(Solved): 2. The surface tension of an aqueous solution of methanol that is \( 50 \% \) methanol by mass is ...

2. The surface tension of an aqueous solution of methanol that is \( 50 \% \) methanol by mass is a linear function of temperature. When the temperature is \( 20^{\circ} \mathrm{C} \), the surface tension of the solution is \( 33.37 \mathrm{mN} / \mathrm{m} \); when the temperature is \( 50^{\circ} \mathrm{C} \), the surface tension of the solution is \( 30.28 \mathrm{mN} / \mathrm{m} \). (a) Determine the function relating the surface tension of an aqueous solution of methanol that is \( 50 \% \) methanol by mass to temperature. (b) What would you predict for the surface tension of an aqueous solution of methanol that is \( 50 \% \) methanol by mass when the temperature is \( 32^{\circ} \mathrm{C} \) ? (c) If the surface tension of an aqueous solution of methanol that is \( 50 \% \) methanol by mass is \( 31.94 \mathrm{mN} / \mathrm{m} \), what would you predict for the temperature? (d) Provide a physical interpretation for the slope of the line relating the surface tension of an aqueous solution of methanol that is \( 50 \% \) methanol by mass to temperature.