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Question: Relative density of silver is 10.8. The density of water is \(10^3kgm^{-3}\). What is the density of...

Relative density of silver is 10.8. The density of water is 103kgm−310^3kgm^{-3}. What is the density of silver in the SI unit?

Explanation

Solution

We know that density of any given substance is the ratio between the mass and the volume of the same substance. Thus clearly, different substances have different densities. Similarly, we also know that relative density is the ratio of density of any given to the density of water. This ratio helps us understand if the substance will float or sink when added to the reference substance, i.e. Water here.
Formula used:
R.D=density  of  substancedensity  of  waterR.D=\dfrac{density\; of \; substance}{density\; of \; water}

Complete answer:
Relative density is also known as the specific gravity, this gives the ratio of density of some given substance with reference to another standard substance. Generally the standard substance is taken as water.
Since density depends on mass and volume, which in turn depend on temperature and pressure. It is always suggested to mention the temperature and pressure of the given substance.
Here, let us assume that the relative density is noted at normal room temperature and at normal pressure.
Then from the definition of relative density, we have
R.D=density  of  substancedensity  of  waterR.D=\dfrac{density\; of \; substance}{density\; of \; water}
Given that R.D=10.8R.D=10.8 of silver. We know that density of water at at normal room temperature and at normal pressure, is 1.0×103kgm−31.0\times 10^3 kgm^{-3}
Then substituting the values, we have,
10.8=density  of  silver1.0×103kgm−310.8=\dfrac{density\; of \; silver}{1.0\times 10^3 kgm^{-3}}
  ⟹  density  of  silver=10.8×103\implies density\; of \; silver=10.8 \times 10^3
Thus the density of silver is found to be 10.8×103kgm−3{10.8 \times 10^3 kgm^{-3}}

Note:
If the relative density of the substance is less than 1 then the substance is less dense than the reference material. Similarly, if the relative density of the substance is greater than 1 then it is denser than the reference. If the relative density is exactly 1 then the densities of the substance and the reference are equal; that is, equal volumes of the two substances have the same mass. Here, clearly since the relative density of silver is greater than 1, we can say that silver is denser than the reference material, here water.