Question

The freezing point depression constant for water is −l.86°C m⁻¹. If 5.00 g Na₂SO₄ is dissolved in 45.0 g H₂O, the freezing point is changed by −3.82°C. Calculate the van't Hoff factor for Na₂SO₄.

विकल्प

• 2.63

• 3.11

• 0.381

• 2.05

Answer 1

2.63

Explanation:

To calculate the van’t Hoff factor (i) for Na₂SO₄, we use the formula for freezing point depression

ΔT_f ​= i K_f​ m

Where

ΔT_f​ = 3.82°C    ...(i)

K_f = 1.86°C m⁻¹

m = molality of the solution

Molar mass of Na₂SO₄ = 23 × 2 + 32 + 16 × 4 = 142 g/mol

Mass of Na₂SO₄ = 5.00 g

Mass of water = 45.0 g = 0.045 kg

Molality = `"moles of solute"/"kg of solvent"`

= `5.00/(1.42 xx 0.045)`

= 0.783 m

3.82 = i × 1.86 × 0.783   ...[From equation (i)]

`i = 3.82/(1.86 xx 0.783)`

i = 2.63