In: Chemistry

# Gas law problems

What volume of air will be expelled from a vessel containing 400 cm3 at 7°C when it is heated to 27° C at the same pressure ?

## Solutions

##### Expert Solution

Given: The volume and temperature

To find: The amount of volume expelled

Solution: As the pressure is constant, we can apply Charle's law.

$$\frac{V_{1}}{T_{1}}=\frac{V_{2}}{T_{2}} \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots . .$$ (i)

Now,

$$\mathrm{V}_{1}$$ =initial volume $$=400 \mathrm{~cm}^{3}$$

$$\mathrm{T}_{1}$$ =initial temperature $$=(273+7) \mathrm{K}=280 \mathrm{~K}$$

$$\mathrm{V}_{2}=$$ final volume =unknown

$$\mathrm{T}_{2}=$$ final temperature $$=(273+27)=300 \mathrm{~K}$$

Now from equation-(i)

$$\frac{400}{280}=\frac{V_{2}}{300}$$

$$V_{2}=428.6 \mathrm{~cm}^{3}$$

Hence, the volume expelled out $$=(428.6-400) \mathrm{cm}^{3}=28.6 \mathrm{~cm}^{3}$$

The volume of the air will be 28.6cm3