# What is the density of the solid in the following problem?

## A 25.20-g sample of a solid is placed in a flask. Toluene, in which the solid is insoluble, is added to the flask so that the total volume of solid and liquid together is 50.0 mL. The solid and toluene together weigh 49.17 g. The density of toluene at the temperature of the experiment is 0.864 g/mL.

Sep 1, 2016

Since mass is known, find the volume of the solid and then calculate the density.

${d}_{s o l i d} = 1.132 \frac{g}{m l}$

#### Explanation:

For finding the density $\left(d\right)$, mass $\left(m\right)$ and volume $\left(V\right)$ must be known:

$d = \frac{m}{V}$ $\left(1\right)$

Mass is known:

$m = 25.2 g$

To find the volume, you know that with the toluene the total volume is 50 ml. Therefore:

${V}_{t o t a l} = {V}_{s o l i d} + {V}_{t o l u e n e}$

${V}_{s o l i d} = {V}_{t o t a l} - {V}_{t o l u e n e}$

${V}_{s o l i d} = 50 - {V}_{t o l u e n e}$ $\left(2\right)$

The volume of toluene can be found through its own density and mass. Its mass:

${m}_{t o t a l} = {m}_{s o l i d} + {m}_{t o l u e n e}$

$49.17 = 25.2 + {m}_{t o l u e n e}$

${m}_{t o l u e n e} = 23.97 g$

So the volume:

${d}_{t o l u e n e} = {m}_{t o l u e n e} / {V}_{t o l u e n e}$

${V}_{t o l u e n e} = {m}_{t o l u e n e} / {d}_{t o l u e n e}$

${V}_{t o l u e n e} = \frac{23.97 g}{0.864 \frac{g}{m l}} = 27.74 m l$

Returning to $\left(2\right)$:

${V}_{s o l i d} = 50 - {V}_{t o l u e n e} = 50 - 27.74 = 22.26 m l$

Finally, the density of the solid:

${d}_{s o l i d} = {m}_{s o l i d} / {d}_{s o l i d} = \frac{25.2 g}{22.26 m l}$

${d}_{s o l i d} = 1.132 \frac{g}{m l}$