Question

An aerosol can contain 400ml of compressed gas at 5.2atm pressure. When gas is sprayed into a large plastic bag, the bag inflates to a volume of 2.14L. What is the pressure of a gas inside the plastic bag?

Answer 1

In a question, it is given-

$$\begin{gathered} \mathrm{T}=\mathrm{constant} \\ {\mathrm{P}}_1=5.2\mathrm{atm} \\ {\mathrm{V}}_1=400\mathrm{ml}(0.4\mathrm{L}) \\ {\mathrm{V}}_2=2.14\mathrm{L} \\ {\mathrm{P}}_2=? \end{gathered}$$

As the temperature is constant and the relation is between volume and pressure Boyle's law is applicable here.

According to Boyle's law-

${\mathrm{P}}_1{\mathrm{V}}_1={\mathrm{P}}_2{\mathrm{V}}_2$

Now putting all the values in the equation-

$$\begin{gathered} 5.2\times 0.4={\mathrm{P}}_2\times 2.14 \\ {\mathrm{P}}_2=\frac{5.2\times 0.4}{2.14} \\ {\mathrm{P}}_2=0.97\mathrm{atm} \end{gathered}$$

So, the final pressure will be 0.97atm.