JEE Advanced · Chemistry · 21. p Block (G15-18)

Paragraph:
The reactions of $\mathrm{Cl}_{2}$ gas with cold-dilute and hot-concentrated $\mathrm{NaOH}$ in water give sodium salts of two (different) oxoacids of chlorine, $\boldsymbol{P}$ and $\boldsymbol{Q}$, respectively. The $\mathrm{Cl}_{2}$ gas reacts with $\mathrm{SO}_{2}$ gas, in presence of charcoal, to give a product $\boldsymbol{R}$. $\boldsymbol{R}$ reacts with white phosphorus to give a compound $\boldsymbol{S}$. On hydrolysis, $\boldsymbol{S}$ gives an oxoacid of phosphorus, $\boldsymbol{T}$.
Question:
$P$ and $Q$, respectively, are the sodium salts of

A Hypochlorous and chloric acids
B Hypochlorus and chlorous acids
C Chloric and perchloric acids
D Chloric and hypochlorous acids

Verified Solution

Answer & Solution

Correct Answer

(A) Hypochlorous and chloric acids

Step-by-step Solution

Detailed explanation

{Cl}_{2} + cold dil. NaOH \to NaOCl + NaCl

{Cl}_{2} + hot conc. NaOH \to {NaClO}_{3} + NaCl

NaOCl

is salt of hypochlorous acid

= P

{NaOCl}_{3}

is salt of chloric acid

= Q

\begin{matrix} {Cl}_{2} + {SO}_{2} & \overset{Charcoal}{⟶} & {SO}_{2} {Cl}_{2} (R) \\ {SO}_{2} {Cl}_{2} + P_{4} & ⟶ & {PCl}_{5} (S) + {SO}_{2} \\ {PCl}_{5} + H_{2} O & ⟶ & H_{3} {PO}_{4} (T) + HCl \end{matrix}

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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From JEE Advanced

Let

f (x) = x + \log_{e} x - x \log_{e} x, x \in (0, \infty) .

•

Column 1 contains information about zeros of

f (x), f^{'} (x)

and

f^{''} (x) .

•

Column 2 contains information about the limiting behaviour of

f (x), f^{'} (x)

and

f^{''} (x)

at infinity.

•

Column 3 contains information about increasing-decreasing nature of

f (x)

and

f^{'} (x) .

Column 1	Column 2	Column 3
(I) $f (x) = 0$ for some $x \in (1, e^{2})$	(i) $\lim_{x \to \infty} f (x) = 0$	(P) $f$ is increasing in (0, 1)
(II) $f^{'} (x) = 0$ for some $x i n (1, e)$	(ii) $\lim_{x \to \infty} f (x) = - \infty$	(Q) $f$ is decreasing in $(e, e^{2})$
(III) $f^{'} (x) = 0$ for some $x \in (0, 1)$	(iii) $\lim_{x \to \infty} f^{'} (x) = - \infty$	(R) $f^{'}$ is increasing in (0, 1)
(IV) $f^{''} (x) = 0$ for some $x \in (1, e)$	(iv) $\lim_{x \to \infty} f^{''} (x) = 0$	(S) $f^{'}$ is decreasing in $(e, e^{2})$

Which of the following options is the only Correct combination?

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Let $f : [0, 1] \to [0, 1]$ be the function defined by $f (x) = \frac{x^{3}}{3} - x^{2} + \frac{5}{9} x + \frac{17}{36}$ . Consider the square region $S = [0, 1] \times [0, 1]$ . Let $G = \{(x, y) \in S : y > f (x)\}$ be called the green region and $R = \{(x, y) \in S : y < f (x)\}$ be called the red region. Let $L_{h} = \{(x, h) \in S : x \in [0, 1]\}$ be the horizontal line drawn at a height $h \in [0, 1]$ . Then which of the following statements is(are) true?

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