In a solution (Open to atmospheric pressure of ),a hydrogen bubble of volume is near a platinum (Pt) electrode at a depth of where the temperature is degree .The bubble rises to the surface of the solution, which is at a temperature of degree . Assume that the temperature of the bubble is the same as that of the surrounding solution and the mass density of the solution is uniformly equal to that of water ( ). If the earth gravitation is and is regarded as an ideal diatomic gas, find the volume of the bubble (in ) just before it reaches the surface of the solution ( = ).
Give your answer to 3 significant figures.
Source: 2nd IJSO Theoretical Problem 1 part 1.
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I racked my head for about 10 minutes to come up with a formula that does not involve R (Universal Gas Constant) and n ( no.of moles of H 2 ).
You just need this one (should I mention crucial ? ) breakthrough.
P V / T = Constant because R is constant and no.of moles is same because mass of H 2 contained in the bubble remained the same throughout.
So final equation becomes,
( P 2 ) ( T 1 ) ( V 2 ) / ( P 1 ) ( T 2 ) = ( V 1 ) Where V 1 is the volume of the H 2 bubble at the surface.
Substitute the given values and you arrive at the answer. But remember Celsius needs to be converted into Kelvin for Ideal Gas laws.