A 1.50 liter 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
balloon is 1.20 liters. How many balloons can
be filled?
Answer in units of balloons
Use PV = nRT and solve for n. Then determine n it takes to fill each balloon.
Then # balloons x (mol/baloon) = total n and solve for # balloons.
To determine the number of balloons that 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 pressure units to a consistent value. One atmosphere (atm) is equal to 760 torr. So, 125 atm can be converted to torr as follows:
125 atm * 760 torr/atm = 95,000 torr
Now, let's calculate the amount of helium in the tank by using the ideal gas law equation:
PV = nRT
Where:
P = pressure (in torr)
V = volume (in liters)
n = number of moles
R = ideal gas constant (0.0821 L·atm/mol·K)
T = temperature (in Kelvin)
Since we want to know the number of balloons that can be filled, we can solve for n (number of moles) using the given values:
n = PV / RT
n = (95,000 torr * 1.50 L) / (0.0821 L·atm/mol·K * T)
Now, let's calculate the number of balloons that can be filled by dividing the amount of helium in the tank by the amount of helium needed for each balloon:
Number of balloons = n / (Volume of each balloon)
Number of balloons = (95,000 torr * 1.50 L) / (0.0821 L·atm/mol·K * T * 1.20 L)
Please note that there is no specific value given for the temperature (T). Therefore, we need the temperature value to provide an accurate answer.
To calculate how many balloons can be filled with the given volume of helium, we need to consider the change in pressure and volume when transferring the helium from the tank to each balloon.
We can use the ideal gas law to relate pressure (P), volume (V), and the number of moles (n) of helium. The ideal gas law equation is:
PV = nRT
Where:
P = pressure
V = volume
n = number of moles
R = ideal gas constant (0.0821 L·atm/mol·K)
T = temperature
In this case, we can assume the temperature is constant, so the equation can be simplified to:
P1V1 = P2V2
Where:
P1 = initial pressure (in the tank) = 125 atm
V1 = initial volume (in the tank) = 1.50 L
P2 = final pressure (in each balloon) = 950 torr (which is equivalent to 0.950 atm)
V2 = final volume (in each balloon) = 1.20 L
Now let's substitute the values into the equation:
(125 atm) (1.50 L) = (0.950 atm) (V2)
Solving for V2:
V2 = (125 atm * 1.50 L) / 0.950 atm
V2 ≈ 197.37 L
Therefore, the volume of helium that can be transferred to each balloon is approximately 197.37 L.
To determine the number of balloons that can be filled, we need to divide the total volume of helium (1.50 L) by the volume required per balloon (1.20 L):
Number of balloons = (1.50 L) / (1.20 L)
Number of balloons ≈ 1.25
So, approximately 1.25 balloons can be filled with the given volume of helium.
However, since we cannot have a fraction of a balloon, the answer should be rounded down to the nearest whole number. Thus, the final answer is 1 balloon.