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A cylinder of compressed gas has a volume of 350 ml and a pressure of 931 torr. What volume in Liters would the gas occupy if allowed to escape into a balloon at a pressure of 113 kPa if temperature and # of molecules remain constant?

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boffeemadrid

Answer:

[tex]0.384\ \text{L}[/tex]

Explanation:

[tex]P_1[/tex] = Initial pressure = 931 torr = [tex]931\times \dfrac{101.325}{760}=124.12\ \text{kPa}[/tex]

[tex]P_2[/tex] = Final pressure = 113 kPa

[tex]V_1[/tex] = Initial volume = 350 mL

[tex]V_2[/tex] = Final volume

From the Boyle's law we have

[tex]P_1V_1=P_2V_2\\\Rightarrow V_2=\dfrac{P_1V_1}{P_2}\\\Rightarrow V_2=\dfrac{124.12\times 350}{113}\\\Rightarrow V_2=384.44\ \text{mL}=0.384\ \text{L}[/tex]

The volume the gas would occupy is [tex]0.384\ \text{L}[/tex].

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