Question

Relative density of silver is 10.8. The density of water is \[{10^3}\,{\text{kg}} \cdot {{\text{m}}^{ - 3}}\]. What is the density of water in the SI unit?

Answer 1

Hint: Use the formula for the relative density of a substance. This formula gives the relation between the relative density of the substance, actual density of the substance and density of a standard substance which is generally taken as density of water at the temperature \[4^\circ {\text{C}}\]. Substitute all the values in the formula and determine the actual density of silver.

Formula used:
The relative density of a material is given by
\[{\text{Relative density of material}} = \dfrac{{{\text{Density of substance}}}}{{{\text{Density of a standard substance}}}}\] …… (1)

Complete step by step solution:
The density of water is \[{10^3}\,{\text{kg}} \cdot {{\text{m}}^{ - 3}}\].Here, water is taken as the standard substance to determine the density of silver.

Rewrite equation (1) for the relative density of silver.
\[{\text{Relative density of silver}} = \dfrac{{{\text{Density of silver}}}}{{{\text{Density of water}}}}\]

Rearrange the above equation for density of silver.
\[{\text{Density of silver}} = \left( {{\text{Relative density of silver}}} \right) \times \left( {{\text{Density of water}}} \right)\]

Substitute 10.8 for relative density of silver and \[{10^3}\,{\text{kg}} \cdot {{\text{m}}^{ - 3}}\] for density of water in the above equation.
\[{\text{Density of silver}} = \left( {{\text{10}}{\text{.8}}} \right) \times \left( {{{10}^3}\,{\text{kg}} \cdot {{\text{m}}^{ - 3}}} \right)\]
\[ \Rightarrow {\text{Density of silver}} = {\text{10}}{\text{.8}} \times {10^3}\,{\text{kg}} \cdot {{\text{m}}^{ - 3}}\]
\[ \therefore {\text{Density of silver}} = {\text{10800}}\,{\text{kg}} \cdot {{\text{m}}^{ - 3}}\]

Hence, the density of silver is \[{\text{10800}}\,{\text{kg}} \cdot {{\text{m}}^{ - 3}}\].

Additional information:
If we need to determine the relative density of a gas then the density of a standard substance is taken as air at temperature \[20^\circ {\text{C}}\].If the relative density of a substance comes out to be less than 1, then the substance will be less dense than the standard substance and if it is more than 1 then the substance is denser than standard substance.

Note: The students should be careful while substituting the values in the formula of relative density of silver. One may substitute the value of relative density of the silver with the unit kilogram per meter cube. But the students should keep in mind that the relative density is a unitless quantity as it is the ratio of densities of two substances.