# Question #9a7e8

Sep 16, 2017

$\text{972 g}$

#### Explanation:

The density of the metal is essentially the mass of exactly ${\text{1 cm}}^{3}$ of osmium, so right from the start, you can look at the density given to you and say that ${\text{1 cm}}^{3}$ of osmium has a mass of $\text{22.5 g}$.

$\text{22.5 g" color(blue)("/cm"^3) " " -> " " color(blue)("1 cm"^3)color(white)(.)"of osmium has a mass of 22.5 g}$

So, you know that your sample fo osmium has a volume of ${\text{43.2 cm}}^{3}$. To find the mass of the sample, use the density of the metal as a conversion factor

$43.2 \textcolor{red}{\cancel{\textcolor{b l a c k}{\text{cm"^3))) * "22.5 g"/(color(blue)(1)color(red)(cancel(color(blue)("cm"^3)))) = color(darkgreen)(ul(color(black)("972 g}}}}$

The answer is rounded to three sig figs.