You have a 22L cylinder of helium at a pressure of 150atm and a temperature of 31C. How many ballons can you fill, each with a volume of 5.0L, on a day when the atmospheric pressure is 755mmHg and the temperature is 22C?
I know I use PV=nRT, but what numbers do I plug in and why couldn't I use p1v1/t1=p2v2/t2?
You may use the other formula if it's easier for you and you plug in the right numbers. DON'T use 5.0 L as V2 and you must change one of the pressures to make the same unit (150 atm must be changed to mm or 755 mm must be changed to atm). And T must be in Kelvin.
For PV = nRT
150 atm = P
V = 22 L
n = ??
R = 0.08205
T = 31 + 273 = 304.
Then use PV = nRT again.
P = 755 mm = 755/760 = ?? atm.
V = solve for this.
n = use from calculation above.
R = same constant as above.
T = 22 + 273 = 295
Then use the volume from this last calculation to determine how many 5.0 L balloons can be filled.
Oh, calculating balloons? That's a gas! Now, let's get those numbers floating around!
First, let's stick with the good old PV=nRT equation. It's a classic! For the initial state, we have a 22L cylinder of helium at 150 atm and 31°C. The final state will be a bunch of balloons, each with a volume of 5.0L, at an atmospheric pressure of 755 mmHg and 22°C.
Now, let's break it down step by step. Here's what you can do:
1. Convert the initial pressure (150 atm) to the final state's unit (mmHg). Since 1 atm is approximately 760 mmHg, the initial pressure would be around 150 * 760 = 114,000 mmHg.
2. Plug in the values into the equation: PV = nRT.
For the initial state:
P1 = 114,000 mmHg (pressure)
V1 = 22 L (volume)
T1 = 31°C + 273 = 304K (temperature)
For the final state:
P2 = 755 mmHg (pressure)
V2 = 5.0 L (volume)
T2 = 22°C + 273 = 295K (temperature)
3. Solve for n (number of moles of helium) using the initial state values: n = (P1 * V1) / (R * T1). R is the gas constant, which is approximately 0.0821 L atm/(mol K).
4. Now, using the number of moles (n), find out how many balloons you can fill.
Since each balloon has a volume of 5.0 L, divide the total volume (22L) by the volume of one balloon (5.0L) to get the number of balloons.
5. Voila! You found out how many balloons you can fill. Now, go ahead and have a blast!
As for why you can't use the equation P1V1/T1 = P2V2/T2, that equation is ideal for comparing initial and final states of gases, assuming constant moles. However, in your case, the number of moles is changing as you fill the balloons, so it won't give you the correct answer. Gases can be tricky like that sometimes!
Hope that brings a balloon of joy to your gas calculations!
To determine the number of balloons that can be filled, 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, and T is the temperature in Kelvin.
First, let's convert the given temperature from Celsius to Kelvin:
Temperature in Kelvin = 31°C + 273.15 = 304.15 K
Now, let's plug in the given values into the ideal gas law equation to find the number of moles of helium gas in the 22L cylinder at 150 atm and 304.15 K:
(150 atm) (22 L) = n (0.0821 L × atm / mol × K) (304.15 K)
Simplifying the equation:
3300 atm × L = n × 24.9999155 L × atm / K
Dividing both sides of the equation by 24.9999155 L × atm / K:
n = (3300 atm × L) / (24.9999155 L × atm / K)
n ≈ 132.01 mol
Now that we have the number of moles of helium gas, let's use the second equation, p1v1/t1 = p2v2/t2, to calculate the number of balloons that can be filled with a volume of 5.0L, considering the given atmospheric pressure and temperature.
Using the equation p1v1/t1 = p2v2/t2, we have:
(150 atm) (22 L) / (304.15 K) = (755 mmHg) (v2) / (295.15 K)
Converting mmHg to atm:
755 mmHg = 755 mmHg / (760 mmHg/1 atm) = 0.9934 atm
Substituting the values into the equation and solving for v2:
(150 atm) (22 L) / (304.15 K) = (0.9934 atm) (v2) / (295.15 K)
Simplifying the equation:
6600 atm L / 304.15 K = 0.0034 atm (v2) / K
Dividing both sides of the equation by 0.0034 atm / K:
v2 = (6600 atm L × K) / (0.0034 atm)
v2 ≈ 1,941,176.47 L
Finally, we can determine the number of balloons filled with a volume of 5.0 L using the number of moles (n) and the volume of a single balloon (v2):
Number of balloons = n × total volume / volume of a single balloon
Number of balloons ≈ 132.01 mol × 22,000 L / 5.0 L
Number of balloons ≈ 579,884.2
Therefore, you can fill approximately 579,884 balloons, each with a volume of 5.0 L, given the provided conditions.