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

Explanation

According to the ideal gas equation:

$PV=nRT$

P = Pressure of the gas = $3.75\times 10^5 Pa$ = 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

$V=\frac{nRT}{P}=\frac{45.6\times 0.0821\times 296.6}{3675}=0.302L$

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

$P\propto \frac{1}{V}$     (At constant temperature and number of moles)

$P_1V_1=P_2V_2$  

where,

$P_1$ = initial pressure of gas  = $3.75\times 10^5 Pa$

$P_2$ = final pressure of gas  = $5.67\times 10^5 Pa$

$V_1$ = initial volume of gas   = 0.302 L

$V_2$ = final volume of gas  = ?

$3.75\times 10^5 \times 0.302=5.67\times 10^5\times V_2$  

$V_2=0.199L$

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