Answer:
[tex]\boxed {\boxed {\sf 6.25 \ L}}[/tex]
Explanation:
We are asked to find the new volume given a change in pressure. Since the temperature remains constant we are only concerned with volume and pressure. We will use Boyle's Law, which states 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]
Initially, the volume of the gas is 2.50 liters and the pressure is 760 millimeters of mercury.
[tex]760 \ mm \ Hg * 2.50 \ L = P_2V_2[/tex]
The pressure is changed to 304 millimeters of mercury, but the volume is unknown.
[tex]760 \ mm \ Hg * 2.50 \ L = 304 \ mm \ Hg * V_2[/tex]
We are solving for the new volume so we must isolate the variable V₂. It is being multiplied by 304 millimeters of mercury. The inverse operation of multiplication is division. Divide both sides by 304 mm Hg.
[tex]\frac {760 \ mm \ Hg * 2.50 \ L }{304 \ mm \ Hg}= \frac{304 \ mm \ Hg * V_2}{304 \ mm \ Hg}[/tex]
[tex]\frac {760 \ mm \ Hg * 2.50 \ L }{304 \ mm \ Hg}= V_2[/tex]
The units of millimeters of mercury cancel out.
[tex]\frac {760 * 2.50 \ L }{304 }= V_2[/tex]
[tex]\frac {1900}{304} \ L =V_2[/tex]
[tex]6.25 \ L =V_2[/tex]
The new volume of the anesthetic gas after the change in pressure is 6.25 liters.
