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Boyles law in use

We know in Boyles law

`P_1\ \ V_1=P_2\ \ V_2`

NOTE:

Temperature remains constant

Also when you sit on an exercise ball it will get smaller

Boyles law mnemonic when you sit on an exercise ball it will get smaller.

This is Boyles law.

`P_1` and `V_1` refer to the pressure and volume before you sit on the exercise ball and `P_2` and `V_2` refer to the pressure and volume after you sit on the exercise ball.

Reducing the volume of a gas increases the pressure of the gas.

Boyles law reduce the volume and increase the pressure

Push the gas into a smaller volume and the gas particles will collide more frequently with the walls. They will exert more pressure.

NOTE 1:

The SI unit used to measure pressure is `Pa` (Pascals)

The SI unit used to measure volume is `m^3` (metre cubed)

 

NOTE 2:

You can use other units for volume and pressure such as `ml`, pounds per square inch, `mm` of mercury or atm (atmospheres) as long as you use the same units either side of the equation.

 

Examples

1. A sample of gas is at atmospheric pressure `(100,000 Pa)` and has volume `50cm^3`

   Determine the new pressure if the volume is decreased to `35cm^3`

Reveal answer

`PV=`constant
`P_1V_1=P_2V_2`

Therefore  `100,000xx50=P_2xx35`

`5,000,000=P_2xx35`

Therefore  `P_2=(5,000,000)/35`

`P_2=142,857\ \Pa`

 

2. A sample of gas has a volume of `12.0\ \l` at a pressure of 1.00 atm. If the pressure of gas is increased to `1000\ \mm\ \ Hg`, what is the new volume of the gas?

Reveal answer

`P_1V_1=P_2V_2`

But we must first get the two pressures in the same units of measurement

`1\ \atm=760\ \mm\ \Hg`

Therefore:

`P_1=760`
`V_1=12`
`P_2=1000`
`V_2=?`

`760xx12=1000V_2`

`9120=1000V_2`

`9120/1000=V_2`

`V_2=9.12l`

 

3. A carbon dioxide gas cylinder contains `180cm^3` of gas at a pressure of `6xx10^6 Pa`. Calculate the volume of the gas at atmospheric pressure, `1.0xx10^5 Pa`

Reveal answer

`P_1V_1=P_2V_2`

`6.3xx10^6xx180=1.0xx10^5xxV_2`

`V_2=(6.3xx10^6xx180)/(1.0xx10^5)`

Therefore `V_2=11340\ \cm^3`
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