Question

Consider two nonelectrolytes \(\mathrm{X}\) and \(\mathrm{Y} . \mathrm{X}\) has a higher molar mass than Y. Twenty-five grams of \(\mathrm{X}\) are dissolved in \(100 \mathrm{~g}\) of solvent \(\mathrm{C}\) and labeled solution 1. Twenty-five grams of \(Y\) are dissolved in \(100 \mathrm{~g}\) of solvent \(\mathrm{C}\) and labeled solution 2. Both solutions have the same density. Which solution has (a) a higher molarity? (b) a higher mass percent? (c) a higher molality? (d) a larger multiplier i? (e) a larger mole fraction of solvent?

Short answer

Question: Compare two nonelectrolyte solutions with the same mass of solvent but different solutes (X and Y) in terms of their molarity, mass percent, molality, i multiplier, and mole fraction of solvent, given that X has a higher molar mass than Y. Answer: Solution 2, which contains solute Y, has a higher molarity and molality compared to solution 1 (with solute X). Solution 1 has a higher mass percent and a larger mole fraction of solvent. Both solutions have the same i multiplier (i=1) since both solutes are nonelectrolytes.

Step-by-step solution

(a) Comparing molarities

Since solution 1 contains a solute with a higher molar mass, it implies that there are fewer moles of solute X in that solution compared to the number of moles of Y in solution 2. Molarity is a measure of the concentration of a solution in terms of moles per liter. Hence, solution 2 has a higher molarity.

(b) Comparing mass percent

The mass percent of a solution is the mass of solute divided by the total mass of the solution times 100. Since both solutions have the same mass of solvent (100 g) and the mass of solute X is greater than the mass of solute Y, solution 1 has a higher mass percent.

(c) Comparing molality

Molality is the measure of the concentration of a solution in terms of moles of solute per kilogram of solvent. Since solution 1 has a solute with a higher molar mass, it will have fewer moles of solute X compared to solution 2 which has more moles of solute Y. Therefore, solution 2 has a higher molality.

(d) Comparing i multipliers

The i (van't Hoff) multiplier is a measure of the number of particles a solute can dissociate into when dissolved. However, in this case, both solutes X and Y are nonelectrolytes which do not dissociate into ions upon dissolution. Thus, both have the same i multiplier (i=1).

(e) Comparing mole fraction of solvent

The mole fraction of the solvent is the ratio of the moles of solvent to the total moles in solution. Since solution 2 has a higher molarity, it implies that it has a larger number of moles of solute Y relative to the moles of solvent compared to solution 1. Therefore, solution 1 has a larger mole fraction of solvent.