Question

A balloon is filled with 4.0L air to an internal pressure of 1.25 atm at 21.2°C. That balloon is carried

to the bottom of a lake, where the temperature is now 10.9°C and the pressure is 5.95 atm.

a. What is the new volume of the balloon?

b. How many moles of air are in the balloon?

Answer 1

(a) We know that PV = nRT

Where

T = Temperature ;P = pressure ; n = No . of moles ;R = gas constant ; V= Volume of the gas

As the gas remains the same , n will constant

So PV / T = constant

Thereby PV/T = P'V'/T'

Where

P = initial pressure = 1.25 atm

V = initial volume = 4.0 L

T = initial temperature = 21.2 ^oC = 21.2+273 = 294.2K

P'= final pressure = 5.95 atm

V' = final volume = ?

T' = final temperature = 10.9 oC = 10.9+273 = 283.9 K

Plug the values we get

V' = (PVT') / (TP') = 0.8 L

(b) We know that ideal gas equation is PV = nRT

Where

T = Temperature = 21.2 = 21.2+273 = 294.2 K

P = pressure = 1.25 atm

n = No . of moles = ?

R = gas constant = 0.0821 L atm / mol - K

V= Volume of the gas = 4.0 L

Plug the values we get n = ( PV) / (RT) = 0.21 moles