Question

If 20 L of a gas at 1 atm is expanded to 50 L at constant $T$, then what is the final pressure?

• A. $20\times \frac{1}{50}$
• B. $50\times \frac{1}{20}$
• C. $1\times \frac{1}{20}\times 50$
• D. None of these

Answer 1

The correct option is A $20\times \frac{1}{50}$

Solution:- (A) $20\times \frac{1}{50}$

From ideal gas equation,

$PV=nRT$

For same no. of moles of a gas at constant temperature,

$PV=\text{Constant}$

$\frac{P_1}{P_2}=\frac{V_2}{V_1}$

Given:-

$P_1=1atm$

$P_2=?$

$V_1=20L$

$V_2=50L$

Therefore,

$\frac{1}{P_2}=\frac{50}{20}$

$\Rightarrow P_2=20\times \frac{1}{50}$

Hence the final pressure will be $20\times \frac{1}{50}$.