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.
I would use PV = nRT and determine the number of moles (n) in the tank. Use it again to determine the number of moles for each balloon at 2. L apiece. Go from there.
To solve this problem, we need to calculate the total volume of H2 gas in the tank and then divide it by the volume of each balloon.This will give us the total number of balloons that can be inflated.
Given:
Tank volume = 14.5 L
Tank pressure = 2.00 × 10^2 atm
Balloon volume = 2.00 L
Balloon pressure = 1.00 atm
Step 1: Convert the tank pressure to the same units used for the balloon pressure.
Since the tank pressure is given in atm, no conversion is needed.
Step 2: Use the ideal gas law to calculate the moles of H2 in the tank.
The ideal gas law equation is 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. Since the temperature remains constant and the gas is H2, we can rewrite the equation as:
n = PV/RT
To calculate the moles of H2, we first need to convert the tank pressure from atm to the SI unit (Pascal).
1 atm = 101325 Pa
So, the tank pressure in Pascal is:
2.00 × 10^2 atm × 101325 Pa/atm = 2.02 × 10^4 Pa
Now, we can use the ideal gas law to find the moles of H2:
n = (2.02 × 10^4 Pa) × (14.5 L) / [(8.314 J/mol·K) × T]
(T is not given, but since it remains constant, it cancels out in the calculations)
n = (2.02 × 10^4 Pa × 14.5 L) / 8.314 J/mol·K
Step 3: Calculate the moles of H2 gas using the given values.
n = (2.02 × 10^4 Pa × 14.5 L) / 8.314 J/mol·K
n ≈ 3889.8 moles
Step 4: Calculate the volume of H2 gas in the tank.
Using the ideal gas law equation, we can rearrange it to find the volume:
V = nRT/P
V = (3889.8 moles × 8.314 J/mol·K × T) / 2.02 × 10^4 Pa
(T is not given, but since it remains constant, it cancels out in the calculations)
V = (3889.8 moles × 8.314 J/mol·K) / 2.02 × 10^4 Pa
V ≈ 16.0 L
Step 5: Determine the number of balloons that can be inflated.
Now we can divide the volume of H2 gas in the tank by the volume of each balloon to find the number of balloons that can be inflated:
Number of balloons = Volume of H2 gas / Volume of each balloon
Number of balloons = 16.0 L / 2.00 L
Number of balloons = 8
Therefore, approximately 8 balloons can be inflated to a pressure of 1.00 atm from the tank.