Gen Chem Question

[iRonDevil91]

H2CO3 (aq) + H20 (l) --> H30+(aq) + HCO3- (aq) ; Ka 1 = 4.3 x 10^-7

HCO3- (aq) + H20 (l) --> H30+ (aq) + CO3 (aq) ; Ka2 = 4.8 x 10^-11

The question stem asks which of the following are equal, and the answer is:

Ka * [H2CO3] / [HCO3-] = Ka2 [ HCO3-] / [CO3]

I am conceptually confused as to how this can be true. The explanation says to write out the equilibrium reactions for both equations, and set the concentration of H30 equal to arrive at the answer. But how can the H30 concentration from eq 1 = H30 concentration from equation 2, given the huge differences in Ka values?

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[theonlytycrane]

In solution there are not two pools of H+ each with its own concentration, there is just [H+]. The Ka of each line gives you a relative idea of how readily each of the two acidic hydrogens dissociate in solution. Converting to pKa and using the H.H. equation would allow you to determine the buffer range for each acidic species.

That answer given tells you that you can find [H+] in one of two ways: using Ka1 or Ka2 multiplied by the appropriate terms.

 

[NextStepTutor_2]

H2CO3 (aq) + H20 (l) --> H30+(aq) + HCO3- (aq) ; Ka 1 = 4.3 x 10^-7

HCO3- (aq) + H20 (l) --> H30+ (aq) + CO3 (aq) ; Ka2 = 4.8 x 10^-11

The question stem asks which of the following are equal, and the answer is:

Ka * [H2CO3] / [HCO3-] = Ka2 [ HCO3-] / [CO3]

I am conceptually confused as to how this can be true. The explanation says to write out the equilibrium reactions for both equations, and set the concentration of H30 equal to arrive at the answer. But how can the H30 concentration from eq 1 = H30 concentration from equation 2, given the huge differences in Ka values?

Recall that this is two steps in the overall equation, not 2 different equations occurring separately. Thus, there will be one equilibrium concentration of [H+].