At a pressure of 2.4 atm a balloon has a volume of 9.8 L. If the pressure is decreased to 0.96 atm (at constant temperature), what is the new volume of the balloon?
P1V1 = P2V2
I know how to set the problem up but when I go to solve I get the wrong answer can you help me please? I really need help
To find the new volume of the balloon, you can use the combined gas law equation. The combined gas law is derived from Boyle's law, Charles's law, and Gay-Lussac's law and relates the pressure, volume, and temperature of a gas.
The combined gas law equation is as follows:
(P1 * V1) / T1 = (P2 * V2) / T2
Where:
P1 and P2 are the initial and final pressures (in atm)
V1 and V2 are the initial and final volumes (in L)
T1 and T2 are the initial and final temperatures (in Kelvin)
In this case, we are given the initial pressure P1 = 2.4 atm and the initial volume V1 = 9.8 L. The problem states that the temperature remains constant, so T1 = T2.
We are also given the final pressure P2 = 0.96 atm and we need to find the final volume V2.
Plugging in the given values into the combined gas law equation, we have:
(2.4 atm * 9.8 L) / T1 = (0.96 atm * V2) / T1
Since T1 = T2, we can cancel out the temperature terms on both sides of the equation:
2.4 atm * 9.8 L = 0.96 atm * V2
Now, we can solve for V2 by rearranging the equation:
V2 = (2.4 atm * 9.8 L) / 0.96 atm
Simplifying the expression, we have:
V2 ≈ 24.41 L
Therefore, the new volume of the balloon, at a pressure of 0.96 atm, would be approximately 24.41 L.