The presence of the radioactive gas radon (Rn) in well water presents a possible health hazard in parts of the United States. (a) Assuming that the solubility of radon in water with 1 atm pressure of the gas over the water at 30 °C is 7.27⨉10^-3 M, what is the Henry's law constant for radon in water at this temperature?

Verified step by step guidance

1. Identify the formula for Henry's Law, which is given by: \( C = k_H \cdot P \), where \( C \) is the concentration of the gas in the solution, \( k_H \) is the Henry's law constant, and \( P \) is the partial pressure of the gas.
2. Recognize that the problem provides the solubility of radon in water as \( 7.27 \times 10^{-3} \) M, which represents \( C \), and the pressure of radon over the water as 1 atm, which represents \( P \).
3. Substitute the given values into the Henry's Law equation: \( 7.27 \times 10^{-3} = k_H \cdot 1 \).
4. Solve for \( k_H \) by dividing both sides of the equation by the pressure (1 atm): \( k_H = \frac{7.27 \times 10^{-3}}{1} \).
5. Conclude that the Henry's law constant \( k_H \) for radon in water at 30 °C is equal to the solubility value, since the pressure is 1 atm.

Key Concepts

Henry's Law

Henry's Law states that the amount of gas that dissolves in a liquid at a given temperature is directly proportional to the partial pressure of that gas above the liquid. This relationship can be expressed mathematically as C = kH * P, where C is the concentration of the gas in the liquid, kH is the Henry's law constant, and P is the partial pressure of the gas.

Solubility

Solubility refers to the maximum amount of a substance that can dissolve in a solvent at a specific temperature and pressure. In the context of gases, solubility is influenced by factors such as temperature and pressure, with higher pressures generally increasing the solubility of gases in liquids.

Units of Henry's Law Constant

The Henry's law constant (kH) can be expressed in various units, depending on the context. Commonly, it is given in mol/(L·atm) or M/atm, indicating the concentration of the gas in moles per liter per unit of pressure in atmospheres. Understanding the units is crucial for correctly applying Henry's Law to calculate gas solubility.