Question

Question #9f08e

Answer 1

Boyle's Law states that pressure is indirectly proportional to volume when the temperature and moles of the gas are constant.

This relationship can be modelled by the equation:

`P_1V_1=P_2V_2`

where:
`P_1=`initial pressure
`V_1=`initial volume
`P_2=`final pressure
`V_2=`final volume

When pressure is indirectly proportional to volume, this means that
say, for example, if the pressure was increased by a factor, the volume would decrease by the `color(red)("same")` factor.

Similarly, if the volume was increased by a factor, the pressure would decrease by the `color(red)("same")` factor.

For example, if the initial pressure was `color(blue)2` `color(blue)(atm)`, the initial volume was `color(blue)4` `color(blue)L`, and the pressure decreased by a factor of `color(blue)(1/2)`, the volume would increase by a factor of `color(blue)2`.

Algebraically, we can solve for the final volume using Boyle's Law formula, assuming that the temperature and moles of the gas are constant:

`P_1V_1=P_2V_2`

`(2atm)(4L)=(1atm)(V_2)`

`V_2=((2color(red)cancelcolor(black)(atm))(4L))/((1color(red)cancelcolor(black)(atm)))`

`V_2=8` `L`

Thus, the volume has increased from `4` `L` to `8` `L`.

Graphically, the relationship between pressure and volume can be represented as: