The pH of `10^(−3)`M `NH_4OH ( K_b =10^(−5) )` is:

Answer

To find the pH of a `10^(-3)` M solution of `NH4OH` (ammonium hydroxide) with a given `K_b` of `10^(-5)`, we can follow these steps:

### Step 1: Identify the given values
- Concentration of `NH4OH` (C) = `10^(-3)` M
- Base dissociation constant (`K_b`) = `10^(-5)`

### Step 2: Calculate the concentration of hydroxide ions (`OH-`)
For weak bases, the concentration of hydroxide ions can be calculated using the formula:
\[ [OH^-] = \sqrt{K_b \times C} \]
Substituting the given values:
\[ [OH^-] = \sqrt{10^{-5} \times 10^{-3}} = \sqrt{10^{-8}} = 10^{-4} \text{ M} \]

### Step 3: Calculate the pOH
The pOH can be calculated using the formula:
\[ pOH = -\log[OH^-] \]
Substituting the concentration of hydroxide ions:
\[ pOH = -\log(10^{-4}) = 4 \]

### Step 4: Calculate the pH
We know that:
\[ pH + pOH = 14 \]
Thus, we can find the pH:
\[ pH = 14 - pOH = 14 - 4 = 10 \]

### Final Answer
The pH of the `10^(-3)` M `NH4OH` solution is **10**.

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