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?

Answer 1

No, they are not the same.

As you are aware, vapor pressure lowering is a colligative property of solutions, meaning that the amount of particles in your solution determines its behavior, not the kind of particles.

This equation now describes the vapor pressure of a solution containing a non-volatile solute.

#color(blue)(P_"sol" = chi_"solvent" * P_"solvent"^@)" "#, where
#P_"sol"# - the vapor pressure of the solution #chi_"solvent"# - the mole fraction of the solvent #P_"solvent"^@# - the vapor pressure of the pure solvent

The amount of solute that each of these two solutions contains will now be the only distinction between them.

Since sucrose has a bigger molar mass than glucose, you can say for a fact that the #"10.0-g"# sample will contain fewer moles than the #"10.0-g"# sample of glucose.

With glucose, you would

#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 sugar, you would need

#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#

Why, then, does the quantity of solute matter in moles?

The number of moles of water divided by the total number of moles in the solution is the mole fraction of water.

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#.

The mole fraction of water in this instance will be

#chi_"water" = n/(n + 0.0555)#
#chi_"water" = n/(n + 0.0292)#

As you can see, the sucrose solution will have a larger mole fraction of water, meaning that the solution's vapor pressure will be closer to that of pure water.

Thus, it can be concluded that the sucrose solution will have a higher vapor pressure than the glucose solution.

#P_"sol sucrose" > P_"sol glucose"#
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Answer 2

The vapor pressures of the two solutions would not be the same. Glucose and sucrose are both non-volatile solutes, meaning they do not evaporate easily. However, they do affect the vapor pressure of the solution differently due to their different molecular weights and structures. Sucrose has a larger molecular weight than glucose, and it also forms stronger intermolecular forces, resulting in a lower vapor pressure compared to the glucose solution.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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