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Chapter 11: Problem 9

Is molality or molarity dependent on temperature? Explain your answer. Why is molality, and not molarity, used in the equations describing freezing-point depression and boiling-point elevation?

Short Answer

Expert verified
Molality is independent of temperature, as it depends on the mass of solvent, while molarity is dependent on temperature, as it depends on the volume of the solution which varies with temperature. Molality is used in equations describing freezing-point depression and boiling-point elevation because it provides an accurate ratio of solute-to-solvent particles that remains constant despite temperature changes, making it suitable for describing colligative properties.

Step by step solution

01

1. Define molality and molarity

Molality (m) is defined as the number of moles of solute (particle) per kilogram of solvent, with the equation: \(m = \frac{\text{moles of solute}}{\text{mass of solvent (kg)}}\). Molarity (M) is defined as the number of moles of solute per liter of solution, with the equation: \(M = \frac{\text{moles of solute}}{\text{volume of solution (L)}}\).
02

2. Molality and temperature

Since molality depends only on the mass of solvent, it remains constant with the changes in temperature, as mass does not change with temperature. Therefore, molality is independent of temperature.
03

3. Molarity and temperature

Molarity depends on the volume of the solution, which can change with temperature since the volume varies with temperature due to thermal expansion or contraction. Thus, molarity is dependent on temperature.
04

4. Focus on molality in colligative properties

Colligative properties are physical properties of solutions that depend on the ratio of solute particles' concentration to the solvent particles' concentration, such as freezing-point depression and boiling-point elevation. As molality is independent of temperature and gives an accurate ratio of solute to solvent particles, it is preferred over molarity in equations describing freezing-point depression and boiling-point elevation.
05

5. Conclusion

Molality is independent of temperature, while molarity is dependent on temperature. Molality is the preferred parameter for describing colligative properties like freezing-point depression and boiling-point elevation, as it offers a consistent measurement of solute-to-solvent concentration despite temperature changes.

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Most popular questions from this chapter

The freezing point of \(t\) -butanol is \(25.50^{\circ} \mathrm{C}\) and \(K_{\mathrm{f}}\) is \(9.1^{\circ} \mathrm{C} \cdot \mathrm{kg} / \mathrm{mol}\) Usually \(t\) -butanol absorbs water on exposure to air. If the freezing point of a 10.0 -g sample of \(t\) -butanol is \(24.59^{\circ} \mathrm{C},\) how many grams of water are present in the sample?

Consider the following solutions: 0.010\(m \mathrm{Na}_{3} \mathrm{PO}_{4}\) in water 0.020 \(m \mathrm{CaBr}_{2}\) in water 0.020 \(m \mathrm{KCl}\) in water 0.020 \(m \mathrm{HF}\) in water \((\mathrm{HF} \text { is a weak acid.) }\) a. Assuming complete dissociation of the soluble salts, which solution(s) would have the same boiling point as 0.040 $\mathrm{m} \mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}\( in water? \)\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}$ is a nonelectrolyte. b. Which solution would have the highest vapor pressure at $28^{\circ} \mathrm{C} ?$ c. Which solution would have the largest freezing-point depression?

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An unknown compound contains only carbon, hydrogen, and oxygen. Combustion analysis of the compound gives mass percents of 31.57\(\% \mathrm{C}\) and 5.30\(\%\) H. The molar mass is determined by measuring the freezing-point depression of an aqueous solution. A freezing point of $-5.20^{\circ} \mathrm{C}\( is recorded for a solution made by dissolving 10.56 \)\mathrm{g}$ of the compound in 25.0 \(\mathrm{g}\) water. Determine the empirical formula, molar mass, and molecular formula of the compound. Assume that the compound is a nonelectrolyte.
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