Question

The density of a gaseous chlorofluorocarbon (CFC) at 23.8 °C and 432 mmHg is 3.23 g/L. What is its molar mass?

Answer 1

Answer:

138.57 g/mol.

Explanation:

The following data were obtained from the question:

Temperature (T) = 23.8 °C

Pressure = 432 mmHg

Density (D) = 3.23 g/L

Next, we shall obtain an expression for the density in relation to molar mass, pressure and temperature.

This can be obtained by using the ideal gas equation as shown below:

PV = nRT.... (1)

Recall:

Mole (n) = maas(m) /Molar mass (M)

n = m/M

Substituting the value of n into equation 1

PV = nRT

PV = mRT/M

Divide both side by P

V = mRT/MP

Divide both side by m

V/m = RT/MP

Invert the above equation

m/V = MP /RT..... (2)

Recall:

Density (D) = mass(m) /volume (V)

D = m/V

Replace m/V with D in equation 2

m/V = MP /RT

D = MP /RT

Thus, with the above formula we can obtain the molar mass of chlorofluorocarbon (CFC) as shown below:

Temperature (T) = 23.8 °C = 23.8 °C + 273 = 296.8 K

Pressure = 432 mmHg = 432/760 = 0.568 atm

Density (D) = 3.23 g/L

Gas constant (R) = 0.0821 atm.L/Kmol

Molar mass (M) =..?

D = MP /RT

3.23 = M x 0.568 / 0.0821 x 296.8

Cross multiply

M x 0.568 = 3.23 x 0.0821 x 296.8

Divide both side by 0.568

M = (3.23 x 0.0821 x 296.8) / 0.568

M = 138.57 g/mol

Therefore the molar mass of CFC is 138.57 g/mol.