Ideal Gas Law Question: Solving for Volume at Surface

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To solve for the volume of the air bubble as it rises from 32 m to the surface, the ideal gas law (PV=nRT) must be applied, considering changes in pressure and temperature. At 32 m depth, the pressure is calculated to be 4.2 atm, and the initial volume is 12 cm³ (0.012 L) at 5°C (278 K). Upon reaching the surface, the pressure drops to 1 atm and the temperature increases to 25°C (298 K). The correct approach involves rearranging the ideal gas law to find the final volume, ensuring all variables are accurately accounted for. The final volume can be determined by substituting the known values into the equation.
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Here's an ideal gas law question:

A scuba diver is 32 m below the surface of a lake, where the temperature is 5°C. He releases an air bubble with a volume of 12 cm^3. The bubble rises to the surface, where the temperature is 25°C. What is the volume of the bubble right before it breaks the surface? (Hint: Remember that the pressure also changes.)

I thought it would be the following:

Initial:
Pressure @ 32m = 4.2atm, since 10m=1atm under water
12cm^3=.012 litres
5C= 278K

Final:
Pressure @ 0m = 1atm
V= unknown
25C= 298K

Then, use PV/T=PV/T... but apparently it's wrong - does anyone know why?
 
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seems right, what's the correct answer?
 
Should be fine, all you have to do is rearrange the final equation you wrote for the second volume and plug the numbers in.
 

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