Question

Find the molar mass of unknown gas which diffuses (a) twice as fast as HI (b) 0.771 times as fast as F2 (c) 1.10 times as fast as H2S

Answer 1

We know the formula,

  r1/r2 = √(M2/M1)

  Where, r1 = rate of diffusion of gas with molar mass M1.

        r2 = rate of diffusion of gas with molar mass M2.

a) 

   Taking, M1 = molar mass of HI

             = 129 g/mol

   Molar mass of unknown gas = M2 g/mol

Given,

   the gas diffuses twice as fast as HI

So, 

 diffusion rate of HI, r1 ×2 = diffusion rate of unknown gas, r2

 Or, r1×2 = r2

 Or, r1/r2 = (1/2)

  

     r1/r2 = √(M2/M1)

  Or, (1/2) = √(M2/129)

  Or, 1/4 = M2/129

  Or, M2 = 129/4

        = 32.25 g/mol

So, molar mass of the unknown gas = 32.25 g/mol

b)

 Taking, M1' = molar mass of F2

              = 38 g/mol

  Molar mass of unknown gas = M2' g/mol Given,

  the gas diffuses 0.771 times faster than F2

 So, 

 diffusion rate of HI, r1 ×0.771= diffusion rate of unknown gas, r2

        Or, r1×0.771 = r2

        Or, r1/r2 = (1/0.771)

         

     r1/r2 = √(M2/M1)

       Or, (1/0.771) = √(M2/38)

       Or, 1/(0.771)² = M2/38

       Or, M2 =38/ 0.594

             = 63.97 g/mol

 So, molar mass of the unknown gas = 63.97 g/mol

C)

Taking, M1 = molar mass of H2S

             = 34 g/mol

Molar mass of unknown gas = M2 g/mol

 Given,

the gas diffuses twice as fast as H2S

 So, 

 diffusion rate of H2S, r1 ×1.10 = diffusion rate of unknown gas, r2

      Or, r1×2 = r2

      Or, r1/r2 = (1/2)

     r1/r2 = √(M2/M1)

       Or, (1/1.10) = √(M2/34)

       Or, 1/1.21= M2/34

       Or, M2 = 34/1.21

              = 28.1 g/mol

So, molar mass of the unknown gas = 28.1 g/mol