# Consider two solutions: one formed by adding 10 g of glucose, C6H12O6, to 1 L of water and another formed by adding 10 g of sucrose, C12H22O11, to 1 L of water. Are the vapor pressures the same?

Nov 20, 2015

No, they are not the same.

#### Explanation:

As you know, vapor pressure lowering is a colligative property of solutions, which implies that it depends solely on how many particles you have present in your solution, and not on the type of particles.

Now, the vapor pressure of a solution that contains a non-volatile solute can be described by this equation

color(blue)(P_"sol" = chi_"solvent" * P_"solvent"^@)" ", where

${P}_{\text{sol}}$ - the vapor pressure of the solution
${\chi}_{\text{solvent}}$ - the mole fraction of the solvent
${P}_{\text{solvent}}^{\circ}$ - the vapor pressure of the pure solvent

Now, the only difference between these two solutions will come from the number of moles of solute each will contain.

Since sucrose has a bigger molar mass than glucose, you can say for a fact that the $\text{10.0-g}$ sample will contain fewer moles than the $\text{10.0-g}$ sample of glucose.

For glucose, you'd have

10.0color(red)(cancel(color(black)("g"))) * ("1 mole C"_6"H"_12"O"_6)/(180.16color(red)(cancel(color(black)("g")))) = "0.0555 moles C"_6"H"_12"O"_6

For sucrose, you'd have

10.0color(red)(cancel(color(black)("g"))) * ("1 mole C"_12"H"_22"O"_11)/(342.3color(red)(cancel(color(black)("g")))) = "0.0292 moles C"_12"H"_22"O"_11

So, why does the number of moles of solute make a difference?

Well, the mole fraction of water is equal to the number of moles of water divided by the total number of moles present in the solution.

Since you have the same amount of water for both solutions, you can say that the number of moles of water will be the same for both, let's say $n$.

In this case, the mole fraction of water will be

• for the glucose solution

${\chi}_{\text{water}} = \frac{n}{n + 0.0555}$

• for the sucrose solution

${\chi}_{\text{water}} = \frac{n}{n + 0.0292}$

As you can see, the mole fraction of water will be bigger in the case of the sucrose solution, which means that the vapor pressure of the solution will be closer to that of pure water.

You can thus say that the vapor pressure of the sucrose solution will be higher than that of the glucose solution

${P}_{\text{sol sucrose" > P_"sol glucose}}$