QJEEAdv22Chd9d7: JEE Advanced 2022 Chemistry - Class 11 JEEAdv22Chd9d7 Solution: To check the principle of multiple proportions, a series of…

Question

Verified Solution • 2025–26 Session moderate

To check the principle of multiple proportions, a series of pure binary compounds

\left(\mathrm{P}_{\mathrm{m}} \mathrm{Q}_{\mathrm{n}}\right)

were analyzed and their composition is tabulated below. The correct option(s) is(are)

A If empirical formula of compound 3 is $P_{3} Q_{4}$ , then the empirical formula of compound 2 is $\mathrm{P}_{3} \mathrm{Q}_{5}$ .
B If empirical formula of compound 3 is $\mathrm{P}_{3} \mathrm{Q}_{2}$ and atomic weight of element $\mathrm{P}$ is 20 , then the atomic weight of $\mathrm{Q}$ is 45 .
C If empirical formula of compound 2 is $P Q$ , then the empirical formula of the compound $\mathbf{1}$ is $\mathrm{P}_{5} \mathrm{Q}_{4}$ .
D If atomic weight of $\mathrm{P}$ and $\mathrm{Q}$ are 70 and 35 , respectively, then the empirical formula of compound $\mathbf{1}$ is $\mathrm{P}_{2} \mathrm{Q}$ .

Accepted Answer

(A) If emperical formula of compound 3 is

P_3 Q_4

then its molar ratio will be

\frac{40}{3} : \frac{60}{4}

=\frac{40}{3} \times \frac{4}{60}=\frac{16}{18}=0.88

If empirical formula of compound 2 is

\mathrm{P}_3 \mathrm{Q}_5

, then its molar ratio

\begin{aligned}&amp; =\frac{44.4}{2} : {\frac{55.6}{5}} \\\\&amp; =\frac{44.4}{2} \times \frac{5}{55.6}=2\end{aligned}

Since molar ratio of both the compound is not equal

So, option (A) is not correct.

(B) If empirical formula of compound 3 is

\mathrm{P}_3 \mathrm{Q}_2

, i.e.,

\begin{aligned}&amp; \frac{40}{M_P}: \frac{60}{M_Q}=\frac{3}{2} \\\\&amp; \Rightarrow \frac{40}{M_P} \times \frac{M_Q}{60}=\frac{3}{2}\end{aligned}

\begin{aligned}\Rightarrow \frac{4 \mathrm{M}_{\mathrm{Q}}}{6 \mathrm{M}_{\mathrm{P}}} &amp; =\frac{3}{2} \\\\\Rightarrow \frac{\mathrm{M}_{\mathrm{Q}}}{\mathrm{M}_{\mathrm{P}}} &amp; =\frac{3}{2} \times \frac{6}{4}=\frac{9}{4}\end{aligned}

and

\mathrm{M}_{\mathrm{P}}=20

(given)

So,

\frac{\mathrm{M}_{\mathrm{Q}}}{20}=\frac{9}{4}

\begin{aligned}&amp; \mathrm{M}_{\mathrm{Q}}=\frac{9 \times 26^5}{4} \\\\&amp; \mathrm{M}_{\mathrm{Q}}=45\end{aligned}

So, option (B) is correct.

(C) If empirical formula of compound 2 is PQ, So the molar ratio is

\frac{44.4}{1}: \frac{55.6}{1}=\frac{44.4}{55.6}=0.79 \sim 0.8

Empirical formula of compound 1 is

P_5 Q_4

so the molar ratio is

\frac{50}{5} : { } \frac{50}{4}

.

=\frac{50}{5} \times \frac{4}{50}=\frac{4}{5}=0.8

Since, molar ratio of both the compound is equal hence, state

(\mathrm{C})

is correct.

So, option (C) is correct.

(D)

\mathrm{M}_{\mathrm{P}}=70, \mathrm{M}_{\mathrm{Q}}=35

Molar ratio of compound 1 is

\begin{aligned}\frac{50}{M_{\mathrm{P}}}: \frac{50}{\mathrm{M}_{\mathrm{Q}}} &amp; =\frac{50}{70}: \frac{50}{35} \\\\&amp; =\frac{50}{70} \times \frac{35}{50}=\frac{1}{2}\end{aligned}

Hence, empirical formula of compound

\mathrm{PQ}_2

.

So, option (D) is incorrect.

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