A student forgot to add the reaction mixture to the round bottomed flask at 27 °C but instead he/she placed the flask on the flame.
Question:

A student forgot to add the reaction mixture to the round bottomed flask at 27 °C but instead he/she placed the flask on the flame. After a lapse of time, he realized his mistake, and using a pyrometer he found the temperature of the flask was 477 °C. What fraction of air would have been expelled out?

Solution:

Let the volume of the round bottomed flask be V.

Then, the volume of air inside the flask at 27° C is V.

Now,

V1 = V

T1 = 27°C = 300 K

V2 =?

T2 = 477° C = 750 K

According to Charles’s law,

$\frac{V_{1}}{T_{1}}=\frac{V_{2}}{T_{2}}$

$\Rightarrow V_{2}=\frac{V_{1} T_{2}}{T_{1}}$

$=\frac{750 \mathrm{~V}}{300}$

$=2.5 \mathrm{~V}$

Therefore, volume of air expelled out = 2.5 V – V = 1.5 V

Hence, fraction of air expelled out $=\frac{1.5 \mathrm{~V}}{2.5 \mathrm{~V}}=\frac{3}{5}$