Chapter 14, Problem 107A

Interpretation Introduction

Interpretation: The density of the metal needs to be determined.

Concept Introduction: The density is related to mass and volume as follows:

  $d=\frac{m}{V}$

Here, m is mass and V is the volume of the metal.

Explanation of Solution

According to the question, the mass of the metal sample is 9.92 g. Also, the measurement for length, breadth, and height are $4.50\text{ cm}\times 1.30\text{ cm}\times 1.60\text{ mm}$ .

Now, density is related to mass and volume as follows:

  $d=\frac{m}{V}$

Here, m is mass and V is the volume of the metal.

From the given dimensions, the volume of metal can be calculated as follows:

  $\begin{array}{c}V=4.50\text{ cm}\times 1.30\text{ cm}\times 1.60\text{ mm}\left(\frac{{10}^{-3}\text{ m}}{1\text{ mm}}\right)\left(\frac{100\text{ cm}}{1\text{ m}}\right)\\ =0.936{\text{ cm}}^3\end{array}$

Now, mass can be calculated from the number of moles and volume as follows:

  $n=\frac{m}{M}$

Or,

  $m=n\times M$

The given mass is 9.92 g. Substitute the values, to calculate density as follows:

  $d=\frac{m}{V}$

Or,

  $\begin{array}{c}d=\frac{9.92\text{ g}}{0.936{\text{ cm}}^3}\\ =10.6{\text{ g/cm}}^3\end{array}$

Therefore, the density of metal is $10.6{\text{ g/cm}}^3$ .