The rapid change of pH near the stoichiometric point of an acid-base titration is the basis of indicator detection. pH of the solution is related to the ratio of the concentrations of the conjugate acid (HIn) and base (In–) forms of the indicator by the expression:

1. $\log \frac{\left[\mathrm{HIn}\right]}{\left[{\mathrm{In}}^{-}\right]}={\mathrm{pK}}_{\mathrm{In}}-\mathrm{pH}$

2. $\log \frac{\left[\mathrm{HIn}\right]}{\left[{\mathrm{In}}^{-}\right]}=\mathrm{pH}-{\mathrm{pK}}_{\mathrm{In}}$

3. $\log \frac{\left[{\mathrm{In}}^{-}\right]}{\left[\mathrm{HIn}\right]}=-pH\; +\hspace{0.17em}{\mathrm{pK}}_{\mathrm{In }}$

4. All of the above.

Case Study:

A buffer solution is defined as a solution whose pH remains practically constant even when small amounts of an acid or a base are added to it. 
Types of buffer solutions : 
(i) Acidic buffer: It is a solution of a mixture of a weak acid and a salt of this weak acid with a strong base (e.g. CH₃COOH + CH₃COONa)
(ii) Basic buffer: It is the solution of a mixture of a weak base and a salt of this weak base with a strong acid (e.g. NH₄OH + NH₄Cl)
Henderson's equation is used to determine pH of buffer mixtures of differ types: 
for acidic buffer Henderson's equation is 
pH= pK_a + log \([Salt] \over [Acid]\)   (k_a = ionisation constant of weak acid )

for basic buffer Henderson's equation is : 

POH = Pk_b + log \([Salt] \over [Base]\)   (k_b = ionisation constant of weak base )

How many moles of HCl are required with 0.01 mole NaCN to prepare a buffer solution of pH =9? 
(k_a of HCN = \(1 \times 10^{-10}\))

1. 0.009 

2. 0.09 

3. 0.9 

4. Buffer solution cannot formed