At `pH lt3.1`, the indicator methyl red is coloured red ,at `pH gt 6.3` , it is yellow and at the intermediate values of the `pH` ,it is orange .What will the colour of indicator be in a `0.1 M` solution of `NH_(4)Br`? Take `pK_(b)(NH_(4)OH)=4.74`.

Options

A. Red
B. Yellow
C. Orange
D. `pH=3.1` so colour cannot be predicted

Explanation

To determine the color of the indicator methyl red in a 0.1 M solution of \( NH_4Br \), we will follow these steps:

### Step 1: Identify the nature of the salt
\( NH_4Br \) is a salt formed from the weak base \( NH_4OH \) (ammonium hydroxide) and the strong acid \( HBr \). Since it is a salt of a weak base and a strong acid, it will undergo hydrolysis in solution.

### Step 2: Use the hydrolysis formula
For salts of weak bases and strong acids, the pH can be calculated using the formula:
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