What is the pH value of `(N)/(100)` KOH solution

Options

A. `10^(-11)`
B. 3
C. 2
D. 11

Explanation

To find the pH value of a \(\frac{1}{100}\) KOH solution, we can follow these steps:

### Step 1: Understand the nature of KOH
KOH (potassium hydroxide) is a strong base. This means it completely dissociates in water to give hydroxide ions (OH⁻).

### Step 2: Calculate the normality
Given that the solution is \(\frac{1}{100}\) KOH, we can express this in terms of normality (N). For KOH, the normality is equal to the molarity since KOH provides one hydroxide ion per molecule.

\[ \text{Normality (N)} = \text{Molarity (M)} \times n \]
Where \(n\) is the number of hydroxide ions produced. For KOH, \(n = 1\).

Thus:
\[ \text{Normality} = \frac{1}{100} \text{ N} \]

### Step 3: Convert normality to molarity
Since the normality is equal to the molarity for KOH, we have:
\[ \text{Molarity} = \frac{1}{100} \text{ M} = 0.01 \text{ M} \]

### Step 4: Calculate the hydroxide ion concentration
In a \(\frac{1}{100}\) KOH solution, the concentration of hydroxide ions [OH⁻] will also be \(0.01 \text{ M}\) because KOH completely dissociates.

\[ [\text{OH}^-] = 0.01 \text{ M} \]

### Step 5: Calculate the pOH
To find the pOH, we use the formula:
\[ \text{pOH} = -\log[\text{OH}^-] \]

Substituting the value:
\[ \text{pOH} = -\log(0.01) = -\log(10^{-2}) = 2 \]

### Step 6: Calculate the pH
Using the relationship between pH and pOH:
\[ \text{pH} + \text{pOH} = 14 \]

We can rearrange this to find pH:
\[ \text{pH} = 14 - \text{pOH} = 14 - 2 = 12 \]

### Final Answer
The pH value of the \(\frac{1}{100}\) KOH solution is **12**.

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