Question

A piece of metal weighing 0.035 kg was submerged in a graduated cylinder containing water. The water level rose from 2.0 mL to 9.0 mL. What is the density in g/mL of the metal

Answer 1

Taking into account the definition of density, the density of the metal is 5 $\frac{g}{mL}$.

What is density

Density is defined as the property that matter, whether solid, liquid or gas, has to compress into a given space.

In other words, density is a quantity that allows us to measure the amount of mass in a certain volume of a substance.

Then, the expression for the calculation of density is the quotient between the mass of a body and the volume it occupies:

$density=\frac{mass}{volume}$

From this expression it can be deduced that density is inversely proportional to volume: the smaller the volume occupied by a given mass, the higher the density.

This case

In this case, the increase in the volume of water in the cylinder is due to the volume of the metal. This means that the volume of the metal can be calculated by taking into account the volume occupied by the water + the metal and the volume occupied by the water alone in the cylinder.

Then, you know that:

• Mass= 0.035 kg= 35 g (being 1 kg=1000 g)
• Volume= Volumen water + the metal - Volume water= 9 mL - 2 mL= 7 mL

Replacing in the definition of density:

$density=\frac{35 g}{7 mL}$

Solving:

density= 5 $\frac{g}{mL}$

In summary, the density of the metal is 5 $\frac{g}{mL}$.

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