Question

A hydrocarbon contains 10.5g of carbon per gram of hydrogen. 1 litre of the vapour of the hydrocarbon at 127°C and 1 atmosphere pressure weighs 2.8g. Find the molecular formula.

Answer 1

Answer : The molecular formula of the hydrocarbon is, $C_7H_8$

Explanation :

First we have to calculate the molecular weight of hydrocarbon.

$PV=nRT\\\\PV=\frac{w}{M}RT$

where,

P = pressure of hydrocarbon = 1 atm

V = volume of hydrocarbon = 1 L

n = number of moles

w = mass of hydrocarbon = 2.8 g

M = molecular weight of hydrocarbon = ?

R = gas constant = 0.0821 L.atm/mole.K

T = temperature of hydrocarbon = $127^oC=273+127=400K$

Now put all the given values in the above formula, we get the molecular weight of hydrocarbon.

$1atm\times 1L=\frac{2.8g}{M}\times 0.0821L.atm/mole.K\times 400K$

$M=91.95g/mole\approx 92g/mole$

Now we have to calculate the molecular formula of the hydrocarbon.

Let the molecular formula represented as, $C_xH_y$

According to the question,

$\frac{12x}{y}=10.5$   ........(1)

$12x+y=92$     .........(2)

By solving the equation 1 and 2, we get the value of 'x' and 'y'.

y = 8

x = 7

Therefore, the molecular formula of hydrocarbon is, $C_7H_8$