Question

A 20 liter cylinder of helium at a pressure of 150 atm and a temperature of 27°C is used to fill a balloon at 1.00 atm and 37°C. What is the volume of the balloon?
A) 2400 Liters

B) 2900 Liters

C) 3000 Liters

D) 3100 Liters

Answer 1

@Missiey

Answer 2

b

Answer 3

want a breakdown of it

Answer 4

P1V1=nRT1
P2V2=nRT2
R=P1V1/nT1=P2V2/nT2
since the number of moles of helium is the same inside the cylinder and balloon it can be cancelled from both sides workout what V2 by plugging in the givens of your question.

Answer 5

You'll want to run the numbers with the equation you got, because b is not the correct answer...don't forget to convert your temperatures into degrees K instead of C!

Answer 6

Another way to look at this is that the number of moles (\(n\)) and the gas constant \(R\) are both constants, so we can replace them with another constant, which we can call whatever we want. I'll use \(k\).

Then the ideal gas law becomes
\[PV = kT\]or\[k = \frac{PV}{T}\]which means pressure and volume vary jointly, and inversely with temperature. Our pressure is going from 150 to 1 atm, so if we hold the temperature constant, our new volume must be 150/1 * the old volume, or 3000 L. However, we also slightly increase the temperature, and for our ratio to remain the same, we must also slight increased the volume to compensate (pressure is fixed), so that gives us our final answer.