Can a Wine with 28.4% Ethanol by Weight Freeze at -10 C?

[TypeFun]

Homework Statement

Wine that is 28.4% ethanol by wt is set outside. Will it freeze if the temp drops to -10 C? (assume water is the solvent)

Homework Equations

\DeltaT_fp = k_fp*molality of solute

The Attempt at a Solution

2.84 g of ethanol/10 g total =.284 mole
\DeltaT_fp= -10 ?

 

[cep]

I don't understand your attempt at a solution. Where are you getting the 10 g from? This problem has two parts: 1) to convert a percent solution into molality (moles solute per kg solvent), and 2) to use the deltaT=imk equation (i=1 for EtOH). Keep in mind that deltaT is the change in freezing point, not the freezing point itself.

So, if you have a solution that is 28.4 percent (volume/volume) ethanol, you have 28.4 mL EtOH in 100 mL total solution. 100-28.4 = volume of solvent (which I assume is water). After finding the volume of the solvent, you can use the respective densities of EtOH and water to convert to mass. From here, you can easily find the molality of the solution, and plug that into the equation. Subtract the resulting value from the freezing point of water (0º C), and there's your answer.

 

[PhaseShifter]

cep seems to have missed that the solution is 28.4% ethanol by weight, not volume. Otherwise, he is correct about the need to calculate molality in ortder to solve the problem.

(This is also one of those situations where I wouldn't trust the volume of the solution to be the sum of volumes of its components--as an experiment sometime you should try mixing 10mL of ethanol with 10mL of water and measure the resulting volume of the mixture.)