PROBLEM 102P

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?

Solution 102P

Here, we are going to identify if the gas used in the above problem is pure helium.

Step 1:

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

Step 2:

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.

Step 3:

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