Questions: A piece of metal (mass = 21.251 g) is placed in 17.00 mL of chloroform in a 25-mL graduated cylinder. The chloroform level increases to 23.48 mL. The best value for density of this metal from these data is

A piece of metal (mass = 21.251 g) is placed in 17.00 mL of chloroform in a 25-mL graduated cylinder. The chloroform level increases to 23.48 mL. The best value for density of this metal from these data is

Transcript text: A piece of metal (mass $=21.251 \mathrm{~g}$ ) is placed in 17.00 mL of chloroform in a $25-\mathrm{mL}$ graduated cylinder. The chloroform level increases to 23.48 mL . The best value for density of this metal from these data is

Solution

Solution Steps

Step 1: Determine the Volume of the Metal

To find the volume of the metal, we need to calculate the difference in the chloroform level before and after the metal is added.

Initial volume of chloroform: $ 17.00 \, \text{mL} $
Final volume of chloroform: $ 23.48 \, \text{mL} $

Volume of the metal: \[ \text{Volume of metal} = \text{Final volume} - \text{Initial volume} = 23.48 \, \text{mL} - 17.00 \, \text{mL} = 6.48 \, \text{mL} \]

Step 2: Calculate the Density of the Metal

Density ($\rho$) is defined as mass ($m$) divided by volume ($V$).

Given: \[ m = 21.251 \, \text{g} \] \[ V = 6.48 \, \text{mL} \]

Density: \[ \rho = \frac{m}{V} = \frac{21.251 \, \text{g}}{6.48 \, \text{mL}} = 3.2782 \, \text{g/mL} \]

Step 3: Round the Density to Four Significant Digits

The density calculated needs to be rounded to four significant digits.

\[ \rho = 3.278 \, \text{g/mL} \]