A 14.5-L tank is filled with H2 to a pressure of 2.00 102 atm. How many balloons (each 2.00 L) can be inflated to a pressure of 1.00 atm from the tank? Assume that there is no temperature change and that the tank cannot be emptied below 1.00 atm pressure.
Use PV = nRT to calculate the number of moles, n, in the 14.5L tank. (Pressure = 200 atm - 1 atm since 1 atm is the minimum). Then use PV = nRT to determine the moles to fill one (1) balloon. Set up a proportion to determine how many balloons can be filled.
Why did the balloon go to the party alone?
Because it didn't have the right gas pressure to attract any friends!
But don't worry, I have an answer for you! To find out how many balloons can be inflated from the tank, we need to consider the change in pressure.
Given that the initial pressure in the tank is 2.00 x 10^2 atm, and we want to inflate the balloons to a pressure of 1.00 atm, we can use the ideal gas law to determine the number of moles of H2 gas in the tank.
PV = nRT
Where:
P = pressure (in atm)
V = volume (in liters)
n = number of moles
R = ideal gas constant (0.0821 L•atm/(mol•K))
T = temperature (in Kelvin)
Since the temperature and volume are constant, we can simplify the equation to:
P1V1 = nRT
n = (P1V1) / (RT)
n = (2.00 x 10^2 atm) x (14.5 L) / (0.0821 L•atm/(mol•K) x T)
We know that the pressure has to be equal to 1.00 atm, so we can rearrange the equation to solve for T:
T = (P1V1) / (nR)
T = (2.00 x 10^2 atm) x (14.5 L) / (1 mol x 0.0821 L•atm/(mol•K))
T = 3.59 x 10^3 K
Now, we can use the ideal gas law again to find the number of moles of gas required to inflate one balloon.
n = PV / RT
n = (1.00 atm) x (2.00 L) / (0.0821 L•atm/(mol•K) x (3.59 x 10^3 K)
n = 5.11 x 10^-2 mol
Finally, to find the number of balloons, we divide the total number of moles in the tank by the number of moles required for each balloon:
Number of balloons = n (total gas) / n (gas per balloon)
Number of balloons = (P1V1) / T / (PV / RT)
Number of balloons = (2.00 x 10^2 atm) x (14.5 L) / (3.59 x 10^3 K) / ((1.00 atm) x (2.00 L) / (0.0821 L•atm/(mol•K) x (3.59 x 10^3 K))
Number of balloons ≈ 202
So, you can inflate approximately 202 balloons from the tank at a pressure of 1.00 atm. Just make sure they don't float away too high!
To solve this problem, we can use Boyle's Law, which states that for a given amount of gas at a constant temperature, the pressure and volume are inversely proportional.
Step 1: Convert the given pressure to the same units as the desired pressure.
The given pressure is 2.00 x 10^2 atm, and we want to convert it to 1.00 atm. Since the two pressures are already in atm, no conversion is needed.
Step 2: Use Boyle's Law to find the volume of gas needed to achieve the desired pressure.
According to Boyle's Law, P1V1 = P2V2, where P1 and V1 are the initial pressure and volume, and P2 and V2 are the final pressure and volume.
Using the formula, we can calculate the volume of gas needed:
(2.00 x 10^2 atm) x (14.5 L) = (1.00 atm) x V2
V2 = (2.00 x 10^2 atm x 14.5 L) / (1.00 atm)
V2 = 2.00 x 10^3 L
Step 3: Determine the number of balloons that can be inflated.
Each balloon has a volume of 2.00 L, so we need to divide the total volume of gas by the volume of each balloon:
Number of balloons = V2 / volume of each balloon
Number of balloons = (2.00 x 10^3 L) / (2.00 L)
Number of balloons = 10^3
Therefore, you can inflate 1000 balloons (each 2.00 L) to a pressure of 1.00 atm from the given tank.
To solve this problem, we need to find out how many balloons can be inflated using the given tank of H2.
First, let's determine the amount of H2 in the tank. We can use the ideal gas law equation to calculate the moles of gas present, given the pressure, volume, and gas constant (R). The formula for the ideal gas law is:
PV = nRT
Where:
P = pressure
V = volume
n = number of moles
R = gas constant (0.0821 L.atm/mol.K)
T = temperature (which is not given but we assume it is constant)
Rearranging the equation, we can solve for n:
n = PV / RT
Substituting the given values:
P = 2.00 x 10^2 atm (pressure in the tank)
V = 14.5 L (volume of the tank)
R = 0.0821 L.atm/mol.K (gas constant)
Assuming the temperature is constant, we can find the number of moles of H2 in the tank.
n = (2.00 x 10^2 atm) x (14.5 L) / (0.0821 L.atm/mol.K)
Calculating this expression, we find the number of moles (n) of H2 in the tank.
Now, we need to determine how many balloons each containing 2.00 L volume can be filled using the H2 in the tank. Since the pressure is decreasing, we can use the ideal gas law again to calculate the new number of moles.
Assuming the temperature and number of moles remain constant, we can use the following equation:
P1V1 = P2V2
Where:
P1 = initial pressure (2.00 x 10^2 atm)
V1 = initial volume (volume of the tank, 14.5 L)
P2 = final pressure (1.00 atm)
V2 = final volume (volume of one balloon, 2.00 L)
Rearranging the equation, we can solve for the final volume, V2:
V2 = (P1V1) / P2
Substituting the given values:
V2 = (2.00 x 10^2 atm x 14.5 L) / 1.00 atm
Calculating this expression, we find the volume V2, which represents the volume of gas required to inflate one balloon.
Finally, we can find the number of balloons that can be inflated by dividing the total number of moles (n) by the volume of one balloon (V2) in moles:
Number of balloons = n / V2
Calculating this expression will give us the final answer, the number of balloons that can be inflated from the tank.