$30 \mathrm{mL}$ of methanol (density $=0.7980 \mathrm{g} {\mathrm{mL}}^{-1}$) on mixing with $70 \mathrm{mL}$ of water (density $=0.9984 \mathrm{g} {\mathrm{mL}}^{-1}$) at $298 \mathrm{K}$ gave a solution of density $0.9575 \mathrm{g} {\mathrm{mL}}^{-1}$. Calculate the molality of solution.

$30 \mathrm{mL}$ of methanol (density $=0.7980 \mathrm{g} {\mathrm{mL}}^{-1}$) on mixing with $70 \mathrm{mL}$ of water (density $=0.9984 \mathrm{g} {\mathrm{mL}}^{-1}$) at $298 \mathrm{K}$ gave a solution of density $0.9575 \mathrm{g} {\mathrm{mL}}^{-1}$. Calculate the molarity.

$30 \mathrm{mL}$ of methanol (density $=0.7980 \mathrm{g} {\mathrm{mL}}^{-1}$) on mixing with $70 \mathrm{mL}$ of water (density $=0.9984 \mathrm{g} {\mathrm{mL}}^{-1}$) at $298 \mathrm{K}$ gave a solution of density $0.9575 \mathrm{g} {\mathrm{mL}}^{-1}$. Calculate the freezing point of the solution in ${}^{\mathrm{o}}\mathrm{C}$ and report the value by rounding off to two significant figures

${\mathrm{K}}_{\mathrm{f}}\left({\mathrm{H}}_2\mathrm{O}\right)=1.86$

Find the molality of a solution (containing a non-volatile solute) if its vapour pressure is $2\%$ below the vapour pressure of pure water.

Round off your to the nearest integer after multiplying with 10.

The gaseous ozone is bubbled through a water-ice mixture at $0°\mathrm{C}$. As ${\mathrm{O}}_3\left(\mathrm{g}\right)$ decomposes to form ${\mathrm{O}}_2\left(\mathrm{g}\right),$ the enthalpy of the reaction is absorbed by the resulting ice. Given that the heat of fusion of ice is $6.0095 \mathrm{kJ} {\mathrm{mol}}^{-1}$, calculate the mass of ice that melts for each gram of ${\mathrm{O}}_3$ that decomposes.

$2{\mathrm{O}}_3\left(\mathrm{g}\right)\to 3{\mathrm{O}}_2\left(\mathrm{g}\right); \mathrm{\Delta H}=-285.4 \mathrm{kJ}$

Give your answer up to two decimal places.

The 'calorie' used in nutrition is actually a kilocalorie. Assume that a human requires $\text{'}2500 \mathrm{cal}\text{'}$ of energy each day for the metabolic activities. What mass of ethanol is needed to provide this energy?

${\mathrm{C}}_2{\mathrm{H}}_5\mathrm{OH} \left(\mathrm{l}\right)+3{\mathrm{O}}_2 \left(\mathrm{g}\right)\to 2{\mathrm{CO}}_2 \left(\mathrm{g}\right)+3{\mathrm{H}}_2\mathrm{O} \left(\mathrm{l}\right); \mathrm{\Delta H}=-1371 \mathrm{kJ}$

If the human body is considered to be a closed system, what would be the temperature increase resulting from this energy intake? Assume a mass of $75 \mathrm{kg}$ and a specific heat of $4 \mathrm{J} {\mathrm{K}}^{-1} {\mathrm{g}}^{-1}$. If the body temperature is to be maintained at a constant value by the evaporation of water, what mass of water must evaporate? Assume that the heat of vaporization of water is $44 \mathrm{kJ} {\mathrm{mol}}^{-1}$.