If we have three different solutions, a, b, and c, each containing 100 g of water, plus respectively 6.84 g of sucrose (c12h22o11), 0.72 g of ethanol, and 0.40 g of sodium hydroxide, which statement is true?

a. c has the lowest freezing point in the group.
b. a, b, and c all have different freezing points.
c. a and c have the same boiling point, but b has a lower one.
d. the boiling point of c is lower than that of a or b e. a, b, and c will all have about the same freezing points

c. A and C have the same boiling point, but B has a lower one.

Explanation:

The freezing point depression is expressed as:

ΔT = kf×m

Where kf is the freezing point depression constant that depends the nature of the solvent and m is molality (mol of solute/kg of solvent)

Boiling point elevation is:

ΔT = kb×m

Where kb is the ebulloscopic constant of the solvent.

As kf, kb and mass of solvent is the same for A, B and C solutions the only difference will be in moles of solute.

A 6,84g of sucrose are:

6,84g× = 0,002 moles

B 0,72g of ethanol are:

0,72g× = 0,0016 moles

C 0,40g of sodium hydroxide are:

0,40g× = 0,001 moles

Using Van't Hoff factor that describes the number of moles in solution that comes from 1 mole of solute before dissolving, moles in solution for A, B and C are:

A. moles in solution: 0,02 moles×1 = 0,02 moles in solution

B. moles in solution: 0,016 moles×1 = 0,016 moles in solution

C. moles in solution: 0,01 moles×2 = 0,02 moles in solution

As A has the same moles in solution of C, the freezing point depression will be the same in A and C, and the lower freezing point depression will be in B.

Also, the boiling point will be higher in A and C, and then in B.

Thus:

a. C has the lowest freezing point in the group.  FALSE. A and C have the lowest feezing point because have the higher freezing point depression.

b. A, B, and C all have different freezing points.  FALSE. As moles of A and C are the same, freezing point will be the same for the solutions.

c. A and C have the same boiling point, but B has a lower one.  TRUE.

d. The boiling point of C is lower than that of A or B . FALSE. Boiling point of C and A is higher than B.

e. A, B, and C will all have about the same freezing points. FALSE

the temperature of the gas, in k, not celsius.