Question

The relative density of aluminum is 3.5. Explain the meaning of the statement.

Answer 1

Hint: Recall the concept of relative density of a substance. Give the definition and formula for relative density of a substance. Then also give the information of the reference materials used in the measurement of the relative density of a substance. Hence, rewrite the same formula for relative density of aluminum and give significance of the relative density of the aluminum by considering water as the reference material.

Complete answer:
The relative density of a substance is the ratio of density of the substance and density of the reference material.
\[{\text{RD}} = \dfrac{{{\rho _{{\text{substance}}}}}}{{{\rho _{{\text{reference}}}}}}\]
Here, \[{\text{RD}}\] is relative density of the substance, \[{\rho _{{\text{substance}}}}\] is actual density of the substance and \[{\rho _{{\text{reference}}}}\] is density of the reference material.

In general, we consider water as the reference material for solids and liquids. The density of water is taken as \[1000\,{\text{kg/}}{{\text{m}}^3}\] of \[1\,{\text{g/c}}{{\text{m}}^3}\] at the temperature \[4^\circ {\text{C}}\] (more precisely at temperature \[3.98^\circ {\text{C}}\]).The reference material to measure the relative density of gases is air at temperature \[20^\circ {\text{C}}\] and pressure \[101.325\,{\text{kPa}}\]. The density of the air is taken as \[1.205\,{\text{kg/}}{{\text{m}}^3}\].

From the formula for the relative density, we can conclude that if the relative density of a substance is less than 1 then the substance is less dense than reference and if the relative density of the substance is more than 1 then the substance is denser than the reference material.

Since we have not taken the reference material used for measurement of relative density of aluminum, let us consider the reference material is water.So, we can write the formula for relative density of aluminum as
\[{\text{R}}{{\text{D}}_{{\text{Al}}}} = \dfrac{{{\rho _{{\text{Al}}}}}}{{{\rho _{{\text{water}}}}}} = 3.5\]
From the above formula, we can state that the density of aluminum is 3.5 times the density of water as the relative density of aluminum is more than 1.One can also explain that the aluminum is 3.5 times heavier than water.

Note:One may consider any reference material as the reference material used in the measurement of relative density of aluminum is not given in the question. But the air is generally used as reference material for measurement of relative density of gases. So, we have considered water as a reference material for measurement of relative density of aluminum.