Answer:
[tex]\boxed {\boxed {\sf P_2 \approx 3.53 \ atm}}[/tex]
Explanation:
In this problem, the temperature stays constant. The volume and pressure change, so we use Boyle's Law. This states that the pressure of a gas is inversely proportional to the volume. The formula is:
[tex]P_1V_1=P_2V_2[/tex]
Now we can substitute any known values into the formula.
Originally, the gas has a volume of 25.0 liters and a pressure of 2.05 atmospheres.
[tex]25.0 \ L * 2.05 \ atm = P_2V_2[/tex]
The volume is decreased to 14.5 liters, but the pressure is unknown.
[tex]25.0 \ L * 2.05 \ atm = P_2 * 14.5 \ L[/tex]
Since we are solving for the new pressure, or P₂, we must isolate the variable. It is being multiplied by 14.5 liters and the inverse of multiplication is division. Divide both sides by 14.5 L .
[tex]\frac {25.0 \ L * 2.05 \ atm }{14.5 \ L}=\frac{P_2 *14.5 \ L}{14.5 \ L}[/tex]
[tex]\frac {25.0 \ L * 2.05 \ atm }{14.5 \ L}= P_2[/tex]
The units of liters cancel.
[tex]\frac {25.0 * 2.05 \ atm }{14.5 }=P_2[/tex]
[tex]\frac {50.25\ atm }{14.5 }=P_2[/tex]
[tex]3.53448276 \ atm = P_2[/tex]
The original values of volume and pressure have 3 significant figures, so our answer must have the same.
For the number we found, that is the hundredth place.
The 4 in the thousandth place (in bold above) tells us to leave the 3 in the hundredth place.
[tex]3.53 \ atm \approx P_2[/tex]
The new pressure is approximately 3.53 atmospheres.
