Question

The freezing point depression constant for water is 1.86°C m⁻¹. If 5 g Na₂SO₄ is dissolved in 45 g H₂O, the freezing point is changed by −3.82°C. Calculate the van't Hoff factor for Na₂SO₄.

Answer 1

The van't Hoff factor for sodium sulfate (Na2SO4) can be calculated using the freezing point depression of the solution, the molality, and the molal freezing-point depression constant for water.

Step-by-step explanation:

The provided problem involves the concept of freezing point depression in a solution, specifically involving the calculation of the van't Hoff factor for sodium sulfate (Na2SO4). To find the van't Hoff factor, denoted by i, we must first use the equation that relates the freezing point depression (ΔTf) to the molality of the solution (m) and the molal freezing-point depression constant for water (Kf). The equation is given as: ΔTf = Kf x m x i.

In this problem, the measured freezing point depression is ΔTf = -3.82°C, and we have Kf = -1.86°C m-1 for water. To find molality, we need to calculate the moles of Na2SO4 which is the mass (5g) divided by the molar mass (142.04 g/mol). Then, we divide the moles by the mass of water in kilograms (0.045 kg), which gives us the molality. With these values, we can rearrange the equation to solve for the van't Hoff factor i.