Question

1. use dimensional analysis and the given densities to make the following conversions: a. 14.8 g of boron to cm³ of boron. the density of boron is 2.34 g/cm³. b. 4.62 g of mercury to cm³ of mercury. the density of mercury is 13.5 g/cm³.

Explanation:

Step1: Recall density formula

Density $
ho=\frac{m}{V}$, where $m$ is mass and $V$ is volume. We can re - arrange it to $V = \frac{m}{
ho}$.

Step2: Solve part a

For boron, $m = 14.8$ g and $
ho=2.34$ g/cm³. Substitute into the volume formula: $V_{boron}=\frac{14.8\ g}{2.34\ g/cm^{3}}$.
$V_{boron}=\frac{14.8}{2.34}\ cm^{3}\approx6.32\ cm^{3}$.

Step3: Solve part b

For mercury, $m = 4.62$ g and $
ho = 13.5$ g/cm³. Substitute into the volume formula: $V_{mercury}=\frac{4.62\ g}{13.5\ g/cm^{3}}$.
$V_{mercury}=\frac{4.62}{13.5}\ cm^{3}\approx0.342\ cm^{3}$.

Answer:

a. $6.32\ cm^{3}$
b. $0.342\ cm^{3}$