1) List the known and unknown quantities.
Initial conditions
Volume: 2.5 L.
Pressure: 1.0 atm.
Temperature: 325.4 K.
Final conditions
Temperature: 275.9 K.
Pressure: 293.4 kPa.
Volume: unknown (mL).
2) Set the equation
The combined gas law.
[tex]\frac{P1V1}{T1}=\frac{P2V2}{T2}[/tex]2.1- Convert kPa to atm.
101.325 kPa = 1 atm
[tex]atm=293.4\text{ }kPa*\frac{1\text{ }atm}{101.325\text{ }kPa}=2.896\text{ }atm[/tex]3) Plug in the known quantities
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[tex]\frac{(1.0\text{ }atm)(2.5\text{ }L)}{325.4\text{ }K}=\frac{(2.896\text{ }atm)(V2)}{275.9\text{ }K}[/tex]Multiply on both sides by 275.9 K.
[tex]\frac{(1.0\text{ }atm)(2.5\text{ }L)}{325.4\text{ }K}*275.9\text{ }K=\frac{(2.896\text{ }atm)(V2)}{275.9\text{ }K}*275.9\text{ }K[/tex]Divide both sides by 2.896 atm.
[tex]\frac{(1.0\text{ }atm)(2.5\text{ }L)(275.9\text{ }K)}{325.4\text{ }K}*\frac{1}{2.896\text{ }atm}=\frac{(2.896atm)(V2)}{2.896\text{ }atm}[/tex].
[tex]V2=\frac{(1.0\text{ }atm)(2.5\text{ }L)(275.9\text{ }K)}{(325.4\text{ }K)(2.896\text{ }atm)}[/tex][tex]V2=0.73\text{ }L[/tex]4) Convert L to mL.
1 L = 1000 mL
[tex]mL=0.73\text{ }L*\frac{1000\text{ }mL}{1\text{ }L}=730\text{ }mL[/tex]The final volume at the unknown depth is 730 mL.
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