Smaller Or Bigger ? (C-M cum Chem)

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

Give your answer to 3 significant figures.


Source: 2nd IJSO Theoretical Problem 1 part 1.

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