# The density of osmium is reported by one source to be  22610 kg/m^3. What is this density in g/cm^3? What is the mass of a block of osmium measuring 10.0cm x 8.0cm x 9.0cm?

Oct 10, 2016

$\rho = 22.61 \cdot g \cdot c {m}^{-} 3$;

$\text{Mass}$ $=$ $16.2 \cdot k g$

#### Explanation:

$\rho = 22610 \cdot k g \cdot {m}^{-} 3$ $=$ $22610 \times {10}^{3} \cdot g \times {\left({10}^{2} \cdot c m\right)}^{-} 3$

$=$ $22610 \times {10}^{3} \cdot g \times {10}^{-} 6 \cdot c {m}^{-} 3$

$=$ $22610 \times {10}^{-} 3 \cdot g \cdot c {m}^{-} 3$

$=$ $22.61 \cdot g \cdot c {m}^{-} 3$

So it is pretty dense stuff.

The mass of the block, is clearly $\text{density"xx"volume}$

$=$ $22.61 \cdot g \cdot \cancel{c {m}^{-} 3} \times 10.0 \cdot \cancel{c m} \times 8.0 \cdot \cancel{c m} \times 9.0 \cdot \cancel{c m}$

$>$ $16.0 \cdot k g$

Multiplication of the units clearly give me an end unit in $g$, as required.

Osmium is one of the densest materials known. It is currently selling for \$13-00*USD*g^-1. How much is your lump worth?