Chapter 3.3, Problem 44SP

Interpretation Introduction

Interpretation : The problem has to be reworked by applying the equation.

Concept Introduction : The connectivity between mass and volume is density. The formula of density is given as:

  $\text{Density =}\frac{\text{mass}}{\text{volume}}$

Answer to Problem 44SP

The volume of boron is $6.32{\text{cm}}^3$ .

Explanation of Solution

Given information:

The density of boron is $2.34{\text{g/cm}}^3$ .

The mass of boron is $14.8\text{g}$ .

Density is defined as the ratio of mass to volume. It gives the connectivity between mass and volume.

The formula of density is given as:

  $\text{Density =}\frac{\text{mass}}{\text{volume}}$

Since the mass and density of boron are given, the volume has to be calculated.

Rewrite the density formula to isolate the volume term.

  $\text{Volume =}\frac{\text{Mass}}{\text{Density}}$

To calculate the volume, substitute the values in above formula:

  $\begin{array}{c}\text{Volume =}\frac{\text{Mass}}{\text{Density}}\\ =\frac{14.8\text{g}}{2.34{\text{g/cm}}^3}\\ =6.32{\text{cm}}^3\end{array}$

The volume of boron is $6.32{\text{cm}}^3$ .

Interpretation Introduction

Interpretation : The problem has to be reworked by applying the equation.

Concept Introduction : The connectivity between mass and volume is density. The formula of density is given as:

  $\text{Density =}\frac{\text{mass}}{\text{volume}}$

Answer to Problem 44SP

The volume of mercury is $3.42\times {10}^{-1}{\text{cm}}^3$ .

Explanation of Solution

Given information:

The density of mercury is $13.5{\text{g/cm}}^3$ .

The mass of mercury is $4.62\text{g}$ .

An effective approach for resolving conversion problems where measurement in one unit is changed to an equivalent measurement in another is dimensional analysis.

Density is defined as the ratio of mass to volume. It gives the connectivity between mass and volume.

The formula of density is given as:

  $\text{Density =}\frac{\text{mass}}{\text{volume}}$

Since the mass and density of mercury are given, the volume has to be calculated.

Rewrite the density formula to isolate the volume term.

  $\text{Volume =}\frac{\text{Mass}}{\text{Density}}$

To calculate the volume, substitute the values in the above formula:

  $\begin{array}{c}\text{Volume =}\frac{\text{Mass}}{\text{Density}}\\ =\frac{4.62\text{g}}{13.5{\text{g/cm}}^3}\\ =0.342{\text{cm}}^3\\ =3.42\times {10}^{-1}{\text{cm}}^3\end{array}$

The volume of mercury is $6.32{\text{cm}}^3$ .