The number of pairs of the solution having the same value of the osmotic pressure from the following is \_\_\_\_. (Assume 100% ionization) A. $0.500\mathrm{M}$ $\mathrm{C}_{2}\mathrm{H}_{5}\mathrm{OH}(\mathrm{aq})$ and $0.25\mathrm{M}$ $\mathrm{KBr}(\mathrm{aq})$ B. $0.100\mathrm{M}$ $\mathrm{K}_{4}\left[\mathrm{Fe}(\mathrm{CN})_{6}\right](\mathrm{aq})$ and $0.100\mathrm{M}$ $\mathrm{FeSO}_{4}\left(\mathrm{NH}_{4}\right)_{2}\mathrm{SO}_{4}(\mathrm{aq})$ C. $0.05\mathrm{M}$ $\mathrm{K}_{4}\left[\mathrm{Fe}(\mathrm{CN})_{6}\right](\mathrm{aq})$ and $0.25\mathrm{M}$ $\mathrm{NaCl}(\mathrm{aq})$ D. $0.15\mathrm{M}$ $\mathrm{NaCl}_{(\mathrm{aq})}$ and $0.1\mathrm{M}$ $\mathrm{BaCl}_{2}(\mathrm{aq})$ E. $0.02\mathrm{M}$ $\mathrm{KCl}.\mathrm{MgCl}_{2}.6\mathrm{H}_{2}\mathrm{O}(\mathrm{aq})$ and $0.05\mathrm{M}$ $\mathrm{KCl}(\mathrm{aq})$

JEE Main · 2023 · 25 Jan 2023 · Shift 2 · Solutions

The number of pairs of the solution having the same value of the osmotic pressure from the following is ____.
(Assume 100% ionization)

A.

0.500 M

C_{2} H_{5} OH (aq)

and

0.25 M

KBr (aq)

0.100 M

K_{4} [Fe (CN)_{6}] (aq)

and

0.100 M

FeSO_{4} (NH_{4})_{2} SO_{4} (aq)

0.05 M

K_{4} [Fe (CN)_{6}] (aq)

and

0.25 M

NaCl (aq)

0.15 M

NaCl_{(aq)}

and

0.1 M

BaCl_{2} (aq)

0.02 M

KCl . MgCl_{2} .6 H_{2} O (aq)

and

0.05 M

KCl (aq)

Answer: 4

Osmotic pressure follows

π = i C R T

, so at a fixed temperature two solutions share the same osmotic pressure when the product

i C

is equal. Ethanol gives

1 \times 0.500 = 0.5

, matching potassium bromide at

2 \times 0.25 = 0.5

. Potassium ferrocyanide gives

5 \times 0.100 = 0.5

, matching Mohr's salt, which also furnishes five ions, at

5 \times 0.100 = 0.5

. Sodium chloride at

2 \times 0.15 = 0.3

matches barium chloride at

3 \times 0.1 = 0.3

. Carnallite,

KCl \cdot MgC l_{2} \cdot 6 H_{2} O

, releasing five ions, gives

5 \times 0.02 = 0.1

, matching potassium chloride at

2 \times 0.05 = 0.1

. Only the ferrocyanide and sodium chloride set,

0.25

against

0.5

, differs. The number of pairs having equal osmotic pressure is four.

JEE Main · 2023 · 25 Jan 2023 · Shift 2 · Integer answer