# Question a4a55

##### 1 Answer
Jun 27, 2017

(c) $- {0.634}^{\text{o""C}}$

#### Explanation:

To solve this problem involving freezing-point depression, we can use the equation

DeltaT_f = m • i • K_f

Where

• $\Delta {T}_{f}$ is the change in freezing point temperature (a positive quantity, although the temperature decreases)

• $m$ is the molality of the solution, equal to the moles of solute per kilogram of solvent (we'll find this)

• $i$ is the van't Hoff factor of the solute, which is given as $1$ (it is this value for basically all nonelectrolytes)

• ${K}_{f}$ is the molal boiling point constant of the solvent, which is given for water as $1.86$ $m / \text{^"o""C}$

We have to find the molality of the sucrose solution.

The number of moles can be found using the given molar mass ($342.30$ $\text{g/mol}$) and mass ($35.0$ $\text{g}$):

35.0cancel("g sucrose")((1color(white)(l)"mol sucrose")/(342.30cancel("g sucrose"))) = 0.102 $\text{mol sucrose}$

And there are

300.0cancel("g H"_2"O")((1color(white)(l)"kg H"_2"O")/(10^3cancel("g H"_2"O"))) = 0.3000 $\text{kg H"_2"O}$

So the molality is

$\text{molality" = "mol solute"/"kg solvent}$

= (0.102color(white)(l)"mol sucrose")/(0.3000color(white)(l)"kg H"_2"O") = color(red)(0.341m

Now, plugging in our known values, we have

DeltaT_f = (0.341cancel(m))(1)(1.86(""^"o""C")/(cancel(m))) = color(blue)(0.634^"o""C"

So option (c) is the correct answer. I was taught that the $\Delta {T}_{f}$ quantity is a positive value (although I disagree with this sometimes!), but just know that this is how much the freezing point lowers.

And since the freezing point lowers, this value is what you would subtract from the normal freezing point of water (${0}^{\text{o""C}}$):

${0}^{\text{o""C" + (-0.634^"o""C") = color(blue)(-0.634^"o""C}}$

And the new freezing point of the solution is thus color(blue)(-0.634^"o""C"#.