Answer:
[tex]\boxed {\boxed {\sf 60 \ mL}}[/tex]
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:
[tex]P_1V_1=P_2V_2[/tex]
Originally the gas has a volume of 30 milliliters and a pressure of 4 atmospheres.
[tex]4 \ atm * 30 \ mL=P_2V_2[/tex]
The pressure is changed to 2 atmospheres, but the new volume is unknown.
[tex]4 \ atm * 30 \ mL = 2 \ atm *V_2[/tex]
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.
[tex]\frac{4 \ atm * 30 \ mL}{ 2 \ atm}= \frac{ 2 \ atm *V_2}{2 \ atm}[/tex]
[tex]\frac{4 \ atm * 30 \ mL}{ 2 \ atm}= V_2[/tex]
The units of atmospheres (atm) cancel.
[tex]\frac{4 * 30 \ mL}{ 2 }= V_2[/tex]
[tex]\frac{120 \ mL}{2}= V_2[/tex]
[tex]60 \ mL= V_2[/tex]
The new volume of the gas is 60 milliliters.
