Question

Carbon combines with oxygen to form three oxides, $C{O}_2$ , $CO$, $C_3{O}_2$. Among which pair of oxides is the law of multiple proportions invalid?

• A. $C{O}_2$ & $CO$
• B. $CO$ & $C_3{O}_2$
• C. $C{O}_2$ & $C_3{O}_2$
• D. It is valid in all cases

Answer 1

The correct option is D It is valid in all cases

According to the law of multiple proportions, when two elements combine to form two or more compounds then the mass of one element that combines with a fixed mass of the other is in ratio of small whole numbers.
Like here in this que,
$C$ + $O_2$ $\to$ $C{O}_2$..........$\left(1\right)$

$C$ + $\frac{1}{2}{O}_2$ $\to$ $CO$..........$\left(2\right)$

$C$ + $\frac{1}{3}{O}_2$ $\to$ $\frac{1}{3}{C}_3{O}_2$..........$\left(3\right)$

It is clearly visible 1 mole of carbon i.e. $12$ gm reacts with different amounts of oxygen in three cases.

Checking options :
$\left(a\right)$ $12$ gm of carbon reacts with $32$ gm of oxygen to form $C{O}_2$ and $16$ gm of oxygen to forms $CO$.
$\therefore$ ratio of masses of oxygen is
$32:16$ = $2:1$
Thus, the law of multiple proportions holds true.
$\left(b\right)$ $12$ gm of carbon reacts with $16$ gm of oxygen to forms $CO$ and $\frac{32}{3}$ gm of oxygen to forms $C_3{O}_2$.
$\therefore$ ratio of masses of oxygen is
$16$ : $\frac{32}{3}$ = $48:32$ = $3:2$
​​​​​​​Thus, the law of multiple proportions holds true.
$\left(c\right)$ $12$ gm of carbon reacts with $32$ gm of oxygen to forms $C{O}_2$ and $\frac{32}{3}$ gm of oxygen to forms $C_3{O}_2$.
$\therefore$ ratio of masses of Oxygen is
$32$ : $\frac{32}{3}$ = $3:1$
​​​​​​​​​​​​​​Thus, the law of multiple proportions holds true.
$\left(d\right)$ the law is valid in all cases.