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Pure water freezes at 273 K and 1 bar. T...

Pure water freezes at 273 K and 1 bar. The addition of 34.5 g of ethanol to 500 g of water changes the freezing point of the solution. Use the freezing point depression constant of water as 2 K `kg mol^(-1).` The figures shown below represent plots of vapour pressure (V.P.) versus temperature (T). [molecular weight of ethanol is` 46 g mol^(-1)` Among the following, the option representing change in the freezing point is

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D

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To solve the problem of determining the change in the freezing point of a solution when 34.5 g of ethanol is added to 500 g of water, we can follow these steps: ### Step 1: Identify the known values - Mass of ethanol (solute), \( W_b = 34.5 \, \text{g} \) - Molecular weight of ethanol, \( M_b = 46 \, \text{g/mol} \) - Mass of water (solvent), \( W_s = 500 \, \text{g} \) - Freezing point depression constant for water, \( K_f = 2 \, \text{K kg/mol} \) ### Step 2: Calculate the number of moles of ethanol Using the formula: \[ \text{Number of moles} = \frac{W_b}{M_b} \] Substituting the values: \[ \text{Number of moles of ethanol} = \frac{34.5 \, \text{g}}{46 \, \text{g/mol}} = 0.75 \, \text{mol} \] ### Step 3: Calculate the mass of the solvent in kg Convert the mass of water from grams to kilograms: \[ W_s = 500 \, \text{g} = 0.5 \, \text{kg} \] ### Step 4: Calculate the molality of the solution Using the formula for molality \( m \): \[ m = \frac{\text{Number of moles of solute}}{\text{Mass of solvent in kg}} = \frac{0.75 \, \text{mol}}{0.5 \, \text{kg}} = 1.5 \, \text{mol/kg} \] ### Step 5: Calculate the freezing point depression Using the formula for freezing point depression: \[ \Delta T_f = K_f \cdot m \] Substituting the values: \[ \Delta T_f = 2 \, \text{K kg/mol} \cdot 1.5 \, \text{mol/kg} = 3 \, \text{K} \] ### Step 6: Calculate the new freezing point The freezing point of pure water is 273 K. Therefore, the new freezing point \( T_f \) is: \[ T_f = 273 \, \text{K} - \Delta T_f = 273 \, \text{K} - 3 \, \text{K} = 270 \, \text{K} \] ### Conclusion The change in the freezing point of the solution is 3 K, and the new freezing point is 270 K. ---
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