To check the principle of multiple proportions, a series of pure … - Vidyadip

MCQ

To check the principle of multiple proportions, a series of pure binary compounds $\left(P_m Q_n\right)$ were analyzed and their composition is tabulated below. The correct option($s$) is(are)

Compound	Weight $\%$ of $P$	Weight $\%$ of $Q$
$1$	$50$	$50$
$2$	$44.4$	$55.6$
$3$	$40$	$60$

$(A)$ If empirical formula of compound $3$ is $P_3 Q_4$, then the empirical formula of compound $2$ is $P_3 Q_5$.

$(B)$ If empirical formula of compound $3$ is $P _3 Q _2$ and atomic weight of element $P$ is $20$ , then the atomic weight of $Q$ is $45$ .

$(C)$ If empirical formula of compound $2$ is $PQ$, then the empirical formula of the compound $1$ is $P _5 Q _4$.

$(D)$ If atomic weight of $P$ and $Q$ are $70$ and $35$ , respectively, then the empirical formula of compound $1$ is $P _2 Q$.

A
$A,B$
B
$A,C$
C
$A,D$
✓
$B,C$

✓

Answer

Correct option: D.

$B,C$

d

Compound	Weight $\%$ of $P$	Weight $\%$ of $Q$
$1$	$50$	$50$
$2$	$44.4$	$55.6$
$3$	$40$	$60$

For option $(A)$

Let atomic mass of $P$ be $M _p$ and atomic mass of $Q$ be $M_Q$ Molar ratio of atoms $P$ : $Q$ in compound $3$ is

$\frac{40}{M_p}: \frac{60}{M_Q}=3: 4$

$\frac{2 M_Q}{3 M_p}=\frac{3}{4} \Rightarrow 9 M_p=8 M_Q$

Molar ratio of atoms $P$ : $Q$ in compound $2$ is

$\frac{44.4}{ M _{ p }}: \frac{55.6}{ M _Q}$

$=44.4 M _{ Q }: 55.6 M _{ P }$

$=44.4 M _{ Q }: 55.6 \times \frac{8 M _Q}{9}$

$=44.4: 55.6 \times \frac{8}{9}$

$=9: 10$

$\Rightarrow$ Empirical formula of compound $2$ is therefore $P _9 Q _{10}$ Option ($A$) in incorrect

For option $(B)$

Molar Ratio of atoms $P : Q$ in compound $3$ is $\frac{40}{ M _{ P }}: \frac{60}{ M _Q}=3: 2$

$\frac{2 M_Q}{3 M_p}=\frac{3}{2} \Rightarrow 9 M_p=4 M_Q$

$\text { If } M_P=20 \quad \Rightarrow M_Q=\frac{9 \times 20}{4}=45$

Option $(B)$ is correct

For option $(C)$

Molar ratio of atoms $P$ : $Q$ in compound $2$ is

$\frac{44.4}{ M _{ p }}: \frac{55.6}{ M _{ Q }}=44.4 M _{ Q }: 55.6 M _{ p }=1: 1$

$\Rightarrow \frac{ M _{ p }}{ M _{ Q }}=\frac{44.4}{55.6}$

Molar ratio of atoms $P$ : $Q$ in compound $1$ is

$\frac{50}{M_p} : \frac{50}{M_Q}=M_Q: M_p$

$=55.6: 44.4$

$\simeq 5: 4$

Hence, empirical formula of compound $1$ is $P _5 Q _4$

Hence, option $(C)$ is correct

For option $(D)$

Molar ratio of atoms $P$ : $Q$ in compound $1$ is

$\frac{50}{ M _{ p }}: \frac{50}{ M _Q} = M _{ Q }: M _{ p }$

$=35: 70=1: 2$

Hence, empirical formula of compound $1$ is $PQ _2$ Hence, option $(D)$ is incorrect

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