Question

An hydrocarbon of relative molecular mass 70 was found to contain 85.7% carbon. Determine :
(a) The molecular formula
(b) The structural formula

Answer 1

Question

An hydrocarbon of relative molecular mass 70 was found to contain 85.7% carbon.

Determine :

(a) The molecular formula

(b) The structural formula

Solution

$\mathrm{M(C_xH_y)} = 70$

$\operatorname{Ar}(\mathrm{C}) = 12$

$\operatorname{Ar}(\mathrm{H}) = 1$

$12 \cdot x + 1 \cdot y = 70$

If carbon content is 85.7, hydrogen content is $(100 - 85.7) = 14.3$

$\mathrm{C_x / H_y = 85.7 / 14.3}$

$12 \cdot x / 1 \cdot y = 85.7 / 14.3$

Thus we have system of two equations with two unknown quantities:

$$\left\{ \begin{array}{l} 12 \cdot x + 1 \cdot y = 70 \\ 12 \cdot x / 1 \cdot y = 85.7 / 14.3, \end{array} \right.$$

Whence

$12 \cdot x \cdot 14.3 = 1 \cdot y \cdot 85.7,$

$171.6 \cdot x = 85.7 \cdot y,$

$y = 171.6 \cdot x / 85.7,$

$y = 2 \cdot x$

$12 \cdot x + 2 \cdot x = 70$

$14 \cdot x = 70$

$x = 5$

$y = 2 \cdot x = 10$

Answer

a) Molecular formula – $\mathrm{C}_{5} \mathrm{H}_{10}$

b) Ten structural isomers are possible: three linear, three branched and four cyclic.

So, ten versions of structural formula are possible: