Question

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 $P _2 Q$.

Answer 1

Answer: (B), (C)

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 $\frac{40}{ M _{ p }}: \frac{60}{ M _{ Q }}=3: 2$
$\frac{2 M _{ Q }}{3 M _{ p }}=\frac{3}{2} \Rightarrow 9 M _{ p }=4 M _{ Q }$
If $M _{ P }=20 \Rightarrow M _{ Q }=\frac{9 \times 20}{4}=45$
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