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Question: What is \({{H}^{+}}\) ion concentration of \(5\times {{10}^{-3}}M\) \({{H}_{2}}C{{O}_{3}}\) solution...

What is H+{{H}^{+}} ion concentration of 5×10−3M5\times {{10}^{-3}}M H2CO3{{H}_{2}}C{{O}_{3}} solution having 10% dissociation?
a.) 10−3M{{10}^{-3}}M
b.) 10−2M{{10}^{-2}}M
c.) 10−1M{{10}^{-1}}M
d.) 5×10−2M5\times {{10}^{-2}}M

Explanation

Solution

Weak electrolytes are the ones that on dissolving in water don’t get 100% ionize. Their unionized part remains in equilibrium with their ionized part and concentration of ions depends upon the degree of ionization and concentration of electrolyte. Here we are having carbonic acid which is a weak dibasic acid. Therefore the number of moles of carbonic acid will get ionized at equilibrium, twice of those hydrogen ion moles we will be having.

Complete step by step answer:
Degree of dissociation: it is equal to the number of moles of electrolyte dissociated when one mole of electrolyte was added into the solution.
So if we assume b moles of carbonic acid were added in V litre water and x mole of carbonic acid got dissociated then
Degree of dissociation α=xb\alpha =\dfrac{x}{b}
x=bαx=b\alpha
Unionized moles of carbonic acid = b−xb-x
Unionized moles of carbonic acid = b−bαb-b\alpha
Unionized moles of carbonic acid = b(1−α)b(1-\alpha )
As we know volume of solution is V litre therefore

If initial concentration of carbonic acid is C then
C=bVC=\dfrac{b}{V}
As carbonic acid is dibasic acid therefore
Number of moles of hydrogen ion = 2bα2b\alpha
Concentration of hydrogen ion = 2bαV\dfrac{2b\alpha }{V}
as we know molar concentration is the ratio of number of moles of the substance with the volume of solution (in Litre), therefore
Concentration of hydrogen ion= 2cα2c\alpha
Carbonic acid is a weak acid and after dissolving in water it dissociates according to following reversible reaction
H2CO3(aq)→2H+(aq)+CO32−(aq){{H}_{2}}C{{O}_{3}}(aq) \rightarrow 2{{H}^{+}}(aq)+CO_{3}^{2-}(aq)

As explained above
Concentration of H+{{H}^{+}} ion = 2cα
[H+][{{H}^{+}}] = 2cα
As C is the concentration of H2CO3{{H}_{2}}C{{O}_{3}} = 5×10−3M5\times {{10}^{-3}}M
degree of dissociation α = 0.1
[H+]=2×5×10−3×0.1[{{H}^{+}}] = 2\times 5\times {{10}^{-3}}\times 0.1
[H+]=10−3M[{{H}^{+}}] = {{10}^{-3}}M
So concentration of H+{{H}^{+}} ion is 10−3M{{10}^{-3}}M

So the correct answer is “A”:
Additional Information: Carbonated beverages contain an acidic molecule called carbonic acid that decomposes when you open a bottle or can of a fizzy drink. The decomposition of carbonic acid produces the characteristic soda fizz. Despite its acidic properties, there's no evidence to suggest that carbonic acid in beverages does you any harm.

Note: Degree of ionization of weak electrolytes is an important measure to compare strengths of weak electrolytes. Higher the degree of ionization stronger will be the electrolyte and that’s why we always define strong electrolyte as a substance that completely dissociates when dissolve into water.