Chapter 5, Problem 74A

Interpretation Introduction

Interpretation : The density of the iron 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 74A

The density of the iron is $\text{7}\text{.8 }\raisebox{1ex}{$\text{g}$}\!\left/ \!\raisebox{-1ex}{$\text{mL}$}\right.$ .

Explanation of Solution

Given information :

The mass is, $m=15.\text{0g}$

The initial volume is, $V_i=1\text{0}\text{.0mL}$

Final volume, $V_f=11.\text{91mL}$

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,

  $\begin{array}{l}{V}_{mp}=V_f-V_i\\ =\text{11}\text{.91mL-10}\text{.0mL}\\ \text{=}\text{1}\text{.91mL}\end{array}$

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

  $\rho =\frac{m}{V}=\frac{\text{15}\text{.0g}}{\text{1}\text{.91mL}}\text{=7}\text{.8}\raisebox{1ex}{$\text{g}$}\!\left/ \!\raisebox{-1ex}{$\text{mL}$}\right.$

Conclusion

The density is $7.8\raisebox{1ex}{$\text{g}$}\!\left/ \!\raisebox{-1ex}{$\text{mL}$}\right.$ .