A 10.0L tank at 0.89°C is filled with 13.2g of chlorine pentafluoride gas and 16.0g of sulfur tetrafluoride 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.chlorine pentafluoride mole fraction: partial pressure: atmsulfur tetrafluoride mole fraction: partial pressure: atm
Question
A 10.0L tank at 0.89°C is filled with 13.2g of chlorine pentafluoride gas and 16.0g of sulfur tetrafluoride 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.chlorine pentafluoride mole fraction: partial pressure: atmsulfur tetrafluoride mole fraction: partial pressure: atm
Solution
First, we need to calculate the number of moles of each gas.
The molar mass of chlorine pentafluoride (ClF5) is approximately 130.45 g/mol and the molar mass of sulfur tetrafluoride (SF4) is approximately 108.07 g/mol.
Number of moles of ClF5 = 13.2 g / 130.45 g/mol = 0.101 mol Number of moles of SF4 = 16.0 g / 108.07 g/mol = 0.148 mol
The total number of moles in the tank is the sum of the moles of ClF5 and SF4, which is 0.101 mol + 0.148 mol = 0.249 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 ClF5 = 0.101 mol / 0.249 mol = 0.4056 Mole fraction of SF4 = 0.148 mol / 0.249 mol = 0.5944
Next, we need to calculate the total pressure in the tank.
The ideal gas law is PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant, and T is the temperature in Kelvin.
First, convert the temperature from Celsius to Kelvin. T = 0.89°C + 273.15 = 274.04 K
Then, rearrange the ideal gas law to solve for P: P = nRT / V
We use R = 0.0821 L·atm/(K·mol), V = 10.0 L, n = 0.249 mol, and T = 274.04 K.
P = (0.249 mol * 0.0821 L·atm/(K·mol) * 274.04 K) / 10.0 L = 5.62 atm
The partial pressure of a gas is the mole fraction of that gas times the total pressure.
Partial pressure of ClF5 = 0.4056 * 5.62 atm = 2.28 atm Partial pressure of SF4 = 0.5944 * 5.62 atm = 3.34 atm
So, the mole fraction and partial pressure of chlorine pentafluoride are 0.406 and 2.28 atm, respectively, and the mole fraction and partial pressure of sulfur tetrafluoride are 0.594 and 3.34 atm, respectively.
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