Question

The Rate of diffusion of a saturated hydrocarbon (Cn H2n+2) gas is 1.206 times that ofSO2 gas under identical conditions. Find the molecular mass and the value of 'n' for the gas.

Answer 1

1. The molecular mass of the hydrocarbon is 44 g/mol
2. The value of n in the compound is 3

How to calculate the molecular mass of value of n?

1. The molecular mass of the hydrocarbon can be calculate as follow:

• Rate of
  `SO_2` gas (R₁) = R
• Rate of hydrocarbon (R₂) = 1.206R
• Molecular mass of
  `SO_2` gas (M₁) = 64 g/mol
• Molecular mass of hydrocarbon (M₂) = ?

`(R_1)/(R_2) = \sqrt{(M_2)/(M_1)} \\\\(R)/(1.206R) = \sqrt{(M_2)/(64)}\\\\(1)/(1.206) = \sqrt{(M_2)/(64)}\\\\((1)/(1.206))^(2) = (M_2)/(64)\\\\M_2 = 64\ *\ ((1)/(1.206))^(2) \\\\M_2 = 44\ g/mol`

2. The value of n can be calculated as shown below:

• Molecular mass of hydrocarbon = 44 g/mol
• Formula of compound =
  `C_nH_(2n+2)`
• Value of n =?

Formula = molecular mass

`C_nH_(2n+2)` = 44

(12 × n) + (2n + 2) = 44

12n + 2n + 2 = 44

14n = 44 - 2

14n = 42

n = 42 / 14

n = 3