Answer:
[tex]\boxed {\boxed {\sf 10.8 \ atm}}[/tex]
Explanation:
We are asked to find the new pressure of a gas after a change in volume. Since the temperature remains constant, we are only concerned with pressure and volume.
We will use Boyle's Law, which states that the volume and pressure of a gas are inversely proportional. The formula for this law is:
[tex]P_1V_1=P_2V_2[/tex]
The gas has an original pressure of 1.51 atmospheres and a volume of 8 liters.
[tex](1.51 \ atm)(8 \ L)=P_2V_2[/tex]
The volume is compressed to 1.12 liters and the new pressure is unknown.
[tex](1.51 \ atm)(8 \ L)=P_2 (1.12 \ L)[/tex]
We are solving for the new pressure, so we must isolate the variable [tex]P_2[/tex]. It is being multiplied by 1.12 liters. The inverse operation of multiplication is division. Divide both sides of the equation by 1.12 L.
[tex]\frac {(1.51 \ atm)(8 \ L)}{1.12 \ L}= \frac{P_2(1.12 \ L)}{1.12 \ L}[/tex]
[tex]\frac {(1.51 \ atm)(8 \ L)}{1.12 \ L}= P_2[/tex]
The units of liters (L) cancel.
[tex]\frac {(1.51 \ atm)(8 )}{1.12}= P_2[/tex]
Multiply the numerator.
[tex]\frac {12.08 \ atm}{1.12}= P_2[/tex]
[tex]10.7857143 \ atm = P_2[/tex]
Round to the nearest tenth. The 8 in the hundredth place tells us to round the 7 in the tenth place up to an 8.
[tex]10.8 \ atm \approx P_2[/tex]
The new pressure after the volume is compressed is approximately 10.8 atmospheres.
