Question

An acid of phosphorus has the following percentage composition; Phosphorus = 38.27%; hydrogen = 2.47%; oxygen = 59.26%. Find the empirical formula of the acid and its molecular formula, given that its relative molecular mass is 162.

Answer 1

Element	% age	At. wt.	Atomic ratio	Simplest ratio
P	38.27	31	${\displaystyle \frac{38.27}{31}}$ = 1.235	${\displaystyle \frac{1.235}{1.235}}$ = 1
H	2.47	1	${\displaystyle \frac{2.47}{1}}$ = 2.47	${\displaystyle \frac{2.47}{1.235}}$ = 2
O	59.26	16	${\displaystyle \frac{59.26}{16}}$ = 3.70	${\displaystyle \frac{3.70}{1.235}}$ = 3

∴ The empirical formula of the given acid = H₂PO₃

Molecular mass of given acid = 162

Empirical formula mass of the acid = 2 × 1 + 31 + 3 × 16

= 2 + 31 + 48

= 81

∴ n = ${\displaystyle \frac{\text{Molecular mass}}{\text{Empirical formula mass}}}$

= ${\displaystyle \frac{162}{81}}$

= 2

∴ The molecular formula of the acid = (H₂PO₃)_n

= (H₂PO₃)₂

= H₄P₂O₆