A cylinder containing 15L 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 2L at a pressure of 1.1 atm. What is the max number of balloons that can be inflated? Assume that the gas in the cylinder is at the same as the inflated balloon. (The empty cylinder will still contain helium at 1.1atm)
I assume that the next to last sentence should read, "Assume that the gas in the cylinder AT THE END is at the same PRESSURE as the inflated balloons.
1. Calculate mols gas in the cylinder initally using PV = nRT. No T is listed so use any T (in kelvin) but always use the same T.
2. Calculate mols gas in the cylinder using PV = nRT. P will be 1.1 atm and T will be the same T used in step 1.
3. Subtract total mols - mols at the end to find mols gas available to fill balloons.
4. Calculate moles required to fill a single balloon from PV = nRT.
5. Now calculate the number of balloons that can be filled. Remember that if you get a fraction to round to the lower number.
Post your work if you get stuck.
To determine the maximum number of balloons that can be inflated, we can use the ideal gas law equation:
PV = nRT
Where:
- P is the pressure
- V is the volume
- n is the number of moles
- R is the ideal gas constant
- T is the temperature
First, let's convert the pressure and volume to the same units (atm and liters):
Pressure of helium in the cylinder:
P1 = 165 atm
Volume of helium in the cylinder:
V1 = 15 L
Pressure of the balloons:
P2 = 1.1 atm
Volume of each balloon:
V2 = 2 L
To determine the number of balloons that can be filled, we need to calculate the number of moles of helium gas in the cylinder and divide it by the number of moles required to fill each balloon.
1. Calculate the number of moles of helium gas in the cylinder:
Using the ideal gas law equation, rearranged to solve for n:
n1 = (P1 * V1) / (RT)
Where R is the ideal gas constant (0.0821 L·atm/(mol·K)) and T is the temperature in Kelvin (which we assume to be constant).
2. Calculate the number of moles of helium gas required to fill each balloon:
Using the ideal gas law equation, rearranged to solve for n:
n2 = (P2 * V2) / (RT)
3. Determine the maximum number of balloons that can be inflated:
n_max = n1 / n2
Now, let's calculate each step:
Step 1: Calculate the number of moles of helium gas in the cylinder (n1)
n1 = (P1 * V1) / (RT)
= (165 atm * 15 L) / (0.0821 L·atm/(mol·K) * T)
Assuming the temperature is constant, we can omit it from the equation.
n1 = (165 atm * 15 L) / (0.0821 L·atm/(mol·K))
≈ 285.15 mol
Step 2: Calculate the number of moles of helium gas required to fill each balloon (n2)
n2 = (P2 * V2) / (RT)
= (1.1 atm * 2 L) / (0.0821 L·atm/(mol·K) * T)
Again, assuming the temperature is constant, we can omit it from the equation.
n2 = (1.1 atm * 2 L) / (0.0821 L·atm/(mol·K))
≈ 0.05357 mol
Step 3: Determine the maximum number of balloons that can be inflated (n_max)
n_max = n1 / n2
= 285.15 mol / 0.05357 mol
≈ 5328.2
Therefore, the maximum number of balloons that can be inflated is approximately 5328.
To determine the maximum number of balloons that can be inflated using the given cylinder of helium gas, we need to calculate the volume of gas required to fill one balloon and then divide the total volume of gas in the cylinder by this value.
First, let's calculate the volume of gas required to fill one balloon. We are given that each balloon needs to be filled to a volume of 2L.
Now, we need to consider the pressure of the gas in the cylinder and the pressure at which the balloons are to be inflated. Since the gas in the cylinder is at a pressure of 165 atm, we'll use the combined gas law to adjust the volume of gas in the cylinder to the same pressure as the balloons.
The combined gas law states: P1 x V1 / T1 = P2 x V2 / T2
Where:
P1 = initial pressure (pressure in the cylinder) = 165 atm
V1 = initial volume (volume in the cylinder) = 15L
T1 = initial temperature (assume constant)
P2 = final pressure (pressure in the balloon) = 1.1 atm
V2 = final volume (volume of one balloon) = 2L
T2 = final temperature (assume constant)
Since we assume the temperatures are constant and cancel out in the equation, we can simplify it further:
P1 x V1 = P2 x V2
Now we can substitute the values into the equation:
(165 atm) x (15L) = (1.1 atm) x (V2)
V2 = (165 atm x 15L) / (1.1 atm)
Simplifying the equation, we get:
V2 = 2250L / 1.1 atm
V2 ≈ 2045.45 L/atm
Next, we divide the total volume of gas in the cylinder (15L) by the volume of gas required to fill one balloon (approximately 2045.45 L/atm):
Number of balloons = Total gas volume / Volume of gas per balloon
Number of balloons = 15L / 2045.45 L/atm
Using the unit analysis, we can convert atm to L:
Number of balloons ≈ 0.007346 atm x 1 balloon / atm
Number of balloons ≈ 0.007346 balloons
Finally, to get a whole number, we round down the result:
Number of balloons = 0
Hence, with the given specifications, the maximum number of balloons that can be inflated using the provided cylinder of helium gas is 0.