How to find out the answer?

Question

when a smaller weather balloon (12.5 L) is full it contains 0.25 mol of helium. However when the technician pulled it out of storage at 25 c its volume was only 8.4 L. Realizing some helium has leaked out, he refilled it. How many moles of helium were added to fill it up at 25 c

1. 0.001 mol
2. 1.0 mol
3. 0.54 mol
4. 0.08 mol
5. 5.4 mol

Answer 1

Assuming the only thing that has changed in the number of moles (temperature, pressure, volume are constant), then volume will be proportional to moles:

0.25 mol / 12.5 L = x mol / 8.4 L

x = 0.168 moles

To get it back to 0.25 moles, we have to add 0.082 moles

Looking at this another way:

V1/n1 = V2/n2

V1 = initial volume = 12.5 L

n1 = initial moles = 0.25 mol

V2 = final volume = 8.4 L

n2 = final moles = ?

12.5 L / 0.25 mol = 8.4 L / x mols

x = 0.168 mols

0.25 mol - 0.168 mol = 0.082 moles need to be added