Acid-base indicator such as methy`1` orange, phenolphthalein, and bromothymol blue ate substances which change colour accroding to the hydrogen ion concentration of the solution to which they are added.
Most indicators are weak acids (or more rarely weak base) in which the undissociated and dissociated forms have different and distinct colours. If methy`1` orange is used as the examples and the un-dissociated forms is written as `HMO`, then dissociation occurs as shown below:
Reaction: `{:(HMOhArr,H^(o+)+,MO^(Theta),,),(Red,"Colourless","Yellow",,):}`
The indicator should have a sharp colour change with the equivalence point of the titration. Usually the colour change of the indicator occurs over a range of about two `pH` units. It should be noted that the eye cannot detect the exact end point of the tiytration. The `pK_(a)` of the indicator should be near the `pH` of the solution at the equivalance point.
Which of the following sitution exists at the equivalence point of titration?

Options

A. `[H^(o+)] = 10^(-7)M`
B. `[H^(o+)] = [overset(Theta)OH]`
C. `[overset(Theta)OH] = 10^(-7)M`
D. `([H^(o+)])/([overset(Theta)OH]) = 10^(-14)`

Explanation

To solve the question regarding the situation at the equivalence point of titration, we need to understand the behavior of acid-base indicators and the conditions at the equivalence point. Here’s a step-by-step solution:

### Step 1: Understand the concept of equivalence point
At the equivalence point of a titration, the amount of acid is stoichiometrically equal to the amount of base. This means that all the acid has reacted with all the base, resulting in a neutralization reaction.

### Step 2: Analyze the properties of water
In pure water at 25°C, the concentration of hydrogen ions \([H^+]\) and hydroxide ions \([OH^-]\) is equal, and both are \(1 \times 10^{-7} \, \text{M}\). The product of these concentrations is given by the ion product of water, \(K_w = [H^+][OH^-] = 1 \times 10^{-14}\).

### Step 3: Evaluate the options given
1. **Option A and C**: Both state that \([H^+] = [OH^-] = 10^{-7} \, \text{M}\). This indicates a neutral solution, which is not the case at the equivalence point of a titration involving a strong acid and a strong base, as the pH will be 7 only if no acid or base is present initially. Thus, these options are incorrect.

2. **Option D**: States that \(\frac{[H^+]}{[OH^-]} = 10^{-14}\). This implies that the concentrations of \(H^+\) and \(OH^-\) are not equal, which contradicts the definition of the equivalence point where they should be equal. Therefore, this option is also incorrect.

3. **Option B**: States that \([H^+] = [OH^-]\). This is true at the equivalence point of a titration, where the solution is neutralized, leading to equal concentrations of hydrogen and hydroxide ions.

### Conclusion
The correct situation that exists at the equivalence point of titration is given by **Option B: \([H^+] = [OH^-]\)**.