A 8.00L tank at 0.84°C is filled with 8.83g of dinitrogen monoxide gas and 17.0g of chlorine pentafluoride 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.dinitrogen monoxide mole fraction: partial pressure: atmchlorine pentafluoride mole fraction: partial pressure: atm
Question
A 8.00L tank at 0.84°C is filled with 8.83g of dinitrogen monoxide gas and 17.0g of chlorine pentafluoride 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.dinitrogen monoxide mole fraction: partial pressure: atmchlorine pentafluoride mole fraction: partial pressure: atm
Solution
First, we need to calculate the number of moles of each gas.
The molar mass of dinitrogen monoxide (N2O) is approximately 44.01 g/mol and the molar mass of chlorine pentafluoride (ClF5) is approximately 90.45 g/mol.
Number of moles of N2O = 8.83 g / 44.01 g/mol = 0.2005 mol Number of moles of ClF5 = 17.0 g / 90.45 g/mol = 0.1879 mol
The total number of moles in the tank is the sum of the moles of each gas: Total moles = 0.2005 mol + 0.1879 mol = 0.3884 mol
The mole fraction of a gas is the number of moles of that gas divided by the total number of moles of all gases.
Mole fraction of N2O = 0.2005 mol / 0.3884 mol = 0.5163 Mole fraction of ClF5 = 0.1879 mol / 0.3884 mol = 0.4837
Next, we calculate the total pressure in the tank using the ideal gas law, PV = nRT. We know the volume (V) is 8.00 L, the number of moles (n) is 0.3884 mol, and the temperature (T) is 0.84°C, which is 273.84 K in Kelvin. The gas constant (R) is 0.0821 L·atm/(K·mol) when the pressure is in atmospheres.
Total pressure = nRT / V = (0.3884 mol * 0.0821 L·atm/(K·mol) * 273.84 K) / 8.00 L = 1.11 atm
The partial pressure of a gas is the mole fraction of that gas times the total pressure.
Partial pressure of N2O = 0.5163 * 1.11 atm = 0.573 atm Partial pressure of ClF5 = 0.4837 * 1.11 atm = 0.537 atm
So, the mole fraction and partial pressure of each gas in the tank are:
Dinitrogen monoxide: Mole fraction: 0.516 Partial pressure: 0.573 atm
Chlorine pentafluoride: Mole fraction: 0.484 Partial pressure: 0.537 atm
Note: The answers are rounded to the correct number of significant digits.
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