Chapter 1, Problem 61A

(a)

To determine

The curve by plotting the values from the table that fits all the points.

Explanation of Solution

Given Info:

Volume ( ${\text{cm}}^3$ )	Mass (g)
10	7.9
20	15.8
30	23.7
40	31.6
50	39.6

Calculation:

Figure (1)

(b)

To determine

Description of the resulting curve.

Answer to Problem 61A

The resulting curve shows a line that passes through the origin and the slope of the line is 0.79.

Explanation of Solution

The resulting curve is line that is passing through the origin with slope $m=0.79$ . The volume in the curve varies with the mass for constant slope.

(c)

To determine

The equation relating the volume to the mass of the alcohol.

Answer to Problem 61A

The equation that relates the volume to the mass of the alcohol is $M=mV$ .

Explanation of Solution

Calculation:

The curve in the figure (1) shows a line passing through the line. The equation that relates the volume to the mass of the alcohol is,

$M=mV$

Here,

• $m$ is the slope of the curve.
• M is the mass of the alcohol.
• V is the volume of the alcohol.

(d)

To determine

The name of the given quantity and the unit of the quantity.

Answer to Problem 61A

The name of the quantity is density and the unit of the quantity is $\text{g}/{\text{cm}}^3$ .

Explanation of Solution

Introduction:

The slope is the ratio of the vertical change with the horizontal change.

The constant in the equation is the slope of the line. The vertical change is the mass and the horizontal change is the volume. The ratio of the mass to volume is the density. The unit of the densityis $\text{g}/{\text{cm}}^3$ .

Conclusion:

Thus, the name of the quantity is density and the unit of the quantity is $\text{g}/{\text{cm}}^3$ .

(e)

To determine

The mass of the alcohol.

Answer to Problem 61A

The mass of the alcohol is $25.675\text{g}$ .

Explanation of Solution

Given Info:

The volume of the alcohol is, $V=32.5{\text{cm}}^3$

The constant of the line is, $m=0.79\text{g}/{\text{cm}}^3$ .

Formula Used:

The expression to calculate the mass of the alcohol is,

$M=mV$

Calculation:

Substitute the values in the above expression.

$\begin{array}{c}M=\left(0.79\text{g}/{\text{cm}}^3\right)\left(32.5{\text{cm}}^3\right)\\ =25.675\text{g}\end{array}$

Thus, the mass of the alcohol is $25.675\text{g}$ .