According to henry's law the solubility of a gas in a liquid

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according to henry’s law the solubility of a gas in a liquid

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LectureNotes said according to Henry’s law the solubility of a gas in a liquid…

Answer: According to Henry’s Law, the solubility of a gas in a liquid is directly proportional to the partial pressure of that gas above the liquid. This relationship can be mathematically expressed as:

C = k_H \cdot P

where:

  • ( C ) is the concentration of the gas in the liquid (solubility).
  • ( k_H ) is Henry’s law constant, which is specific to the gas-liquid pair and temperature.
  • ( P ) is the partial pressure of the gas above the liquid.

Key Points:

  1. Direct Proportionality: The higher the partial pressure of the gas, the greater its solubility in the liquid. Conversely, if the partial pressure decreases, the solubility also decreases.

  2. Henry’s Law Constant: This constant (( k_H )) varies depending on the type of gas, the solvent, and the temperature. For example, carbon dioxide has a different ( k_H ) value in water than oxygen does.

  3. Temperature Dependence: The solubility of gases typically decreases with an increase in temperature. This is because gases tend to escape from the liquid phase into the vapor phase at higher temperatures.

Applications of Henry’s Law:

  1. Carbonated Beverages: The fizz in carbonated drinks is due to carbon dioxide dissolved in the liquid under high pressure. When the bottle is opened, the pressure is released, and the gas escapes, forming bubbles.

  2. Scuba Diving: Divers must be cautious of the solubility of gases like nitrogen in their blood. At higher pressures underwater, more nitrogen dissolves in the blood. Rapid ascent can cause the nitrogen to come out of solution quickly, leading to decompression sickness (the bends).

  3. Environmental Science: Henry’s Law helps in understanding how pollutants like carbon dioxide and sulfur dioxide dissolve in water bodies, influencing aquatic life and water chemistry.

Example Problem:

Question: If the partial pressure of oxygen above water is 0.21 atm at 25°C, and the Henry’s law constant for oxygen in water at this temperature is 1.3 \times 10^{-3} \text{mol/(L·atm)} , what is the solubility of oxygen in water?

Solution:

Given:

  • P = 0.21 \text{ atm}
  • k_H = 1.3 \times 10^{-3} \text{ mol/(L·atm)}

Using Henry’s Law:

C = k_H \cdot P

Substitute the values:

C = (1.3 \times 10^{-3} \text{ mol/(L·atm)}) \times (0.21 \text{ atm})

Calculate:

C = 2.73 \times 10^{-4} \text{ mol/L}

Therefore, the solubility of oxygen in water at 25°C and a partial pressure of 0.21 atm is 2.73 \times 10^{-4} \text{ mol/L}.

This comprehensive explanation of Henry’s Law provides a clear understanding of the relationship between gas solubility and pressure, along with practical examples and a solved problem for better grasping the concept.

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LectureNotes said according to Henry’s law the solubility of a gas in a liquid…

Answer: According to Henry’s Law, the solubility of a gas in a liquid is directly proportional to the partial pressure of that gas above the liquid. This relationship can be mathematically expressed as:

C = k_H \cdot P

where:

  • ( C ) is the concentration of the gas in the liquid (solubility).
  • ( k_H ) is Henry’s law constant, which is specific to the gas-liquid pair and temperature.
  • ( P ) is the partial pressure of the gas above the liquid.

Explanation:

  1. Direct Proportionality: Henry’s Law states that if you increase the partial pressure of a gas above a liquid, the amount of gas that dissolves in the liquid also increases. Conversely, if the partial pressure decreases, the solubility of the gas in the liquid decreases. This is because the gas molecules are in dynamic equilibrium between the gas phase and the liquid phase.

  2. Henry’s Law Constant: The constant ( k_H ) varies for different gases and solvents and is also dependent on temperature. This constant essentially tells us how easily a gas dissolves in a liquid at a given temperature and pressure. For example, carbon dioxide has a different ( k_H ) value in water than oxygen does, meaning they have different solubilities under the same conditions.

  3. Temperature Dependence: The solubility of gases typically decreases with an increase in temperature. This is because higher temperatures provide more kinetic energy to the gas molecules, making them more likely to escape from the liquid phase into the vapor phase.

Applications of Henry’s Law:

  1. Carbonated Beverages: In carbonated drinks, carbon dioxide is dissolved in the liquid under high pressure. When the bottle is opened, the pressure is reduced, causing the gas to escape and form bubbles.

  2. Scuba Diving: Divers must be aware of the solubility of gases like nitrogen in their blood. At higher pressures underwater, more nitrogen dissolves in the blood. Rapid ascent can cause the nitrogen to come out of solution quickly, leading to decompression sickness (the bends).

  3. Environmental Science: Henry’s Law helps in understanding how pollutants like carbon dioxide and sulfur dioxide dissolve in water bodies, affecting aquatic life and water chemistry.

Example Problem:

Question: If the partial pressure of oxygen above water is 0.21 atm at 25°C, and the Henry’s law constant for oxygen in water at this temperature is 1.3 \times 10^{-3} \text{mol/(L·atm)}, what is the solubility of oxygen in water?

Solution:

Given:

  • ( P = 0.21 \text{ atm} )
  • ( k_H = 1.3 \times 10^{-3} \text{ mol/(L·atm)} )

Using Henry’s Law:

C = k_H \cdot P

Substitute the values:

C = (1.3 \times 10^{-3} \text{ mol/(L·atm)}) \times (0.21 \text{ atm})

Calculate:

C = 2.73 \times 10^{-4} \text{ mol/L}

Therefore, the solubility of oxygen in water at 25°C and a partial pressure of 0.21 atm is ( 2.73 \times 10^{-4} \text{ mol/L} ).

This detailed explanation of Henry’s Law clarifies the relationship between gas solubility and pressure, providing practical examples and a solved problem to aid in understanding the concept fully.