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Chapter 13: Problem 18

For dilute aqueous solutions in which the density of the solution is roughly equal to that of the pure solvent, the molarity of the solution is equal to its molality. Show that this statement is correct for a \(0.010 \mathrm{M}\) urea \(\left.\left[\mathrm{(NH}_{2}\right)_{2} \mathrm{CO}\right]\) solution.

Short Answer

Expert verified
The molality of the 0.010 M and 1 kg water solution of urea is 0.010 mol/kg. Since this value equals the given molarity, we can see how for dilute aqueous solutions the molarity of the solution can indeed equal to its molality.

Step by step solution

01

Calculate the moles of solute

First, we find the number of moles of solute. From the problem, we know the molarity (\(M\)) is 0.010 M. We use the formula for molarity, \(M = n/V\), to solve for the number of moles (\(n\)). Let's assume we have 1 L of solution. Then, \(n = M * V\) = 0.010 M * 1 L = 0.010 moles of urea.
02

Calculate the mass of the solvent (water)

Since we are dealing with a solution where it's density is almost equal to that of the pure solvent (which is water in this case), we can estimate that the mass of water in our 1L solution is about 1kg. This is because the density of water is approximately 1 kg/L.
03

Calculate molality of the solution

Next, we calculate the molality (\(m\)). Molality is the number of moles of solute per kilograms of solvent. Using our values from the previous steps, we have \(m = n/M_{solvent}\) = 0.010 moles/1 kg = 0.010 mol/kg.

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Most popular questions from this chapter

The solubility of \(\mathrm{KNO}_{3}\) is \(155 \mathrm{~g}\) per \(100 \mathrm{~g}\) of water at \(75^{\circ} \mathrm{C}\) and \(38.0 \mathrm{~g}\) at \(25^{\circ} \mathrm{C}\). What mass (in grams) of \(\mathrm{KNO}_{3}\) will crystallize out of solution if exactly \(100 \mathrm{~g}\) of its saturated solution at \(75^{\circ} \mathrm{C}\) are cooled to \(25^{\circ} \mathrm{C} ?\)

Calculate the molalities of these aqueous solutions: (a) \(1.22 M\) sugar \(\left(\mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}\right)\) solution (density of solution \(=1.12 \mathrm{~g} / \mathrm{mL}\) ), (b) \(0.87 \mathrm{M} \mathrm{NaOH}\) solution (density of solution \(=1.04 \mathrm{~g} / \mathrm{mL}),(\mathrm{c})\) \(5.24 \mathrm{M} \mathrm{NaHCO}_{3}\) solution (density of solution \(=\) \(1.19 \mathrm{~g} / \mathrm{mL})\)

Explain why molality is used for boiling-point elevation and freezing-point depression calculations and molarity is used in osmotic pressure calculations.

Which of these two aqueous solutions has (a) the higher boiling point, (b) the higher freezing point, and (c) the lower vapor pressure: \(0.35 \mathrm{~m} \mathrm{CaCl}_{2}\) or \(0.90 \mathrm{~m}\) urea? State your reasons.

Calculate the amount of water (in grams) that must be added to (a) \(5.00 \mathrm{~g}\) of urea \(\left[\left(\mathrm{NH}_{2}\right)_{2} \mathrm{CO}\right]\) in the preparation of a 16.2 percent by mass solution and (b) \(26.2 \mathrm{~g}\) of \(\mathrm{MgCl}_{2}\) in the preparation of a 1.5 percent by mass solution.
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