Question

30 ml of gas is changed from 4 atm to 2 atm what is the new volume

Answer 1

`\boxed {\boxed {\sf 60 \ mL}}`

Step-by-step explanation:

In this problem, volume and pressure are changing, so we use Boyle's Law. This states that the volume of a gas is inversely proportional to the pressure. The formula for this law is:

`P_1V_1=P_2V_2`

Originally the gas has a volume of 30 milliliters and a pressure of 4 atmospheres.

`4 \ atm * 30 \ mL=P_2V_2`

The pressure is changed to 2 atmospheres, but the new volume is unknown.

`4 \ atm * 30 \ mL = 2 \ atm *V_2`

We want to solve for the new volume (V₂). It is being multiplied by 2 atmopsheres. The inverse operation of multiplication is division, so we divide both sides by 2 atm.

`(4 \ atm * 30 \ mL)/( 2 \ atm)= ( 2 \ atm *V_2)/(2 \ atm)`

`(4 \ atm * 30 \ mL)/( 2 \ atm)= V_2`

The units of atmospheres (atm) cancel.

`(4 * 30 \ mL)/( 2 )= V_2`

`(120 \ mL)/(2)= V_2`

`60 \ mL= V_2`

The new volume of the gas is 60 milliliters.