Question

A sealed container holds gaseous oxygen and liquid water. Which of the following would increase the amount of oxygen dissolved in the water? A. expanding the size of the container B. adding an inert gas to the container C. decreasing the temperature of the container. D. shaking the container

Short answer

C. Decreasing the temperature of the container.

Step-by-step solution

- Understanding the Problem

The task is to determine which action would increase the amount of oxygen dissolved in the liquid water within a sealed container that also holds gaseous oxygen.

- Analyze Each Option

Consider how each given option affects the solubility of oxygen in water. Use principles of chemistry and solubility to evaluate each option.

- Expand the Size of the Container

Option A suggests expanding the size of the container. Increasing the volume of the container reduces the pressure of the gas according to Boyle's Law, which could decrease the solubility of oxygen in the water. Therefore, this option is unlikely to increase the dissolved oxygen.

- Adding an Inert Gas

Option B suggests adding an inert gas to the container. Adding an inert gas will not change the partial pressure of oxygen but will increase the total pressure within the container. This does not directly affect the solubility of oxygen in water significantly.

- Decreasing Temperature

Option C suggests decreasing the temperature of the container. Henry's Law states that gas solubility in liquids increases as the temperature decreases. Therefore, lowering the temperature should increase the amount of oxygen dissolved in the water.

- Shaking the Container

Option D suggests shaking the container. Shaking might distribute the oxygen in water more rapidly but does not necessarily increase long-term solubility. It can sometimes even decrease gas solubility by allowing the gas to escape.

- Conclusion

From the analysis, the most viable option to increase the solubility of oxygen in water is decreasing the temperature. The other options either have minimal impact or could reduce the amount of oxygen dissolved in the water.

Key concepts

Henry's Law

Henry's Law is crucial in understanding how gases dissolve in liquids. It states that at a constant temperature, the amount of gas that dissolves in a liquid is directly proportional to the partial pressure of the gas above the liquid. Mathematically, it is represented as:
Henry's Law: \(C = k_H \times P\)
where:

• \(C\): concentration of the dissolved gas (in mol/L or similar units)
• \(k_H\): Henry's Law constant, specific to each gas-liquid pair (units vary)
• \(P\): partial pressure of the gas above the liquid (in atm or similar units)
  If the partial pressure of the gas increases, more gas will dissolve in the liquid. This is why in fizzy drinks, carbon dioxide is present under high pressure to keep it dissolved in the beverage.
  Applying Henry's Law to our problem ensures we understand how changes in partial pressure can affect the solubility of oxygen in water. However, this also depends on other factors like temperature.

Temperature Effect on Solubility

Temperature plays a significant role in gas solubility. Generally, the solubility of gases in liquids decreases as temperature increases. This inverse relationship can be explained through the kinetic theory of gases:

• Higher temperatures provide gas molecules with more energy, allowing them to escape from the liquid phase more easily.
• Conversely, lowering the temperature reduces molecular movement, making it easier for gases to stay dissolved.

In our exercise, we identified that decreasing the temperature of the container would increase the amount of oxygen dissolved in the water. This principle is directly supported by Henry's Law.
Practical examples include:
• Cold soda retains its fizz longer due to higher gas solubility at lower temperatures.
• Marine life thrives better in colder waters where oxygen levels are higher.

Boyle's Law

Boyle's Law is essential in understanding the behavior of gases under pressure changes. It states that the pressure of a given amount of gas held at constant temperature is inversely proportional to the volume of the gas. The Law is expressed as:
Boyle's Law: \(P_1 V_1 = P_2 V_2\)
where:

• \(P_1\): initial pressure
• \(V_1\): initial volume
• \(P_2\) and \(V_2\): pressure and volume after a change
  In the context of our problem, expanding the size of the container (Option A) would decrease the pressure of the gas. According to Boyle's Law, this expansion causes a decrease in gas pressure, which could lead to a lower solubility of oxygen in water. Hence, we can exclude this option as a means to increase dissolved oxygen.

Partial Pressure

Partial pressure refers to the pressure exerted by a single type of gas in a mixture of gases. It is a part of the total pressure exerted by the gas mixture. The partial pressure of gas is critical in determining its solubility in liquids through Henry's Law.
In our problem, adding an inert gas (Option B) increases the total pressure in the container but does not change the partial pressure of oxygen. Since the solubility of oxygen depends on its partial pressure, adding an inert gas will not significantly impact the dissolved oxygen levels.
Practical instances include:

• Scuba divers using gas mixtures with controlled partial pressures to avoid conditions like nitrogen narcosis.
• In medical respiratory treatments, controlling oxygen partial pressure ensures effective patient oxygenation.