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### Theory:

We already discussed about density.

The density of a substance is defined as mass per unit volume.

It is mathematically represented by,

It is mathematically represented by,

$\mathit{Density}=\frac{\mathit{Mass}}{\mathit{Volume}}$

The unit of density is $\mathit{kg}/{m}^{3}$.

The density of a particular substance, under specific conditions, remains the same. Therefore, the density of a substance is one of its characteristic properties. It is different for different substances.

For example, the density of water is \(1000\) $\mathit{kg}/{m}^{3}$, while that of gold is \(19300\) $\mathit{kg}/{m}^{3}$. The density of a given sample of a material can help us to determine its purity. It is easy to express the density of a substance in comparison with that of water.

For example, the density of water is \(1000\) $\mathit{kg}/{m}^{3}$, while that of gold is \(19300\) $\mathit{kg}/{m}^{3}$. The density of a given sample of a material can help us to determine its purity. It is easy to express the density of a substance in comparison with that of water.

The relative density of a substance is the ratio of its density to that of water at \(4°\) \(C\).

$\mathit{Relative}\phantom{\rule{0.147em}{0ex}}\mathit{density}=\frac{\mathit{Density}\phantom{\rule{0.147em}{0ex}}\mathit{of}\phantom{\rule{0.147em}{0ex}}a\phantom{\rule{0.147em}{0ex}}\mathit{substance}}{\mathit{Density}\phantom{\rule{0.147em}{0ex}}\mathit{of}\phantom{\rule{0.147em}{0ex}}\mathit{water}\phantom{\rule{0.147em}{0ex}}\mathit{at}\phantom{\rule{0.147em}{0ex}}4\mathrm{\xb0}\phantom{\rule{0.147em}{0ex}}C}$

The relative density has similar quantities in numerator and denominator. Therefore, it has no unit.

**Example**:

**1**. The density of water is ${10}^{3}$ $\mathit{kg}/{m}^{3}$. Find the density of silver, whose relative density is \(10.8\).

**Given data**:

Relative density of silver \(=\) \(10.8\)

Density of water \(=\) ${10}^{3}$ $\mathit{kg}/{m}^{3}$

**To find**: Density of the given material

$\mathit{Relative}\phantom{\rule{0.147em}{0ex}}\mathit{density}=\frac{\mathit{Density}\phantom{\rule{0.147em}{0ex}}\mathit{of}\phantom{\rule{0.147em}{0ex}}a\phantom{\rule{0.147em}{0ex}}\mathit{substance}}{\mathit{Density}\phantom{\rule{0.147em}{0ex}}\mathit{of}\phantom{\rule{0.147em}{0ex}}\mathit{water}\phantom{\rule{0.147em}{0ex}}\mathit{at}\phantom{\rule{0.147em}{0ex}}4\mathrm{\xb0}\phantom{\rule{0.147em}{0ex}}C}$

Apply the known values,

$\begin{array}{l}10.8=\frac{\mathit{Density}\phantom{\rule{0.147em}{0ex}}\mathit{of}\phantom{\rule{0.147em}{0ex}}\mathit{silver}}{{10}^{3}}\\ \mathit{By}\phantom{\rule{0.147em}{0ex}}\mathit{simplifying},\\ \mathit{Density}\phantom{\rule{0.147em}{0ex}}\mathit{of}\phantom{\rule{0.147em}{0ex}}\mathit{gold}=10.8\times {10}^{3}\mathit{kg}/{m}^{3}\end{array}$

**Measurement of relative density**:

- Relative density can be measured using a Pycnometer, also called a density bottle.
- It consists of a ground glass stopper with a tiny hole through it. The function of the hole in the stopper is that when the bottle is filled, and the stopper is inserted, the excess liquid rises through the hole and goes down, outside of the bottle.
- In this way, the bottle will always contain the same volume of whatever liquid is filled in, provided the temperature remains constant. Thus, the density of a given volume of a substance to the density of the equal volume of a referenced substance is called relative density or specific gravity of the given substance.
- If the referenced substance is water, then the term specific gravity is used.

*Pycnometer*