A balloon is filled with He to a pressure of 1.06 atm. The volume of the balloon at 25oC is 1.30 x 104 L. How many cylinders of He gas are needed to fill the balloon if the pressure in the cylinder at 20oC is 98.5 atm and the volume of the cylinder is 40.0 L. [You may have some He left in one of the cylinders.]
a)1
b) 2
c) 3
d) 4
e) 5
Actually, you don't need ANY He gas to fill the balloon. The problem says it is filled with He to those particular parameters. However, I presume the person writing the problem intended us to calculate the number of cylinders of He needed IF the balloon were empty.
Can't you use PV = nRT for the balloon and solve for n (number of mols He needed)? Then calculate n for the gas cylinders to see how much each cylinder contains? From there you can determine the number of cylinders needed. I have a fraction so remember to round that up to the next cylinder. Check my thinking. Post your work if you get stuck.
To solve this problem, we can begin by using the ideal gas law equation:
PV = nRT
Where:
P = pressure
V = volume
n = number of moles
R = ideal gas constant
T = temperature
We need to find the number of cylinders needed to fill the balloon, so we need to calculate the number of moles of helium gas necessary.
First, we need to calculate the number of moles of helium gas in the balloon. We can rearrange the ideal gas law equation to solve for the number of moles:
n = PV / RT
Given:
P_balloon = 1.06 atm
V_balloon = 1.30 x 10^4 L
T_balloon = 25°C = 298 K
Plugging in the values into the equation:
n_balloon = (1.06 atm) * (1.30 x 10^4 L) / [(0.0821 L·atm/mol·K) * (298 K)]
Now, we need to calculate the number of moles of helium gas in one cylinder. Using the same approach:
P_cylinder = 98.5 atm
V_cylinder = 40.0 L
T_cylinder = 20°C = 293 K
n_cylinder = (98.5 atm) * (40.0 L) / [(0.0821 L·atm/mol·K) * (293 K)]
Next, we can calculate the number of cylinders needed:
Number of cylinders = n_balloon / n_cylinder
Finally, we can substitute the values into the equation and calculate the number of cylinders needed to fill the balloon.