a balloon has a volume of 456 mL at a pressure of 1.0 atm. it is taken under water in a submarine to depth. where the air pressure in the submarine is 3.3 atm. what is the volume of the balloon? assume constant temperature?
P1V1 = P2V2
Aur
To find the volume of the balloon at a different pressure, we can use Boyle's Law, which states that the pressure and volume of a gas are inversely proportional when temperature is constant.
Boyle's Law equation:
P1 * V1 = P2 * V2
Where:
P1 = Initial pressure (1.0 atm)
V1 = Initial volume (456 mL)
P2 = Final pressure (3.3 atm)
V2 = Final volume (unknown)
We can rearrange the equation to solve for V2:
V2 = (P1 * V1) / P2
Substituting the given values into the equation:
V2 = (1.0 atm * 456 mL) / 3.3 atm
Calculating:
V2 = 456 mL * 1.0 / 3.3
V2 ≈ 138.18 mL
Therefore, the volume of the balloon at a pressure of 3.3 atm is approximately 138.18 mL.
To determine the volume of the balloon at a new pressure, we can use Boyle's Law. Boyle's Law states that at constant temperature, the product of pressure and volume is constant.
The equation for Boyle's Law is:
P1 * V1 = P2 * V2
Where:
P1 = initial pressure (1.0 atm)
V1 = initial volume (456 mL)
P2 = final pressure (3.3 atm)
V2 = final volume (unknown)
We can rearrange the equation to solve for V2:
V2 = (P1 * V1) / P2
Now we can substitute the given values into the equation:
V2 = (1.0 atm * 456 mL) / 3.3 atm
To calculate the volume, we need to convert mL to liters since atm is in liters:
V2 = (1.0 atm * 0.456 L) / 3.3 atm
Simplifying the equation gives us:
V2 = 0.456 L / 3.3
V2 ≈ 0.1382 L
Therefore, the volume of the balloon at a pressure of 3.3 atm is approximately 0.1382 liters.