1.50 liters tank filled with helium at 125 atm is used to fill balloons. The pressure in each balloon is 950 torr and the volume of each is 1.20 liters. How many ballons can be filled?
Well, let's do some math(ematics)!
First, we need to convert the pressure of the tank from atm to torr. We have 125 atm, and there are 760 torr in 1 atm. So, 125 atm x 760 torr/atm = 95000 torr.
Now, let's find out how much helium each balloon contains. The difference between the pressure in each balloon and the pressure inside the tank is 95000 torr - 950 torr = 94050 torr.
Next, we can use the ideal gas law equation, PV = nRT, to find the number of moles of helium in each balloon.
We have the volume (V) of each balloon, which is 1.20 L, and the pressure (P) inside the balloon, which is 94050 torr. We also know that the gas constant (R) is 0.0821 L•atm/mol•K, and the temperature (T) is not given.
Since the temperature is not given, and assuming it remains constant, we can take it out of the equation. So the equation becomes PV = nRT -> n = PV/RT.
Now, let's plug in the values: n = (94050 torr x 1.20 L) / (0.0821 L•atm/mol•K).
Calculating this, we find that n ≈ 1387 moles.
Now, let's find how many moles of helium are in the tank by using the same equation: n = (125 atm x 1.50 L) / (0.0821 L•atm/mol•K).
Calculating this, we find that n ≈ 226 moles.
Finally, divide the total number of moles by the number of moles per balloon to find how many balloons can be filled: 226 moles / 1387 moles/balloon ≈ 0.16 balloons.
Hmm, that's an interesting result! It seems we can fill about 0.16 balloons. I'm not sure how to have a fraction of a balloon though... Maybe you can inflate half of a balloon? Just kidding, I'm clowning around! Since we can't have a fraction of a balloon, the answer is actually 0. Let's keep the tank for another party!
To determine how many balloons can be filled, we need to compare the initial volume and pressure of the helium tank with the volume and pressure of each balloon.
1. Convert the initial pressure of the helium tank from atm to torr:
125 atm x 760 torr/atm = 95,000 torr
2. Determine the volume of helium in the tank:
Volume of helium in the tank = 1.50 liters
3. Determine the number of moles of helium in the tank using the Ideal Gas Law equation:
PV = nRT, where:
P = pressure of the helium tank (95,000 torr),
V = volume of the helium tank (1.50 liters),
n = number of moles,
R = ideal gas constant (0.08206 L·atm/mol·K),
T = temperature (assuming constant)
Rearranging the equation to solve for n, we have:
n = PV / RT
4. Assuming constant temperature, we can solve for n:
n = (95,000 torr x 1.50 liters) / (0.08206 L·atm/mol·K x T)
5. Now let's analyze the conditions in each balloon. The pressure in each balloon is given as 950 torr, and the volume of each balloon is 1.20 liters.
6. Use the Ideal Gas Law equation to determine the number of moles of helium in each balloon:
PV = nRT, where:
P = pressure in the balloon (950 torr),
V = volume of the balloon (1.20 liters),
n = number of moles of helium in each balloon,
R = ideal gas constant (0.08206 L·atm/mol·K),
T = temperature (assuming constant)
Rearranging the equation to solve for n, we have:
n = PV / RT
7. Assuming constant temperature, we can solve for n:
n = (950 torr x 1.20 liters) / (0.08206 L·atm/mol·K x T)
8. Since the temperature is assumed constant, the temperature cancels out, and we can compare the number of moles in the tank to the number of moles in each balloon.
9. To find out how many balloons can be filled, divide the number of moles in the tank by the number of moles in each balloon:
Number of balloons = moles in tank / moles in each balloon
10. Substitute the expressions for moles in the equation:
Number of balloons = (PV_tank / RT) / (PV_balloon / RT)
11. Cancel out the R and T terms from the equation:
Number of balloons = (PV_tank) / (PV_balloon)
12. Substitute the values:
Number of balloons = (95,000 torr x 1.50 liters) / (950 torr x 1.20 liters)
13. Calculate the result:
Number of balloons = 142.5 / 1140
Number of balloons ≈ 0.125
Therefore, approximately 0.125 (or 1/8) of a balloon can be filled with the helium in the tank. Since you cannot have a fraction of a balloon, the tank cannot fill any complete balloons in these conditions.
To find out how many balloons can be filled, we need to compare the amount of helium in the tank to the amount of helium required to fill each balloon.
First, let's convert the given pressure in the tank from atm to torr:
125 atm × 760 torr/atm = 95,000 torr
Now, let's use the combined gas law to calculate the number of moles of helium in the tank:
P₁V₁/T₁ = P₂V₂/T₂
Where:
P₁ = initial pressure (95,000 torr)
V₁ = initial volume (1.50 liters)
T₁ = initial temperature (let's assume it's constant)
P₂ = final pressure (950 torr)
V₂ = final volume (1.20 liters)
T₂ = final temperature (also assumed constant)
Since T₁ and T₂ are constant, we can simplify the equation to:
(P₁ × V₁) / P₂ = V₂
Now let's plug in the values:
(95,000 torr × 1.50 liters) / 950 torr = V₂
= 150,000 / 950 = V₂
≈ 157.89 liters ≈ 158 balloons
So, approximately 158 balloons can be filled with the given amount of helium in the tank.
I would use PV = nRT and solve for n for the 1.5 L tank at 125 atm. You aren't given T so just make up a convenient T and use it in this and the next calcn.
Then use PV = nRT again for the balloons to determine moles for each balloon, then divide the larger number by the smaller number to find the number of balloons that can be filled.