If the pressure of the gas in a 2.31 L balloon is 0.120 atm and the volume increases to 7.14 L, what will be the final pressure of the air within the balloon? Round to the nearest hundredth. Don't forget the units.
P1V1=P2V2 if temperature is constant.
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To find the final pressure of the air within the balloon, we can use Boyle's Law, which states that the pressure and volume of a gas are inversely proportional at constant temperature.
Boyle's Law equation:
P1 * V1 = P2 * V2
where:
P1 = initial pressure of the gas
V1 = initial volume of the gas
P2 = final pressure of the gas (what we're trying to find)
V2 = final volume of the gas
Given:
P1 = 0.120 atm (initial pressure)
V1 = 2.31 L (initial volume)
V2 = 7.14 L (final volume)
We can rewrite the equation as:
(0.120 atm) * (2.31 L) = P2 * (7.14 L)
Simplifying:
0.2772 atm * L = 7.14 P2 * L
Now, we can cancel out the L (liters) on both sides of the equation:
0.2772 atm = 7.14 P2
To isolate P2, divide both sides by 7.14:
P2 = 0.2772 atm / 7.14
Calculating P2:
P2 ≈ 0.03874 atm
So, the final pressure of the air within the balloon will be approximately 0.03874 atm.