Question 7deb5

May 29, 2017

The answer is (c) $\text{236 g}$

Explanation:

Molality is simply a measure of the number of moles of solute present for every $\text{1 kg}$ of solvent.

This means that a $\text{1-molal}$ glucose solution will contain $1$ mole of glucose for every $\text{1 kg}$ of solvent.

$\text{1 molal " implies " 1 mole glucose" color(white)(.)color(blue)("for every")color(white)(.)"1 kg water}$

As you know, you have

$\text{1 kg} = {10}^{3}$ $\text{g}$

This means that your solution will contain

$\text{1 molal " implies " 1 mole glucose" color(white)(.)color(blue)("for every")color(white)(.)10^3color(white)(.)"g water}$

Now, the mass of a solution is always equal to

$\text{mass solution = mass solute + mass solvent}$

This means that the mass of a $\text{1-molal}$ glucose solution that contains $1$ mole of glucose and ${10}^{3}$ $\text{g}$ of water will be equal to

$\text{mass 1-molal solution" = "mass of 1 mole glucose" + 10^3color(white)(.)"g}$

To find the mass of $1$ mole of glucose, use the compound's molar mass

1 color(red)(cancel(color(black)("mole glucose"))) * "180.156 g"/(1color(red)(cancel(color(black)("mole glucose")))) = "180.156 g"

This means that the mass of above solution will be

$\text{mass 1-molal solution" = "180.156 g" + 10^3color(white)(.)"g}$

$\text{mass 1-molal solution = 1180.156 g}$

Now, you need your target solution to contain

$\frac{\text{0.2 moles glucose" = "1 mole glucose}}{\textcolor{red}{5}}$

Since solutions are homogeneous mixtures, i.e. they have the same composition throughout, you can say that the mass of solution that will contain $0.2$ moles of glucose will be

"mass solution" = "1180.156 g"/color(red)(5) ~~ color(darkgreen)(ul(color(black)("236 g")))#