Acid-base indicators are either weak organic acids or weak organic bases. Indicator change colour in dilute solution when the hydonium ion concentration reaches a particular calur For example. Phenolphthalein is a coloureless stbstance in any aqueous solution with a pH less than 8.3 In between the pH range 8.3 to 10, transition of colour (colourless to pink ) takes place and if pH of solution is greater than 10 solution is dark pink. Considering an acid indicator Hln, the equilibrium involving it and its conjgate base `In^(-)` can be represented as :
`" " underset("acidic from")(HIn)hArrH^(+)underset("basic from")(In^(-))`
pH of solution can be computed as :
`" " pH=pK_(In)+log.([IN^(-)])/([HIn])`
In general, transition of colour takes place in between the pH range `pK_(In+-1.`
What is equilibrium constant for the reaction :
`HB(aq.)+NaA(aq.)hArrHA(aq.)+NaB(aq.)` ?

Options

A. 10
B. 0.1
C. `10^(-7)`
D. None of these

Answer

To find the equilibrium constant for the reaction:

\[ \text{HB(aq)} + \text{NaA(aq)} \rightleftharpoons \text{HA(aq)} + \text{NaB(aq)} \]

we can follow these steps:

### Step 1: Understand the Concept of Equilibrium Constant
The equilibrium constant (K) for a reaction at equilibrium is defined as the ratio of the concentrations of the products to the concentrations of the reactants, each raised to the power of their coefficients in the balanced equation.

### Step 2: Identify the Acid-Base Indicators
In this reaction, HB and HA are the acid and conjugate base pairs, respectively. NaA and NaB are the sodium salts of the acids, which do not affect the equilibrium constant directly since they are spectator ions.

### Step 3: Relate pH and pKa
At the half-equivalence point, the pH of the solution is equal to the pKa of the acid. This means that for HB, when the pH is 5, we have:

\[ \text{pKa}_{HB} = 5 \]

And for HA, we have:

\[ \text{pKa}_{HA} = 6 \]

### Step 4: Calculate the Ionization Constants
The ionization constants (Ka) can be calculated from the pKa values:

\[ K_{a, HB} = 10^{-pKa_{HB}} = 10^{-5} \]
\[ K_{a, HA} = 10^{-pKa_{HA}} = 10^{-6} \]

### Step 5: Determine the Equilibrium Constant (K)
The equilibrium constant for the reaction can be expressed in terms of the ionization constants of the acids:

\[ K = \frac{K_{a, HB}}{K_{a, HA}} = \frac{10^{-5}}{10^{-6}} = 10^{1} = 10 \]

### Conclusion
Thus, the equilibrium constant for the reaction is:

\[ K = 10 \]