Chapter 3.3, Problem 43SP

Interpretation Introduction

Interpretation : By the use of dimensional analysis, the given density is to be converted.

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

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 43SP

The desired conversion is finding the volume of boron. 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 $14.8\text{g}$ .

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:

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

To convert $14.8\text{g}$ of boron to ${\text{cm}}^3$ of boron, the volume of the boron is supposed to be calculated by using the formula.

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 desired conversion is finding the volume of boron. The volume of boron is $6.32{\text{cm}}^3$ .

Interpretation Introduction

Interpretation : By the use of dimensional analysis, the given density is to be converted.

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

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 43SP

The desired conversion is finding the volume of mercury. 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

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

To convert $4.62\text{g}$ of mercury to ${\text{cm}}^3$ of mercury, the volume of the boron is supposed to be calculated by using the formula.

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 desired conversion is finding the volume of mercury. The volume of mercury is $6.32{\text{cm}}^3$ .