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9. A balloon with a volume of 100.21 L at 21 °C and 0.981 atm is released and just barely clears the top of Mount Crumpet in British Columbia. If the final volume of the balloon is 144.53 L at a temperature of 5.24 °C, what is the pressure experienced by the balloon as it clears Mount Crumpet?

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boffeemadrid

Answer:

0.71868 atm

Explanation:

[tex]P_1[/tex] = Initial pressure = 0.981 atm

[tex]T_1[/tex] = Initial Temperature = 21 °C

[tex]V_1[/tex] = Initial volume = 100.21 L

[tex]P_2[/tex] = Final pressure

[tex]T_2[/tex] = Final Temperature = 5.24 °C

[tex]V_1[/tex] = Final volume = 144.53 L

From ideal gas law we have

[tex]\dfrac{P_1V_1}{T_1}=\dfrac{P_2V_2}{T_2}\\\Rightarrow P_2=\dfrac{P_1V_1T_2}{T_1V_2}\\\Rightarrow P_2=\dfrac{0.981\times 100.21(273.15+21)}{(5.24+273.15)\times 144.53}\\\Rightarrow P_2=0.71868\ atm[/tex]

The pressure experienced by the balloon as it clears Mount Crumpet is 0.71868 atm

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