Question

A compressed cylinder of gas contains 45.6 mol of N2 gas at a pressure of 3.75 x 105 Pa and a temperature of 23.6°C. What volume of gas has been released into the atmosphere if the final pressure in the cylinder is 5.67 x 105 Pa? Assume ideal behavior and that the gas temperature is unchanged.

Answer 1

Answer: 0.102 Liters

Step-by-step explanation

According to the ideal gas equation:

`PV=nRT`

P = Pressure of the gas =
`3.75* 10^5 Pa` = 3675 atm (1 kPa= 0.0098 atm)

V= Volume of the gas = ?

T= Temperature of the gas = 23.6°C = 296.6 K
`0^00C=273K`

R= Gas constant = 0.0821 atmL/K mol

n= moles of gas = 45.6

`V=(nRT)/(P)=(45.6* 0.0821* 296.6)/(3675)=0.302L`

Boyle's Law: This law states that pressure is inversely proportional to the volume of the gas at constant temperature and number of moles.

`P\propto (1)/(V)` (At constant temperature and number of moles)

`P_1V_1=P_2V_2`

where,

`P_1` = initial pressure of gas =
`3.75* 10^5 Pa`

`P_2` = final pressure of gas =
`5.67* 10^5 Pa`

`V_1` = initial volume of gas = 0.302 L

`V_2` = final volume of gas = ?

`3.75* 10^5 * 0.302=5.67* 10^5* V_2`

`V_2=0.199L`

The final volume has to be 0.199 L, thus (0.302-0.199) L= 0.102 L must release into the atmosphere.

Therefore the answer is 0.102 L