Adding helium to a balloon increased its volume from 360.9 mL to 3.532 L. If the final number of moles of helium in the balloon is 22.3 mol, what was the initial number of moles of helium in the balloon? Assume the balloon contained only helium initially.
To solve this problem, we need to use the ideal gas law, which states:
PV = nRT
Where:
P is the pressure of the gas (constant)
V is the volume of the gas
n is the number of moles of gas
R is the ideal gas constant
T is the temperature in Kelvin (constant)
Since the pressure and temperature are constant in this problem, we can simplify the equation to:
V1/n1 = V2/n2
Where:
V1 is the initial volume of the gas
n1 is the initial number of moles of gas
V2 is the final volume of the gas
n2 is the final number of moles of gas
We can rearrange this equation to solve for n1:
n1 = (V1 * n2) / V2
Plugging in the values given in the problem:
V1 = 360.9 mL = 360.9 * 10^-3 L
n2 = 22.3 mol
V2 = 3.532 L
n1 = (360.9 * 10^-3 L * 22.3 mol) / 3.532 L
Calculating this expression will give us the initial number of moles of helium in the balloon.
To solve this problem, we can use the ideal gas law equation, which states that 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.
First, we need to convert the volumes from mL to L. We know that 1 L is equal to 1000 mL.
Initial volume = 360.9 mL = 360.9 mL / 1000 mL/L = 0.3609 L
Final volume = 3.532 L
Next, we can set up a ratio using the initial and final volumes to find the change in volume:
Initial volume / Final volume = Initial moles / Final moles
0.3609 L / 3.532 L = Initial moles / 22.3 mol
Now, we can solve for the initial moles:
Initial moles = (0.3609 L / 3.532 L) * 22.3 mol
Initial moles = 0.03686 mol
Therefore, the initial number of moles of helium in the balloon was approximately 0.03686 mol.