Question

The density of an unknown gas at 98°C and 740 mmHg is 2.50 g/L. What is the molar mass of the gas with work showed?

Answer 1

Answer:

78.2 g/mol  

Step-by-step explanation:

We can use the Ideal Gas Law to solve this problem:

       pV = nRT

Since n = m/M, the equation becomes

      pV = (m/M)RT     Multiply each side by M

   pVM = mRT               Divide each side by pV

        M = (mRT)/(pV)

Data:

ρ = 2.50 g/L

R = 0.082 16 L·atm·K⁻¹mol⁻¹

T =98 °C

p = 740 mmHg

Calculation:

(a) Convert temperature to kelvins

T = (98 + 273.15) = 371.15 K

(b) Convert pressure to atmospheres

p = 740 × 1/760 =0.9737 atm

(c) Calculate the molar mass

Assume V = 1 L.

   Then m = 2.50 g

            M = (2.50 × 0.082 06 × 371.15)/(0.9737 × 1)

                = 76.14/0.9737

                = 78.2 g/mol