Chapter 5, Problem 75A

Interpretation Introduction

Interpretation : The density of the metal is to be calculated.

Concept Introduction :

The density is the mass per unit volume, which is given as,

  $\rho =\frac{m}{V}$

Where, $\rho$ is the density

  $V$ is the volume,

  $m$ is the mass

Answer to Problem 75A

The density of the metal pellets is 3.7 g/mL

Explanation of Solution

Given information :

The mass is, $m=33.42\text{g}$

The initial volume is, $V_i=12.\text{7mL}$

Final volume, $V_f=2\text{1}\text{.6mL}$

Formula used:

The density is defined as,

  $\rho =\frac{m}{V}$

And,

The volume of metal pellets is,

  $V_{mp}\text{=final}\text{volume}\text{of}\text{water-initial}\text{volume}\text{of}\text{water}$

Firstly, calculate the volume of metal pellets by substitute the values in above formula,

The volume of metal pellets is,

  $\begin{array}{l}{V}_{mp}=V_f-V_i\\ =\text{21}\text{.6mL-12}\text{.7mL}\\ \text{=}\text{8}\text{.9mL}\end{array}$

Now, use the values of mass and volume in the density formula, then the result is,

  $\rho =\frac{m}{V}=\frac{33.42g}{8.9mL}=3.7g/mL$

Conclusion

The density is 3.7 g/mL.