Question

The relation between density and pressure is given by:
(A) Boyle’s law
(B) Charle’s law
(C) Gay-lussac’s law
(D) Avogadro’s law

Answer 1

Hint: Density is mass by volume in general way. As we know, pressure is related to volume by the ideal gas equation i.e., pressure is inversely proportional to volume but volume is also inversely proportional to density. This is stated in a gas law directly.

Complete step-by-step solution:
Pressure is the term used for measurement of force acting on a unit area. Density accounts for the measure of how closely any given entity is packed, or in general terms, it is the ratio of the mass of the entity to its volume. Change in pressure will be directly reflected in a change in density and vice-versa because pressure is related to volume by Boyle’s law.
Boyle’s law states that for a given mass and at a constant temperature, the pressure P times volume V is always constant.
\[PV = C\], where C is a constant. From this we get that pressure is inversely proportional to volume.
\[P \propto \dfrac{1}{V}\]or , this means, pressure decreases on increase in volume or vice-versa.
We know that density \[\rho \] is mass(m) by volume(V) for a given substance.
\[\rho \propto \dfrac{m}{V}\], this means that density decreases on increasing the volume.
From these two relations we get that, \[\rho \propto P\], i.e. pressure is directly proportional to density of a substance or increase in pressure will increase the density and vice-versa.
Therefore, the relation between pressure and density is given by Boyle’s law.
Whereas, Charle’s law states that at constant pressure, volume of an ideal gas is directly proportional to the absolute temperature. Gay-lussac’s law states that at constant volume, pressure of a gas is directly proportional to the absolute temperature of a given mass. Avogadro’s law states that equal volume of all gases at same temperature and pressure have the same number of molecules.
Therefore, the relation between pressure and density is given by Boyle’s law.

Hence, the correct option is (A).

Note: We can also understand it by ideal gas equation, \[PV{\text{ }} = {\text{ }}nRT\]. It states that pressure of an ideal gas is directly proportional to number of moles of a substance and temperature but inversely proportional to the volume.