Chapter 17, Problem 77A

(a)

Interpretation Introduction

Interpretation: Using the given values of heat as dependent variable, the graph should be plotted.

Concept Introduction: The energy required to change the amount of a substance from liquid to gaseous state is said to be heat of vaporization.

Answer to Problem 77A

  

Explanation of Solution

Given information:

Mass of CCl4(g)	Heat
	(J)	(cal)
2.9	652	156
7.5	1689	404
17	3825	915
26.2	5894	1410
39.8	8945	2140
51	11453	2740

The given values of mass and heat in cal is used to plot the graph. The x-axis represents the mass of CCl₄ in grams and y-axis represents heat in cal. So,

  

From the graph, it can be concluded that heat (cal) is in direct relation with mass of CCl₄(g) as the value of heat increases with increase in mass.

(b)

Interpretation Introduction

Interpretation: The slope of the line should be determined.

Concept Introduction: The formula used to find the slope of straight line is:

  $\text{m = }\frac{\left({\text{y}}_{\text{2}}{\text{ – y}}_{\text{1}}\right)}{{\text{(x}}_{\text{2}}{\text{ – x}}_{\text{1}}\text{)}}$

Answer to Problem 77A

The slope of the line is $53.79$ .

Explanation of Solution

The values taken for graph plotting are:

Mass of CCl4(g)	Heat (cal)
2.9	156
7.5	404
17	915
26.2	1410
39.8	2140
51	2740

Now, for calculating the slope the value of ${\text{x}}_{\text{1}},{\text{ x}}_2,{\text{ y}}_{\text{1}}$ and ${\text{y}}_2$ be 7.5, 17, 404 and 915. So,

  $\begin{array}{l}\text{m = }\frac{\left({\text{y}}_{\text{2}}{\text{ – y}}_{\text{1}}\right)}{{\text{(x}}_{\text{2}}{\text{ – x}}_{\text{1}}\text{)}}\\ \text{m = }\frac{915-404}{\text{17-7}\text{.5}}\\ \text{m = }\frac{511}{\text{9}\text{.5}}\\ \text{m = }53.79\end{array}$

Hence, the slope of the line is $53.79$ .

(c)

Interpretation Introduction

Interpretation: The comparison of heat of vaporization of CCl₄(l) with the slope of line should be done.

Concept Introduction: The energy required to change the amount of a substance from liquid to gaseous state is said to be heat of vaporization.

Explanation of Solution

The heat of vaporization of CCl₄(l) is $53.8\text{ cal/g}$ and the value of slope of the line is $53.79$ . On comparing the two values it can be concluded that both the values are very close to each other.