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Answer :
Final answer:
Using Dalton's Law of partial pressures, the partial pressures for gases X, Y, and Z in a mixture are calculated based on the mole fraction of each gas. After calculations, the correct partial pressures are found to be d) 489.6 torr for X, 100.8 torr for Y, and 22.4 torr for Z.
Explanation:
To find the partial pressures of the gases X, Y, and Z when they are in a mixture, we use Dalton's Law of partial pressures. This law states that the total pressure of a mixture of gases is equal to the sum of the partial pressures of the individual gases. The partial pressure of each gas is proportional to the number of moles of that gas present in the mixture.
To calculate the partial pressures, we first find the total number of moles of gases in the mixture:
Number of moles of X = 1.6 mol
Number of moles of Y = 0.39 mol
Number of moles of Z = 0.089 mol
Total number of moles = 1.6 mol + 0.39 mol + 0.089 mol = 2.079 mol
Next, we calculate the mole fraction for each gas by dividing the number of moles of that gas by the total number of moles:
Mole fraction of X = 1.6 mol / 2.079 mol
Mole fraction of Y = 0.39 mol / 2.079 mol
Mole fraction of Z = 0.089 mol / 2.079 mol
Then, we multiply each mole fraction by the total pressure to find the partial pressure of each gas:
Partial pressure of X = Mole fraction of X × Total pressure
Partial pressure of Y = Mole fraction of Y × Total pressure
Partial pressure of Z = Mole fraction of Z × Total pressure
After performing these calculations, we find that the correct partial pressures for the gases in torr are:
Partial pressure of X = 489.6 torr
Partial pressure of Y = 100.8 torr
Partial pressure of Z = 22.4 torr
Thus, the correct answer is (d) 489.6 torr, 100.8 torr, 22.4 torr.
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