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Question

A small bubble rises from the bottom of a lake, where the temperature and the pressure are 8 C and 6.0 atm respectively, to the water's surface, where the temperature is 25 C and the pressure is 1.0 atm. Calculate the final volume of the bubble if its initial volume was 2 mL.

A
14 mL
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B
12.72 mL
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C
11.31 mL
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D
15 mL
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Solution

The correct option is B 12.72 mL
We know, PV=nRT

At the bottom of the lake,
P1V1=n1RT1 ... (1)

At the surface of the lake,
P2V2=n2RT2 ... (2)

The moles of gas in the bubble remains constant, so n1=n2.
Dividing (1) and (2) we get,
P1V1P2V2=T1T2

V2=V1×P1P2×T2T1
=2.0 mL×6.0 atm1.0 atm×298 K281 K
=12.72 mL

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