Chapter U5.99, Problem 7E

Interpretation Introduction

Interpretation: The amount of ethanol vaporizes on transferring 5000 cal is to be calculated.

Concept introduction: The quantity of heat needed to convert 1 mole of liquid to a gas at its boiling point is termed as enthalpy of vaporization. There are many units of expressing the heat, such as calories, $\text{kJ}\text{/}\text{mol}$ etc.

Answer to Problem 7E

The amount of ethanol vaporizes on transferring 5000 cal is $24.97\text{g}$ .

Explanation of Solution

The enthalpy of vaporization of ethanol is $\Delta H_{\text{vap}}=38.6\text{kJ}\text{/}\text{mol}$ and given the amount of heat transferred is 5000 cal.

Use the following information to calculate the mass of ethanol evaporate.

  $\begin{array}{c}1\text{cal}\text{=}4.184\text{J}\\ \text{1}\text{kJ=1000}\text{J}\\ \text{Molar}\text{mass}\text{of}\text{ethanol}\text{=46}\text{.07}\text{g}\end{array}$

  $\begin{array}{c}\text{Gram}\text{of}\text{ethanol}\text{vaporize=}\text{5000}\cancel{\text{cal}}\times \frac{4.184\cancel{\text{J}}}{1\cancel{\text{cal}}}\times \frac{1\cancel{\text{kJ}}}{1000\cancel{\text{J}}}\times \frac{\cancel{1\text{mol}}}{38.6\cancel{\text{kJ}}}\times \frac{46.07\text{g}}{\cancel{1\text{mol}}}\\ =24.97\text{g}\end{array}$

Conclusion

  $24.97\text{g}$ of ethanol vaporizes on transferring 5000 calories of heat.