A cylinder containing 11.0L of helium gas at a pressure of 165atm is to be used to fill birthday balloons to a volume of 2.50L per balloon and at a pressure of 1.10atm. What is the maximum number of balloons that can be inflated at a constant temperature? (remember that 11.0L of gas at 1.10atm will remain in the "exhausted" cylinder.)
I'm stuck and I keep confusing myself. This is what I got using Boyle's law:
P1=165atm P2=1.10atm
V1=11.0L V2=2.50L
P1V1=1815 P2V2= 2.75
To get the number of balloons, do I divide 1815 by 2.75 to get 660?
no
To solve this problem, you are on the right track by using Boyle's law, which states that the pressure and volume of a gas are inversely proportional at constant temperature. However, to calculate the maximum number of balloons that can be inflated, we need to consider the total volume of helium gas available and the volume of each balloon.
First, we need to calculate the total volume of helium gas in the cylinder. We are given that the initial volume of the cylinder is 11.0L, and we know that this volume will remain in the cylinder after all the balloons are inflated. So, we can subtract this volume from the total volume to find the helium gas available for the balloons:
Total Volume of Helium Gas Available = Initial Volume of Cylinder - Remaining Volume in Cylinder
= 11.0L - 2.50L (Volume of each balloon)
= 8.50L
Now, since the pressure and temperature are constant, we can use Boyle's law to find the maximum number of balloons that can be inflated. Boyle's law equation is:
P1 * V1 = P2 * V2
Given:
P1 = 165 atm (initial pressure of the helium gas in the cylinder)
V1 = Total Volume of Helium Gas Available (8.50L)
P2 = 1.10 atm (pressure at which each balloon is to be filled)
V2 = 2.50L (volume of each balloon)
Plugging in the values into the equation:
165 atm * 8.50L = 1.10 atm * (2.50L * number of balloons)
Number of balloons = (165 atm * 8.50L) / (1.10 atm * 2.50L)
After canceling out the units and simplifying the equation:
Number of balloons ≈ 108.18
Since we cannot have a fraction of a balloon, we must round down to the nearest whole number. Therefore, the maximum number of balloons that can be inflated at a constant temperature is 108.