Question

In a saturated solution at \(25^{\circ} \mathrm{C}\) and 1 bar, for the following solutes, which condition will increase solubility? (a) \(\operatorname{Ar}(g),\) decrease temperature; (b) \(\mathrm{NaCl}(\mathrm{s})\) increase pressure; (c) \(\mathrm{N}_{2}\), decrease pressure; (d) \(\mathrm{CO}_{2}\) increase volume.

Short answer

Only decreasing the temperature will increase the solubility of Ar(g). Changing pressure will not have a significant effect on NaCl's solubility and decreasing the pressure will decrease N2's solubility. Increasing the volume doesn't directly impact CO2's solubility.

Step-by-step solution

Review the General Principles affecting Solubility

Generally, there are three major factors that affect solubility: temperature, pressure, and nature of the solute and solvent. The solubility of a gas in a liquid decreases with increase in temperature and increases with increase in pressure according to Henry's law. The solubility of solids in liquids usually increases with increase in temperature, while the effect of pressure on the solubility of solids and liquids in liquids is insignificant.

Apply the Principles to the Given Solutes

(a) For argon gas (\(Ar(g)\)), decreasing the temperature will increase the solubility because gas solubility increases as temperature decreases. (b) For sodium chloride (\(\mathrm{NaCl}(s)\)), changing the pressure will not have a significant impact on its solubility because it is a solid. (c) For nitrogen gas (\(\mathrm{N}_{2}(g)\)), decreasing the pressure will decrease, not increase, its solubility in the solvent. The solubility of a gas decreases as the pressure decreases. (d) For carbon dioxide (\(\mathrm{CO}_{2}\)), increasing the volume will not have a significant effect on the solubility because the volume of the container does not directly affect the solubility.

Conclude the Conditions for Increased Solubility

In conclusion, only for argon gas, a decrease in temperature will increase its solubility. The solubility of NaCl and \(N_2\) will not be increased under the described conditions; while volume change doesn't directly impact \(CO_2\) solubility.

Key concepts

Henry's Law

Henry's Law is a fundamental concept that describes the relationship between the solubility of gases in liquids and the pressure of the gas above the liquid. This law states that the amount of gas that dissolves in a liquid is directly proportional to the partial pressure of the gas above the liquid. In simpler terms, as you increase the pressure of the gas, more of it will dissolve in the liquid.

For example, in a closed soda bottle, carbon dioxide is dissolved under high pressure, which keeps the soda fizzy. Once you open the bottle and release the pressure, the gas begins to escape, leading to a loss of fizz. This is a practical demonstration of Henry’s Law. Importantly, this principle explains why nitrogen in the atmosphere dissolves in water under certain conditions, and an increase in pressure can increase the amount of nitrogen that waters can hold.

Effect of Temperature on Solubility

The effect of temperature on solubility depends heavily on the type of solute. For gases, solubility typically decreases with increasing temperature. This is because higher temperatures provide energy to gas molecules, making them more likely to escape from the liquid into the gas phase.

Think about what happens when you heat water on the stove; bubbles of dissolved air rise as the water warms. This is an example where the increase in temperature decreases the solubility of the gases, such as oxygen and nitrogen, in water. On the other hand, solids tend to become more soluble as the temperature increases, because the additional heat allows the solid particles to dissolve more easily in the liquid.

Effect of Pressure on Solubility

The solubility of solids and liquids is relatively unaffected by changes in pressure. However, the solubility of gases is significantly influenced by pressure, as noted by Henry's Law. Essentially, increasing the pressure of a gas increases its solubility in a liquid because the gas molecules are "pushed" into the liquid more effectively.

This principle is utilized in various applications, such as increasing the pressure in a carbonated beverage to dissolve more carbon dioxide. When you open a can of soda, the pressure is released, and you can observe the characteristic fizz due to the gas escaping the liquid.

Gas Solubility

Gas solubility refers to how well a gas can dissolve in a liquid. This property depends significantly on both the nature of the gas and the conditions under which it is dissolved. Generally, gases that react chemically with water, such as carbon dioxide, tend to have higher solubility.

Two principal factors affecting gas solubility are temperature and pressure:

• Lower temperatures generally increase gas solubility.
• Higher pressures almost always lead to increased gas solubility, as described by Henry's Law.

Unlike solids, where pressure has a negligible effect, gases respond dramatically to changes in pressure and temperature. This explains the behavior of dissolved gases in beverages and natural bodies of water.