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Q.

The freezing point depression constant for water is –1.860C m^–1. If 5.00 g Na₂SO₄ is dissolved in 45.0 g H₂O, the freezing point is changed by –3.82⁰C, calculate the van't Hoff factor for Na₂SO₄.

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a

2.05

b

3.11

c

0.381

d

2.63

answer is B.

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Detailed Solution

K_f(H₂O) = 1.86KKgmole^-1

$W_{Na_2SO_4}=5g\\GMW\;of\;Na_2SO_4=142g\\W_{H_2O}=45g\\\Delta T_f=3.82^oc(or)3.82K$

Note: $\Delta T$ can be in celcius(or)Kelvin scale.

Magnitude of change in temp. will be the same irrespective of the scale in which the temp. is measured

$\Delta T_f=iK_fm\\3.82=i(1.86)(\frac{5}{142}X\frac{1000}{45})\\i=2.62$

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The freezing point depression constant for water is –1.860C m–1. If 5.00 g Na2SO4 is dissolved in 45.0 g H2O, the freezing point is changed by –3.820C, calculate the van't Hoff factor for Na2SO4.