Question

The pressure of 2.0 L of an ideal gas in a flexible container is decreased to one-eighth of its original pressure, and its absolute temperature is decreased to one-ninth of the original. What is the final volume of the gas?

Answer 1

Answer: The final volume of the gas is 1.78 L

Explanation:

To calculate the volume when temperature and pressure has changed, we use the equation given by combined gas law.

The equation follows:

$\frac{P_1V_1}{T_1}=\frac{P_2V_2}{T_2}$

where,

$P_1,V_1\text{ and }T_1$ are the initial pressure, volume and temperature of the gas

$P_2,V_2\text{ and }T_2$ are the final pressure, volume and temperature of the gas

We are given:

$P_1=P_1\\V_1=2L\\T_1=T_1\\P_2=\frac{P_1}{8}\\V_2=?\\T_2=\frac{T_1}{9}$  

Putting values in above equation, we get:

$\frac{P_1\times 2}{T_1}=\frac{(P_1/8)\times V_2}{(T_1/9)}\\\\V_2=\frac{P_1\times (T_1/9)\times 2}{T_1\times (P_1/8)}=\frac{16}{9}=1.78L$

Hence, the final volume of the gas is 1.78 L