30 mL of methanol (density 0.7980 g/mL) on mixing with 70 mL of water (density 0.9984 g/mL) at 298 K gave a solution of density 0.9575 g/mL. Calculate (i) mole fraction, (ii) molality, (iii) molarity, and (iv) f.p. of the solution. `K_f(H_2O) = 1.86` .

Explanation

To solve the problem step by step, we will calculate the required values: mole fraction, molality, molarity, and the freezing point of the solution.

### Given Data:
- Volume of methanol (V_m) = 30 mL
- Density of methanol (d_m) = 0.7980 g/mL
- Volume of water (V_w) = 70 mL
- Density of water (d_w) = 0.9984 g/mL
- Density of the solution (d_s) = 0.9575 g/mL
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