Question

A gas, behaving ideally, has a pressure P1 and at a volume V1. The pressure of the gas is changed to P2. Using Avogadro’s, Charles’, or Boyle’s law, develop an expression that would solve for the new volume V2.

Answer 1

Boyle's Law

`\therefore P_1.V_1=P_2.V_2`

Step-by-step explanation:

Given that:

initially:

pressure of gas,
`= P_1`

volume of gas,
`= V_1`

finally:

pressure of gas,
`= P_2`

volume of gas,
`= V_2`

To solve for final volume
`V_2`

According to Avogadro’s law the volume of an ideal gas is directly proportional to the no. of moles of the gas under a constant temperature and pressure.

According to the Charles' law, at constant pressure the volume of a given mass of an ideal gas is directly proportional to its temperature.

But here we have a change in the pressure of the Gas so we cannot apply Avogadro’s law and Charles' law.

Here nothing is said about the temperature, so we consider the Boyle's Law which states that at constant temperature the volume of a given mass of an ideal gas is inversely proportional to its pressure.

Mathematically:

`P_1\propto (1)/(V_1)`

`\Rightarrow P_1.V_1=k\ \rm(constant)`

`\therefore P_1.V_1=P_2.V_2`