A radiator was filled with $10:L$ of water to which $2.5:L$ of methanol (density $\,=\,0.8:g.mL^{-1}$) were added. At $9::00:pm$, the vehicle is parked outdoors where the temperature is $0^{\circ}C$. The temperature is decreasing at a uniform rate of $0.5^{\circ}C/min$. Upto what time will there be no danger to the radiator of the car. $K_f:(water)\,=\,1.86:kg.mol^{-1}:K$. Assume methanol to be non-volatile.

First calculate the mass of methanol by multiplying 2500 mL by the density of 0.8 g/mL, resulting in 2000 g, which equals 62.37 moles. The mass of water is 10 kg, so the molality of the solution is 62.37 moles divided by 10 kg, or 6.237 m. Using the freezing point depression formula, the change in temperature equals the cryoscopic constant of 1.86 multiplied by 6.237, giving a depression of 11.6 degrees Celsius. Since the temperature drops at a rate of 0.5 degrees Celsius per minute, dividing 11.6 by 0.5 gives a safe time limit of 23.25 minutes.

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