A cylinder containing 15.0 L of helium gas at a pressure of 165 atm is to be used to fill party balloons. Each balloon must be filled to a volume of 2.0 L at a pressure of 1.1 atm. What is the maximum number of balloons that can be inflated? Assume that the gas in the cylinder is at the same temperature as the inflated balloons. (HINT: The "empty" cylinder will still contain helium at 1.1 atm.)
*gary sounds*
To determine the maximum number of balloons that can be inflated, we need to find out how many balloons can be filled with the amount of helium in the cylinder.
First, we need to calculate how much helium is needed to fill one balloon. The volume of one balloon is given as 2.0 L.
Next, we need to compare the initial pressure of the helium gas in the cylinder (165 atm) to the pressure in a filled balloon (1.1 atm). Since the temperature is assumed to be the same, we can use the ideal gas law to compare the initial and final conditions.
The ideal gas law equation is:
PV = nRT
Where:
P = Pressure
V = Volume
n = Number of moles
R = Ideal gas constant
T = Temperature
For the initial conditions in the cylinder, we can rearrange the ideal gas law equation to solve for the number of moles:
n1 = PV1 / RT
For the final conditions in one filled balloon, we can rearrange the ideal gas law equation to solve for the number of moles:
n2 = PV2 / RT
Since the temperature is constant, we can cancel it out in the equation. Therefore, we can rewrite the equations as:
n1 = PV1 / R
n2 = PV2 / R
Substituting the values given in the question:
P1 = 165 atm
P2 = 1.1 atm
V1 = 15.0 L
V2 = 2.0 L
Let's calculate the number of moles for the initial and final conditions:
n1 = (165 atm * 15.0 L) / R
n2 = (1.1 atm * 2.0 L) / R
Since both n1 and n2 are at the same temperature, we can use the same R value for both calculations.
Now, we can determine the maximum number of balloons that can be inflated by dividing n1 by n2:
Max number of balloons = n1 / n2
Keep in mind that balloons cannot be fractionally inflated, so the maximum number of balloons would be the whole number value of the result.
While I don't have access to the current value of the ideal gas constant (R) at the moment, you can find its value in reliable sources such as textbooks or online scientific references. Once you have the value of R, you can substitute it into the equations and perform the calculations to find the maximum number of inflated balloons.
Remember to use the same units for pressure and volume to ensure accuracy in calculations.
Use PV = nRT and calcualate mols in the cylinder.
Use PV = nRT and calculate mols left when the cylinder is "empty".
Subtract to see mols He available to fill balloons.
Use PV = nRT and calculate mols needed to fill one balloon.
mols He/1 balloon x # balloons = total mols He available.