Refer to this equation: Ka = [H3O+]halfway [A-]halfway / [HA]halfway = [H30+]hal

Question

Refer to this equation: Ka = [H3O+]halfway [A-]halfway / [HA]halfway = [H30+]halfway

and consider carefully whether you could simply have used the pH value of the solution at the very beginning of the titration, before any base had been added, to determine either or both the molar mass and the Ka value. Which of the following is the best conclusion?

A) The intitial solution pH depends only on the concentration of the weak acid, so measuring the initial pH is sufficient to determine the concentration. The Ka can then be calculated.

B) The initial solution pH depends only on the Ka of the weak acid, so measuring the initial pH is sufficient to determine the Ka. The concentration can then be calculated.

C) The initial solution pH depends on both the Ka and the concentration of the weak acid, so measuring the inital pH is insufficient to determine both these unknowns.

D) The initial solution pH depends on both the Ka and the concentration of the weak acid, so measuring the initial pH very accurately may be sufficient to determine both unknowns.

Explanation / Answer

Equation : Ka = [H3O+]halfway [A-]halfway / [HA]halfway = [H30+]halfway

In this equation during titration of a weak acid with a strong base , the pH of a solution can be firstly used to determine concentration and from that concentration we can find out the Ka value.

So, the initial solution pH depends on both the Ka and the concentration of the weak acid, so measuring the inital pH is insufficient to determine both these unknowns.

so the option C is correct.

Example : we have weak acid Acetic acid

CH3COOH(aq) + H2O(l)----> H3O+(aq) + CH3COO-(aq)
Ka = [ H3O+(aq) ] [CH3COO-(aq)]   / [ CH3COOH(aq)  ]   

at halfway pH= -log[H3O+(aq) ]

and [H3O+(aq) ] = 10^-pH

so if we know the pH of the weak acid , wecan put it and determine the concentration.

Further [ [ H3O+(aq) ]= [CH3COO-(aq)]  

Ka = [ H3O+(aq) ] [CH3COO-(aq)]   / [ CH3COOH(aq)  ]

Therefore putting their values of hydronium ion and acetate ion in ka equation we can find Ka

Thus the option C is correct

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