Question

A sample of a gas in a rigid cylinder with a movable piston has a volume of a lamp then .2 L at STP. What is the volume of this gas at 202.6 kPa and 300 Calvin?

Answer 1

Answer: The new volume of the gas is 0.11 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

At STP:

The temperature at this condition is taken as 273 K and the pressure at this condition is taken as 1 atm or 101.3 kPa.

We are given:

$P_1=101.3kPa\\V_1=0.2L\\T_1=273K\\P_2=202.6kPa\\V_2=?\\T_2=300K$

Putting values in above equation, we get:

$\frac{101.3kPa\times 0.2L}{273K}=\frac{202.6kPa\times V_2}{300K}\\\\V_2=\frac{101.3\times 0.2\times 300}{273\times 202.6}=0.11L$

Hence, the new volume of the gas is 0.11 L