The presence of the radioactive gas radon (Rn) in well water presents a possible health hazard in parts of the United States. (b) A sample consisting of various gases contains 3.5 × 10^-6 mole fraction of radon. This gas at a total pressure of 32 atm is shaken with water at 30 °C. Calculate the molar concentration of radon in the water.

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1. Identify the given information: the mole fraction of radon in the gas mixture is 3.5 × 10^{-6}, the total pressure of the gas is 32 atm, and the temperature is 30 °C.
2. Use Henry's Law to relate the concentration of a gas in a liquid to its partial pressure above the liquid. Henry's Law is given by: C = k_H * P, where C is the concentration of the gas in the liquid, k_H is Henry's Law constant for the gas at a specific temperature, and P is the partial pressure of the gas.
3. Calculate the partial pressure of radon using its mole fraction and the total pressure: P_{Rn} = (mole fraction of Rn) * (total pressure) = 3.5 × 10^{-6} * 32 atm.
4. Find the value of Henry's Law constant (k_H) for radon at 30 °C from a reliable source or table, as it is specific to each gas and temperature.
5. Substitute the values of k_H and P_{Rn} into Henry's Law equation to find the molar concentration of radon in the water: C = k_H * P_{Rn}.