Chapter 1, Problem 3ASA

Finding the density of a solid.

The student then emptied the flask and dried it once again. To the empty flask she added pieces of a metal until the flask was about three-fourths full. She weighed the stoppered flask and its metal contents and found that the mass was $116.150\text{g}$. She then filled the flask with water, stoppered it, and obtained a total mass of $119.827\text{g}$ for the flask, stopper, metal, and water. Find the density of the metal.

a. To find the density of the metal we need to know its mass and volume. We can easily obtain its mass by the method of differences:

$\text{Mass}\text{of}\text{metal}=\_\_\_\_\_\_ \text{g}-\_\_\_\_\_\_\_ \text{g}=\_\_\_\_\_\_ \text{g}$

b. To determine the volume of metal, we note that the volume of the flask must equal the volume of the metal plus the volume of water in the filled flask containing both metal and water. If we can find the volume of water, we can obtain the volume of metal by the method of differences. To obtain the volume of the water we first calculate its mass:

$\begin{array}{l}\text{Mass}\text{of}\text{water }=\text{ mass}\text{of}\left(\text{flask}+\text{ stopper}+\text{metal+ water}\right)-\text{ mass}\text{of}\left(\text{flask}+\text{ stopper}+\text{metal}\right)\hfill \\ \text{Mass of water }=\_\_\_\_\_ \text{g}-\_\_\_\_\_\_ \text{g}=\_\_\_\_\_\_ \text{g}\hfill \\ \hfill \end{array}$

The volume of water is found from its density, as in lb. Note that $\text{1 mL}=1{\text{ cm}}^{\text{3}}$. Make the calculation.

$\text{Volume}\text{of}\text{water }=\_\_\_\_\_\_\text{mL }=\_\_\_\_\_\_{\text{cm}}^{\text{3}}$

c. From the volume of the water, we calculate the volume of metal:

$\begin{array}{l}\text{Volume of metal}=\text{volume of flask}-\text{volume of water}\\ \text{Volume of metal}=\_\_\_\_\_\_\_\_{\text{cm}}^{\text{3}}-\_\_\_\_\_\_\_{\text{cm}}^{\text{3}}=\_\_\_\_\_\_\_{\text{cm}}^{\text{3}}\end{array}$

From the mass and volume of metal, we find the density, using the equation in 1b. Make the calculation.

$\text{Density of metal}=\_\_\_\_\_\_\_\_\text{g}/{\text{cm}}^{\text{3}}$