Answered: What is the approximate boiling-point…

Chemistry

10th Edition

ISBN:9781305957404

Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste

Publisher:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste

Chapter1: Chemical Foundations

Section: Chapter Questions

Problem 1RQ: Define and explain the differences between the following terms. a. law and theory b. theory and...

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Question

What is the approximate boiling-point elevation for the solution?

Expert Solution

Step 1-Introduction

The property of a solution varies with the amount of the solute molecules present in the solution irrespective of the nature of the solute molecules is termed as the colligative properties. The presence of the non-volatile impurities alters the certain physical properties of the solvent and hence the colligative properties are solvent properties affected by the presence of the external solute. The notable colligative properties are as follows:

i) depression in freezing point

ii) elevation in boiling point

iii) lowering of the vapor pressure

iv) osmotic pressure.

Step 2-Elevation in boiling point of the solution

The pure liquid boils at a temperature at which the vapor pressure becomes equal to the atmospheric pressure. Let the boiling point of the liquid be X°C. The addition of the non-volatile solute to the liquid decreases the vapor pressure of the liquid. So the liquid should be heated to a higher temperature than the temperature required for the pure liquid. After that only the vapor pressure of the solute added liquid equals the atmospheric pressure.

The increase in the boiling ( $∆ T_{b}$ ) of the solution can be related to the molar mass of the solute as follows:

$\begin{array}{rcl} M_{2} & = & \frac{K_{b} w_{2}}{w_{1} ∆ T_{b}} . . . (1) \\ M_{2} & = & M o l a r m a s s o f t h e a d d e d s o l u t e (g / m o l) \\ K_{b} & = & M o l a l b o i l i n g p o i n t e l e v a t i o n c o n s \tan t (K k g / m o l) \\ w_{2} & = & M a s s o f t h e s o l u t e (k g) \\ w_{1} & = & M a s s o f t h e s o l v e n t (k g) \\ ∆ T_{b} & = & T h e c h a n g e i n t e m p e r a t u r e (K) \end{array}$

Representative example:

if the mass of the added solute is $6 \times 10^{- 3} k g$ and the mass of the water is $250 \times 10^{- 3} k g$ , the elevation of the boiling point ( $∆ T_{b}$ ) as follows:

$\begin{array}{rcl} K_{b} o f w a t e r & = & 0.52 K K g / m o l \\ w_{2} & = & 6 \times 10^{- 3} k g \\ w_{1} & = & 250 \times 10^{- 3} k g \\ M_{2} o f t h e s o l u t e & = & 131.1 \times 10^{- 3} k g / m o l \\ ∆ T_{b} & = & \frac{(0.52 K k g / m o l) (6 \times 10^{- 3} k g)}{(250 \times 10^{- 3} k g) (131.1 \times 10^{- 3} k g / m o l)} \\ = & 0.095 K \end{array}$

The increase in the boiling point of the water solution is as follows:

$\begin{array}{rcl} B o i l i n g p o i n t & = & 100 ° C + 0.095 ° C \\ = & 100.095 ° C \end{array}$

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