a sodium chloride solution containing 144 g of water that has a melting point of

Question

a sodium chloride solution containing 144 g of water that has a melting point of -1.0 C.    

Above is the original MC text for this part of Problem 14.88. To solve this problem you definitely need to know what the van't Hoff factors are all about. If you don't, go first back to the textbook towards the end of chapter 14. Other than that, the key equation here is essentially the freezing point depression equation again we used in Problem 14.75 except for the inclusion of the van't Hoff factor. That I had you work on the algebra first for Problem 14.75 is paying off now. The main difference for solving this problem here is that besides including the van't Hoff factor we need to solve for the mass of solute. So please provide me with the final algebraic equation for solute mass. Use the same symbols as before and use "i" as the symbol for the van't Hoff factor. Also, please use again the subscripts 1 and 2 for the masses and molecular weights to distinguish between solvent and solute, respectively.

Explanation / Answer

delta Tf = i x Kf x m

To - Tf = 1.9 x 1.86 x m

1.0 = 3.534 x m

m = 0.283

molality = 0.283 m

molality = moles of solute / mass of solvent in kg

0.283 = moles of solute / 0.144

moles of solute = 0.0408

moles = mass / molar mass

0.0408 = mass / 58.5

mass of solute = 2.384 g

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