Answer: The pressure inside the bottle is 2473 kPa
Explanation:
Combined gas law is the combination of Boyle's law, Charles's law, Avogadros law and Gay-Lussac's law.
The combined gas equation is,
[tex]\frac{P_1V_1}{n_1RT_1}=\frac{P_2V_2}{n_2RT_2}[/tex]
where,
[tex]P_1[/tex] = initial pressure of gas = 4120 kPa
[tex]P_2[/tex] = final pressure of gas = ?
[tex]V_1[/tex] = initial volume of gas = v
[tex]V_2[/tex] = final volume of gas = v
[tex]n_1[/tex] = initial moles of gas = n
[tex]n_2[/tex] = final moles of gas =[tex]n-\frac{34.9}{100}\times n=0.651n[/tex]
[tex]T_1[/tex] = initial temperature of gas = [tex]29.0^oC=273+29.0=302.0K[/tex]
[tex]T_2[/tex] = final temperature of gas = [tex]5.5^oC=273+5.5=278.5K[/tex]
Now put all the given values in the above equation, we get:
[tex]\frac{4120\times v}{n\times R\times 302.0}=\frac{P_2\times v}{0.651n\times R\times 278.5}[/tex]
[tex]P_2=2473kPa[/tex]
Thus the pressure inside the bottle, if 34.9 percent of the gas is released and the temperature of the gas drops to 5.5 °C is 2473 kPa
