Smaller Or Bigger ? (C-M cum Chem)

In a H C l HCl solution (Open to atmospheric pressure of 1 1 a t m atm ),a hydrogen bubble of 8.00 8.00 m m 3 mm^3 volume is near a platinum (Pt) electrode at a depth of 15.00 15.00 c m cm where the temperature is 25.0 25.0 degree C e l s i u s Celsius .The bubble rises to the surface of the H C l HCl solution, which is at a temperature of 27.0 27.0 degree C e l s i u s Celsius . 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 ( 1.00 × 1 0 3 kg/m 3 1.00\times 10^3\text{ kg/m}^3 ). If the earth gravitation is 9.80 m/s 2 9.80\text{ m/s}^2 and H 2 H_2 is regarded as an ideal diatomic gas, find the volume of the bubble (in m m 3 mm^3 ) just before it reaches the surface of the solution ( 1 1 a t m atm = 1.013 1.013 × × 1 0 5 10^5 P a Pa ).

Give your answer to 3 significant figures.


Source: 2nd IJSO Theoretical Problem 1 part 1.


The answer is 8.06.

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1 solution

Ayon Ghosh
Mar 4, 2017

I racked my head for about 10 minutes to come up with a formula that does not involve R R (Universal Gas Constant) and n n ( no.of moles of H 2 H_2 ).

You just need this one (should I mention crucial ? ) breakthrough.

P P V V / / T T = Constant because R is constant and no.of moles is same because mass of H 2 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 ) (P_2)(T_1)(V_2) / (P_1)(T_2) = (V_1) Where V 1 V_1 is the volume of the H 2 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.

For higher accuracy, you will have to consider that the pressure inside the bubble is 2 T r \frac{2T}{r} more than external pressure (T is surface tension of water). But , it adds about 58 pascals(T=72mN/m) for bubble of radius 1.24 mm.

Ajinkya Shivashankar - 4 years, 3 months ago

@Ajinkya Shivashankar ,It was not mentioned in the question. Infact,I did not even know if my answer was correct or not ( no solutions given ),but to check it I posted it on here and I know now its correct :-)

Ayon Ghosh - 4 years, 3 months ago

@Ajinkya Shivashankar I dont think I @ mentioned you so I did it again.

Ayon Ghosh - 4 years, 3 months ago

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