Final answer:
To find the molar mass of an unknown gas, the mass difference of an evacuated flask before and after filling it with the gas was used. The Ideal Gas Law was applied after converting pressure to atm, volume to liters, and temperature to kelvins. Using these values, the molar mass was calculated to be 273.22 g/mol.
Step-by-step explanation:
The student asked how to calculate the molar mass of an unknown gas using the mass of an evacuated 250 ml flask before and after it is filled with the gas at a known pressure and temperature. To do this, we need to use the Ideal Gas Law which is PV = nRT, where P is pressure, V is volume, n is the number of moles, R is the ideal gas constant, and T is temperature in kelvins. First, we need to convert all measurements to the correct units: pressure in atm, volume in liters, and temperature in kelvins. We can find the number of moles of the gas using the difference in mass of the flask (1 g), and then use the Ideal Gas Law to solve for the molar mass.
To calculate the mass of the gas alone, we subtract the mass of the empty flask from the mass of the filled flask, which is 144.147 g - 143.147 g = 1.00 g of gas. Now, convert the pressure from torr to atm (263 torr / 760 torr/atm = 0.346 atm) and temperature from °C to K (25 °C + 273.15 = 298.15 K). The volume of the gas is given in milliliters and must be converted into liters (250 ml = 0.250 L).
Next, we plug these values into the Ideal Gas Law equation and solve for n:
PV = nRT(0.346 atm)(0.250 L) = n(0.0821 L·atm/K·mol)(298.15 K)
Now solve for n (the number of moles):
n = (0.346 atm × 0.250 L) / (0.0821 L.atm/K.mol × 298.15 K)n = 0.00366 mol
Finally, we can calculate the molar mass (MM) of the gas by dividing the mass of the gas by the number of moles:
MM = mass / nMM = 1.00 g / 0.00366 molMM = 273.22 g/molThis is the molar mass of the unknown gas.