Bromothymol blue is an indicator with a `K_(a)` value of `6xx10^(-5).` What `%` of this indicator is in its basic form at a pH of 5 ?

Options

A. 40
B. `85.7`
C. `14.3`
D. 60

Answer

To solve the problem of determining the percentage of Bromothymol blue in its basic form at a pH of 5, we can follow these steps:

### Step 1: Understand the dissociation of Bromothymol blue
Bromothymol blue (HIn) can dissociate into its acidic form (HIn) and basic form (In⁻):
\[ \text{HIn} \rightleftharpoons \text{H}^+ + \text{In}^- \]

### Step 2: Use the given pH to find the concentration of H⁺ ions
Given that the pH is 5, we can find the concentration of hydrogen ions (H⁺) using the formula:
\[ \text{pH} = -\log[\text{H}^+] \]
From this, we can calculate:
\[ [\text{H}^+] = 10^{-\text{pH}} = 10^{-5} \, \text{M} \]

### Step 3: Set up the equilibrium expression for Ka
The acid dissociation constant (Ka) for the dissociation of Bromothymol blue is given as:
\[ K_a = \frac{[\text{H}^+][\text{In}^-]}{[\text{HIn}]} \]
Substituting the known values:
- Let the initial concentration of HIn be 100 M (this is a hypothetical value for calculation).
- After dissociation, the concentration of HIn will be \( 100 - x \) and the concentration of In⁻ will be \( x \).

### Step 4: Substitute values into the Ka expression
Using the Ka value:
\[ K_a = 6 \times 10^{-5} = \frac{(10^{-5})(x)}{(100 - x)} \]

### Step 5: Solve for x
Rearranging the equation gives:
\[ 6 \times 10^{-5} (100 - x) = 10^{-5} x \]
Expanding this:
\[ 6 \times 10^{-3} - 6 \times 10^{-5} x = 10^{-5} x \]
Combine like terms:
\[ 6 \times 10^{-3} = 6 \times 10^{-5} x + 10^{-5} x \]
\[ 6 \times 10^{-3} = 7 \times 10^{-5} x \]
Now, solve for x:
\[ x = \frac{6 \times 10^{-3}}{7 \times 10^{-5}} \]
\[ x \approx 85.7 \, \text{M} \]

### Step 6: Calculate the percentage of the basic form
To find the percentage of the indicator in its basic form:
\[ \text{Percentage of In}^- = \frac{x}{100} \times 100\% = \frac{85.7}{100} \times 100\% = 85.7\% \]

### Final Answer
The percentage of Bromothymol blue in its basic form at a pH of 5 is **85.7%**.

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