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1

### AIPMT 2007

0.5 molal aqueous solution of a weak acid (HX) is 20% ionised. If Kf for water is 1.86 K kg mol$$-$$1, the lowering in freezing point of the solution is
A
0.56 K
B
1.12 K
C
$$-$$ 0.56 K
D
$$-$$ 1.12 K

## Explanation

HX H+ + X-
Initially 1 0 0
At equilibrium 1 - $$\alpha$$ $$\alpha$$ $$\alpha$$

Total moles = 1 – $$\alpha$$ + $$\alpha$$ + $$\alpha$$ = 1 + $$\alpha$$

$$\therefore$$ i = $${{1 + \alpha } \over 1}$$

Given, $$\alpha$$ = 20% = 0.2

$$\therefore$$ i = 1 + $$\alpha$$ = 1 + 0.2 = 1.2

$$\Delta$$Tf = ikf m = 1.2 × 1.86 × 0.5 = 1.12 K
2

### AIPMT 2007

Concentrated aqueous sulphuric acid is 98% H2SO4 by mass and has a density of 1.80 g mL$$-$$1. Volume of acid required to make one litre of 0.1 M H2SO4 solution is
A
16.65 mL
B
22.20 mL
C
5.55 mL
D
11.10 mL

## Explanation

Normality = $${{98 \times 1.8 \times 10} \over {49}}$$ = 36 N

N2 = 0.1 $$\times$$ 2 = 0.2 N

N2V2 = N1V1

$$\Rightarrow$$ 36 $$\times$$ V = 0.2 $$\times$$ 1000

$$\Rightarrow$$ V = $${{0.2 \times 1000} \over {36}}$$ = 5.55 mL
3

### AIPMT 2006

1.00 g of a non-electrolyte solute (molar mass 250 g mol$$-$$1) was dissolved in 51.2 g of benzene. If the freezing point depression constant, Kf of benzene is 5.12 K kg mol$$-$$1, the freezing point of benzene will be lowered by
A
0.2 K
B
0.4 K
C
0.3 K
D
0.5 K

## Explanation

Molality of non-electrolyte solute

= $${1 \over {250 \times 0.0512}}$$ = 0.0781 m

$$\Delta$$Tf = kf m

= 5.12 × 0.0781 = 0.4 K
4

### AIPMT 2006

A solution containing 10 g per dm3 of urea (molecular mass = 60 g mol$$-$$1) is isotonic with a 5% solution of a nonvolatile solute is
A
200 g mol$$-$$1
B
250 g mol$$-$$1
C
300 g mol$$-$$1
D
350 g mol$$-$$1

## Explanation

For isotonic solution,

osmotic pressure of urea = osmotic pressure of nonvolatile solute

$${{10} \over {60 \times 1000}}$$ = $${5 \over {m \times 100}}$$

$$\Rightarrow$$ m = 300 g mol–1

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