The freezing point depression constant for water is 1.86°C kg mol$^{-1}$. If 5.00 g of Na$_2$SO$_4$ is dissolved in 45.0 g of H$_2$O, the freezing point is changed by −3.82°C. Calculate the van't Hoff factor for Na$_2$SO$_4$.

CBSE Class 12 · 2011 · AIPMT · SolutionsLong Answer

The freezing point depression constant for water is 1.86°C kg mol

^{- 1}

. If 5.00 g of Na

_{2}

_{4}

is dissolved in 45.0 g of H

_{2}

O, the freezing point is changed by −3.82°C. Calculate the van't Hoff factor for Na

_{2}

_{4}

Answer: i ≈ 2.63

Molality (

M

of Na

_{2}

_{4}

= 142 g mol

^{- 1}

m = \frac{5.00/142}{0.0450} = 0.7825 mol kg^{- 1}

Calculated depression (no dissociation):

Δ T_{f}^{c a l c} = 1.86 \times 0.7825 = 1.455 K

van't Hoff factor:

i = \frac{Δ T _{f}^{o b s}}{Δ T _{f}^{c a l c}} = \frac{3.82}{1.455}

i = 2.63

CBSE Class 12 Board · 2011 · AIPMT · Subjective