A 118-mL flask is evacuated, and its mass is measured as 97.129 g. When the flask is filled with 768 torr of helium gas at 35 °C, it is found to have a mass of 97.171 g. Is the gas pure helium?
Here, we are going to identify if the gas used in the above problem is pure helium.
From ideal gas equation, we have,
pV = nRT ----(1)
Where, p = pressure
V = volume of the gas
n = number of moles of the gas
R = universal gas constant and its value is 0.0821 L atm K-1 mol-1
T = temperature
Given, volume of the flask(V) = 118 mL = 118/1000 L = 0.118 L
Pressure(p) = 768 torr = 768 x 0.00131579 atm = 1.01 atm
Temperature(T) = 35 oC = 35 + 273 K = 308 K
Substituting the values in equation (1), we get,
n = pV / RT
n = (1.01 atm x 0.118 L) / (308 K x 0.0821 L atm K-1 mol-1)
= (0.11918 L atm) / (25.2868 L atm mol-1)
n = 0.0047 mol.
Now, 1 mol of He gas = molar mass of helium gas
0.0047 mol of He gas = 0.0047 x molar mass of He gas
= 0.0047 mol x 4.003 g/mol
= 0.019 g