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Chapter 1: Problem 11

Which of the following describes the effect on boiling point when a nonvolatile solute is added to a liquid? 1\. \(\Delta T_b=K_b M\) 2\. \(\Delta T_b=K_b / M\) 3\. \(\Delta T_b=K_b m\) 4\. \(\quad \Delta T_b=K_b / m\)

Short Answer

Expert verified
The correct formula that describes the effect on the boiling point when a nonvolatile solute is added to a liquid is \(\Delta T_b=K_b m\) (Option 3).

Step by step solution

01

Understand the concepts involved

Firstly, we need to understand what each symbol in the formulas represents. In all of the formulas, \(\Delta T_b\) represents the change in boiling point, and \(K_b\) represents the molal boiling-point elevation constant. The only difference between the formulas is the presence or absence of "m" and "M" and how they are related to the other variables. In this context, "m" represents the molality of the solute, which is defined as the number of moles of solute per kilogram of solvent. "M" represents the molar concentration of the solute, which is defined as the number of moles of solute per liter of solution. Since the effect on boiling point is related to the molality of the solute, the correct formula should include "m" and not "M".
02

Eliminate the incorrect formulas

Now that we know that "m" should be present in the correct formula, we can eliminate options 1 and 2 as they have "M" in the formula. We are left with options 3 and 4: 3\. \(\Delta T_b=K_b m\) 4\. \(\Delta T_b=K_b / m\)
03

Determine the correct relationship between the variables

When a nonvolatile solute is added to a liquid, the boiling point increases. This increase in boiling point is directly proportional to the molality of the solute. This means that as the molality (m) of the solute increases, the change in boiling point (\(\Delta T_b\)) should also increase. From the remaining options, the formula that correctly represents this relationship is: 3\. \(\Delta T_b=K_b m\) Option 4 suggests that \(\Delta T_b\) would decrease with increasing molality, which contradicts the known relationship between these variables.
04

Conclusion

The correct formula that describes the effect on the boiling point when a nonvolatile solute is added to a liquid is: \(\Delta T_b=K_b m\) (Option 3)

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