Respuesta :
Answer: 0.102 Liters
Explanation
According to the ideal gas equation:
[tex]PV=nRT[/tex]
P = Pressure of the gas = [tex]3.75\times 10^5 Pa[/tex] = 3675 atm (1 kPa= 0.0098 atm)
V= Volume of the gas = ?
T= Temperature of the gas = 23.6°C = 296.6 K [tex]0^00C=273K[/tex]
R= Gas constant = 0.0821 atmL/K mol
n= moles of gas = 45.6
[tex]V=\frac{nRT}{P}=\frac{45.6\times 0.0821\times 296.6}{3675}=0.302L[/tex]
Boyle's Law: This law states that pressure is inversely proportional to the volume of the gas at constant temperature and number of moles.
[tex]P\propto \frac{1}{V}[/tex] (At constant temperature and number of moles)
[tex]P_1V_1=P_2V_2[/tex]
where,
[tex]P_1[/tex] = initial pressure of gas = [tex]3.75\times 10^5 Pa[/tex]
[tex]P_2[/tex] = final pressure of gas = [tex]5.67\times 10^5 Pa[/tex]
[tex]V_1[/tex] = initial volume of gas = 0.302 L
[tex]V_2[/tex] = final volume of gas = ?
[tex]3.75\times 10^5 \times 0.302=5.67\times 10^5\times V_2[/tex]
[tex]V_2=0.199L[/tex]
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
