If $\alpha$ is the degree of dissociation of $\mathrm{Na}_{2} \mathrm{SO}_{4}$, the vant Hoff's factor (i) used for calculating the molecular mass is

JEE Main · 2005 · 08 May 2005 · Offline · Solutions

α

is the degree of dissociation of

Na_{2} SO_{4}

, the vant Hoff's factor (i) used for calculating the molecular mass is

(A) $1 + α$
(B) $1 - α$
(C) $1 + 2 α$ ✓ Correct
(D) $1 - 2 α$

Answer: (C)

Solution

The van't Hoff factor counts how many particles you actually end up with per formula unit dissolved. Starting from one mole of

Na X_{2} SO X_{4}

that dissociates to the extent

α

Na X_{2} SO X_{4} 2 Na X^{+} + SO X_{4} X^{2 -}

, you are left with

1 - α

moles undissociated, together with

2 α

moles of

Na X^{+}

and

α

moles of

SO X_{4} X^{2 -}

. Adding these gives a total of

(1 - α) + 2 α + α = 1 + 2 α

particles, so

i = 1 + 2 α

JEE Main · 2005 · 08 May 2005 · Offline · Single correct option

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