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?

Answer 1

Step-by-step explanation:

The given data is as follows.

`V_(1)` = 20 liter,
`V_(2)` = ?

`P_(1)` = 150 atm,
`P_(2)` = 1.00 atm

`T_(1)` = 27 + 273 = 300 K,
`T_(2)` = 37 + 273 = 310 K

Therefore, calculate the value of
`V_(2)` as follows

`(P_(1)V_(1))/(T_(1))` =
`(P_(2)V_(2))/(T_(2))`

`(150 atm * 20 liter)/(300 K)` =
`(1.00 atm * V_(2))/(310 K)}`

`V_(2) = (10 atm L K^(-1) * 310 K)/(1.00 atm)`

= 3100 liter

Therefore, we can conclude that the volume of the balloon is 3100 liter.

Answer 2

The number of moles will remain the same in the two cases

so we can equate using ideal gas equation which is PV =nRT

Where

P = Pressure

V = volume

n = moles

R = gas constant

T = temperature

for the two conditions

`(P_(1)V_(1))/(T_(1))=(P_(2)V_(2))/(T_(2))`

Putting values

`(P_(1)V_(1))/(T_(1)) =(150X20)/(300)=(P_(2)V_(2))/(T_(2))=(1XV_(2))/(310)`

Thus

V2 = 3100 L