To calculate the density of mercury, we will follow a step-by-step process using the given mass and volume data. The formula for density ([tex]\( \rho \)[/tex]) is:
[tex]\[ \text{Density} = \frac{\text{Mass}}{\text{Volume}} \][/tex]
Given:
- Mass of mercury ([tex]\( \text{M} \)[/tex]) [tex]\(= 57 \, \text{g} \)[/tex]
- Volume of mercury ([tex]\( \text{V} \)[/tex]) [tex]\( = 4.2 \, \text{mL}\)[/tex]
Let's substitute these values into the density formula:
[tex]\[ \text{Density} = \frac{57 \, \text{g}}{4.2 \, \text{mL}} \][/tex]
Performing the division:
[tex]\[ \text{Density} = \frac{57}{4.2} \approx 13.571428571428571 \, \text{g/cm}^3 \][/tex]
To express the density to the nearest tenth, we round 13.571428571428571 to one decimal place.
So, the density of mercury, rounded to the nearest tenth, is:
[tex]\[ 13.6 \, \text{g/cm}^3 \][/tex]
Therefore, the density of mercury is [tex]\( 13.6 \, \text{g/cm}^3 \)[/tex].
