the increased fizziness of a carbonated drink when it's stored under pressure.

Temperature's effect, however, can vary depending on the nature of the solute. For gases, an increase in temperature usually decreases solubility, because gas molecules have more energy to escape into the air. For many solids, increasing temperature increases solubility, as the solute particles have more energy to interact with the solvent and form solutions. These effects can be intertwined; a rise in temperature might lead to a decrease in solubility despite an increase in pressure, or an increase in pressure could boost solubility despite a drop in temperature. The exact behavior will depend on the enthalpy change of the solution process and the specific substance involved.