A 8.00L tank at 21.3°C is filled with 4.97g of sulfur tetrafluoride gas and 7.33g of dinitrogen difluoride gas. You can assume both gases behave as ideal gases under these conditions.Calculate the mole fraction and partial pressure of each gas in the tank. Be sure your answers have the correct number of significant digits.sulfur tetrafluoride mole fraction: partial pressure: atmdinitrogen difluoride mole fraction: partial pressure: atm
Question
A 8.00L tank at 21.3°C is filled with 4.97g of sulfur tetrafluoride gas and 7.33g of dinitrogen difluoride gas. You can assume both gases behave as ideal gases under these conditions.Calculate the mole fraction and partial pressure of each gas in the tank. Be sure your answers have the correct number of significant digits.sulfur tetrafluoride mole fraction: partial pressure: atmdinitrogen difluoride mole fraction: partial pressure: atm
Solution
First, we need to calculate the number of moles of each gas.
The molar mass of sulfur tetrafluoride (SF4) is approximately 108 g/mol and the molar mass of dinitrogen difluoride (N2F2) is approximately 66 g/mol.
Number of moles of SF4 = 4.97 g / 108 g/mol = 0.0460 mol Number of moles of N2F2 = 7.33 g / 66 g/mol = 0.111 mol
The total number of moles = 0.0460 mol + 0.111 mol = 0.157 mol
The mole fraction is the number of moles of a component divided by the total number of moles of all components.
Mole fraction of SF4 = 0.0460 mol / 0.157 mol = 0.293 Mole fraction of N2F2 = 0.111 mol / 0.157 mol = 0.707
Next, we calculate the total pressure using the ideal gas law, PV = nRT. We know the volume (V) is 8.00 L, the number of moles (n) is 0.157 mol, and the temperature (T) is 21.3°C = 294.45 K. The ideal gas constant (R) is 0.0821 L·atm/(K·mol).
Total pressure (P) = nRT / V = (0.157 mol * 0.0821 L·atm/(K·mol) * 294.45 K) / 8.00 L = 0.478 atm
The partial pressure of a gas is the mole fraction of that gas times the total pressure.
Partial pressure of SF4 = 0.293 * 0.478 atm = 0.140 atm Partial pressure of N2F2 = 0.707 * 0.478 atm = 0.338 atm
So, the mole fraction and partial pressure of sulfur tetrafluoride are 0.293 and 0.140 atm, respectively, and the mole fraction and partial pressure of dinitrogen difluoride are 0.707 and 0.338 atm, respectively.
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