Question

a balloon has a volume of 1.20 L at 24.0 C. The balloon is heated to 48.0 C. Calculate the new volume of the balloon.

Answer 1

To solve this excescise we use the ideal gas equation:

`P.V=n.R.T`

Where:

P is the pressure of the gas

V is the volume

T is the temperature

R is the ideal gas constant

n is the number of moles

As the balloon is a closed recipient n is the same in state 1 (T: 24°C) and state 2 (T: 48°C).

R is a constant so also remains the same.

The pressure is also a constant in this case as the only thing that we do to the balloon is heat it.

So therefore:

`(V_1)/(T_1)=(V_2)/(T_2)=(n.R)/(P)`

Now we calculate the volume at 48°C (V2):

`V_2=(V_(1.)T_2)/(T_1)=\frac{1.2L.48\degree C{}}{24\degree C}=2.4L`

As we can see as the temperature rises the volume of the gas increases because the molecules have more kinetic energt and they remain farther apart.

The answer then is the new volume of the balloon is 2.4L