Answer:
[tex]\boxed {\boxed {\sf A. \ 2082 \ mL}}[/tex]
Explanation:
We are asked to find the initial volume of a gas 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]
The pressure was initially 248.71 millimeters of mercury, but the volume is unknown.
[tex]248.71 \ mm \ Hg * V_1 = P_2V_2[/tex]
The pressure is increased to 911.6 millimeters of mercury and the volume is 568 milliliters.
[tex]248.71 \ mm \ Hg * V_1 = 911.6 \ mm \ Hg * 568 \ mL[/tex]
We are solving for the initial volume, so we must isolate the variable V₁. It is being multiplied by 248.71 millimeters of mercury. The inverse operation of multiplication is division, so we divide both sides by 248.71 mm Hg.
[tex]\frac {248.71 \ mm \ Hg * V_1 } {248.71 \ mm \ Hg}= \frac{911.6 \ mm \ Hg * 568 \ mL }{248.71 \ mm \ Hg}[/tex]
[tex]V_1 = \frac{911.6 \ mm \ Hg * 568 \ mL }{248.71 \ mm \ Hg}[/tex]
The units of millimeters of mercury (mm Hg) cancel.
[tex]V_1 = \frac{911.6 * 568 \ mL }{248.71 }[/tex]
[tex]V_1 = \frac {517788.8} {248.71 } \ mL[/tex]
[tex]V_1 = 2081.897793 \ mL[/tex]
Let's round to the nearest whole number. The 8 in the tenths place tells us to round the 1 up to a 2.
[tex]V_1= 2082 \ mL[/tex]
The gas initially occupied a volume of 2082 milliliters and choice A is correct.
