Question

A solid sample of a metal is submerged in a large graduated cylinder. The water level in the graduate was 55.25 mL and the final level was 61.00 mL. If the mass of the object was determined to be 23.795 g, what is the density of the metal?

Answer 1

ρm=4.14g/ml :metal density

Step-by-step explanation:

Conceptual analysis

We apply the formula to calculate the density:

ρ= m /V Formula (1)

Where:

ρ:density in g/mL

m: mass in g (grams)

V= volume in ml (milliliters)

Known data

`V_(il)`: final volume of liquid=55.25 ml

`V_(fl)`: final volume of liquid=61.00 ml

ms: metal mass=23.795 g

Problem development

The volume of the metal (vm) is equal to the change in volume of the liquid.

`V_(m) = V_(fl)-V_(il)  =61.00 ml - 55.25 ml =5.75ml`

We replace the data in formula (1 )to calculate the density of the metal(ρm):

ρm= mm /Vm=23.795 g/5.75ml

ρm=4.14g/ml