Question

Question #9a7e8

Answer 1

`"972 g"`

Explanation:

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

`"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 `"43.2 cm"^3`. To find the mass of the sample, use the density of the metal as a conversion factor

`43.2 color(red)(cancel(color(black)("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.