Ionic EquilibriumHard

Question

An acid base indicator which is a weak acid has a pKa value = 5.5. At what concentration ratio of sodium acetate to acetic acid would the indicator show a colour half way between those of its acid and conjugate base forms? The pKa value of acetic acid = 4.75 [Antilog (0.75) = 5.62, Antilog (0.79) = 6.3, Antilog (0.69) = 4.93].

Options

A.4.93: 1
B.6.3: 1
C.5.62: 1
D.2.37: 1

Solution

$5.5 = 4.75 + \log\frac{\left\lbrack ACo^{-} \right\rbrack_{o}}{\lbrack ACOH\rbrack_{o}}$

$\therefore\frac{\left\lbrack ACo^{-} \right\rbrack_{o}}{\lbrack ACOH\rbrack_{o}} = \frac{5.62}{1}$

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