Question

In a hydrocarbon, the mass % of C and H are 90% and 10% respectively. If 20 g of given hydrocarbon in vapor phase occupies a volume of 5.6 L at STP, then the molecular formula of the hydrocarbon is ?

Answer 1

STP (Standard Temperature and Pressure, 0°C and one atmosphere pressure)

T = 0 °C = 273 K

P = 1 atm

Ideal gas law:

$PV=n R T$

Molar gas constant

$R=0.082058 \frac{L\times atm}{K\times mol}$

$n = \frac{PV}{RT}$

$n = \frac{1 \times 5.6}{0.082058 \times 273} = 0.25 mol$

$M = \frac {m}{n}$

$M = \frac {20 }{ 0.25} = 80 \frac {g}{mol}$

$M(C_xH_y) = (12 \times x) + (1 \times y) = 80 \frac {g}{mol}$

Proportion:

12x – 90 %

1y – 10 %

$y = \frac {120x}{90} = 1.33x$

$12x + 1.33x = 80$

$13.33x = 80$

$x = \frac {80}{13.33} = 6$

$y = 1.33 \times6 = 8$

Answer: C₆H₈