Question

State and explain van’t Hoff-Boyle’s law.

Answer 1

Hint: The van’t Hoff-Boyle’s law is derived and stated from the ideal gas equation. To solve this we must know the ideal gas law. The ideal gas law states for a given mass of an ideal gas and a constant volume of an ideal gas, the pressure exerted by the molecules of an ideal gas is directly proportional to its absolute temperature.

Complete step by step answer:
We know that the expression for the ideal gas law is as follows:
$PV = nRT$
Where, $P$ is the pressure of the gas,
              $V$ is the volume of the gas,
              $n$ is the number of moles of gas,
             $R$ is the universal gas constant,
             $T$ is the temperature of the gas.
From the expression for the ideal gas law we can see that the pressure of the gas is inversely proportional to the volume of the gas. The same is stated by van’t Hoff-Boyle’s law.
The van’t Hoff-Boyle’s law states that at constant temperature the volume of an ideal gas is inversely proportional to the pressure of the gas.
The expression for van’t Hoff-Boyle’s law is as follows:
${\text{P}} \propto \dfrac{1}{{\text{V}}}$
Where ${\text{P}}$ is the pressure,
             ${\text{V}}$ is the volume.
The significance of van’t Hoff-Boyle’s law is that the law gives information about the behaviour of gases.

Note: We know that the van’t Hoff-Boyle’s law states that at constant temperature the volume of an ideal gas is inversely proportional to the pressure of the gas. Thus, as the volume of the gas increases, the pressure decreases or as the volume of the gas decreases, the pressure increases.