Question

The density of gold is \[19.32\,g\,c{{m}^{-3}}\]. Find its relative density.

Answer 1

Hint: The relative density is also called the specific gravity. The relative density of the substance is the ratio of the density of the substance by the density of water at\[4{}^\circ C\] . using this formula we will compute the relative density of the given substance, that is, the gold.
Formula used:
\[RD=\dfrac{{{\rho }_{\text{substance}}}}{{{\rho }_{\text{reference}}}}\]

Complete answer:
From the given information, we have the data as follows.
The amount of mass per unit of volume of an object/substance is called density. The unit of the density is gram per cubic cm or gram per millilitre.
The relative density is calculated as the ratio of the density of a substance to the density of reference material. In the case of liquid, the reference material is water at \[4{}^\circ C\]and in the case of gases, the reference material is the air at room temperature.
As the relative density is the ratio of 2 densities, it has no unit.
 The general formula for computing the relative density is given as follows.
\[RD=\dfrac{{{\rho }_{\text{substance}}}}{{{\rho }_{\text{reference}}}}\]
Where RD is the relative density, \[{{\rho }_{\text{substance}}}\] is the density of the substance to be measured and \[{{\rho }_{\text{reference}}}\]is the density of the reference material.
In the case of solids, the relative density of the substance is the ratio of the density of the substance by the density of water at\[4{}^\circ C\]. So, the mathematical representation of the same is given as follows.
\[R{{D}_{sub}}=\dfrac{\text{Density of substance}}{1\,g\,c{{m}^{-3}}}\]
We will be using this formula to compute the relative density of gold.
Substitute the values in the above equation.
\[\begin{align}
  & R{{D}_{gold}}=\dfrac{19.32\,g\,c{{m}^{-3}}}{1\,g\,c{{m}^{-3}}} \\
 & \therefore R{{D}_{gold}}=19.32 \\
\end{align}\]
\[\therefore \] The relative density of gold is 19.32.

Note:
The relative density of the solid is the weight of the solid in the air by the loss of the weight of the solids in water. The relative density of the liquid is the loss of weight of solid in liquid by the loss of the weight of solid in water.