Questions: 2. What is the density of a 7.485 gram piece of metal that causes the level of water in a graduated cylinder to rise from 5.2 to 6.8 mL when the metal is submerged in the water? Consider significant figures when doing the calculation.

Solution Steps

The volume of the metal can be determined by the change in water level in the graduated cylinder. The initial water level is 5.2 mL, and the final water level is 6.8 mL. The volume of the metal is the difference between these two levels:

\[ \text{Volume of metal} = 6.8 \, \text{mL} - 5.2 \, \text{mL} = 1.6 \, \text{mL} \]

Density is defined as mass divided by volume. The mass of the metal is given as 7.485 grams, and the volume we calculated is 1.6 mL. Therefore, the density \( \rho \) is:

\[ \rho = \frac{\text{mass}}{\text{volume}} = \frac{7.485 \, \text{g}}{1.6 \, \text{mL}} \]

Perform the division to find the density:

\[ \rho = 4.678125 \, \text{g/mL} \]

The mass of the metal is given to four significant figures (7.485 g), and the volume is given to two significant figures (1.6 mL). The result should be reported with the least number of significant figures, which is two.

Thus, the density of the metal, rounded to two significant figures, is:

\[ \rho = 4.7 \, \text{g/mL} \]

Final Answer