You are given a sample of 1 mole of argon, 2 moles of xenon, and 3 moles of radon. At a total pressure of 400 kPa, what are the partial pressures of the gases?

a. Argon: 50 kPa, Xenon: 100 kPa, Radon: 150 kPa
b. Argon: 100 kPa, Xenon: 150 kPa, Radon: 200 kPa
c. Argon: 150 kPa, Xenon: 200 kPa, Radon: 250 kPa
d. Argon: 200 kPa, Xenon: 250 kPa, Radon: 300 kPa

To determine the partial pressures of each gas, we use Dalton's law of partial pressures, which states that the total pressure exerted by a mixture of gases is equal to the sum of the partial pressures of each individual gas. First, we find the mole fractions of each gas by dividing the moles of each gas by the total moles (1 + 2 + 3 = 6 moles). The mole fraction for argon is 1/6, for xenon is 2/6 or 1/3, and for radon is 3/6 or 1/2. Then, we multiply each mole fraction by the total pressure of 400 kPa to find the partial pressures. For argon: (1/6) * 400 kPa = 66.67 kPa, for xenon: (1/3) * 400 kPa = 133.33 kPa, and for radon: (1/2) * 400 kPa = 200 kPa.

This calculation demonstrates how Dalton's law can be applied to determine the partial pressures of gases in a mixture based on their respective mole fractions.

The mole fractions represent the proportion of each gas in the mixture, and multiplying them by the total pressure gives the partial pressure of each gas. Hence, option c) provides the correct partial pressures for argon, xenon, and radon in the given mixture, as calculated.(option c)