Chapter EH, Problem 38R

Solution

Interpretation: The mass of the sample of diamond and graphite needs to be determined.

Concept Introduction: The volume of a solid is equal to the volume of water displaced by it when a solid is immersed in it.

The density is related to mass and volume as follows:

  $d=\frac{m}{V}$

Here, m is mass and V is volume.

Mass of diamond and graphite is 16.19 g and 10.12 g respectively.

The density of pure diamond is $3.52{\text{ g/cm}}^3$ . The density of graphite is $2.20{\text{ g/cm}}^3$ . The volume of water displaced by samples of diamond and graphite each is 4.60 mL.

First, calculate the mass of the diamond. The volume displaced by the sample of the diamond is 4.60 mL thus, it is equal to its volume. Density of a diamond is $3.52{\text{ g/cm}}^3$ , thus, its mass can be calculated as follows:

  $m=d\times V$

Substitute the values,

  $\begin{array}{c}m=\left(3.52{\text{ g/cm}}^3\right)\left(4.60\text{ mL}\right)\left(\frac{1{\text{ cm}}^3}{1\text{ mL}}\right)\\ =16.19\text{ g}\end{array}$

Thus, the mass of the diamond is 16.19 g.

Similarly, the mass of graphite will be:

  $\begin{array}{c}m=\left(2.20{\text{ g/cm}}^3\right)\left(4.60\text{ mL}\right)\left(\frac{1{\text{ cm}}^3}{1\text{ mL}}\right)\\ =10.12\text{ g}\end{array}$

Thus, the mass of graphite is 10.12 g.

Therefore, the mass of diamond and graphite is 16.19 g and 10.12 g respectively.