Calculate the pH value of a solution of 0.1 M `NH_(3) (K_(b)=1.8xx10^(-5))`

Explanation

To calculate the pH of a 0.1 M solution of ammonia (NH₃) with a given Kb value of 1.8 x 10^(-5), follow these steps:

### Step 1: Calculate pKb
The relationship between Kb and pKb is given by:
\[ \text{pKb} = -\log(Kb) \]
Substituting the value of Kb:
\[ \text{pKb} = -\log(1.8 \times 10^{-5}) \]
Using a calculator, we find:
\[ \text{pKb} \approx 4.744 \]

### Step 2: Use the formula to find pOH
We can use the formula:
\[ \text{pOH} = \frac{1}{2} \text{pKb} - \log[C] \]
where C is the concentration of the base (0.1 M in this case). First, we express 0.1 M as \(10^{-1}\):
\[ \text{pOH} = \frac{1}{2} \times 4.744 - \log(10^{-1}) \]

### Step 3: Calculate the logarithm
The logarithm of \(10^{-1}\) is:
\[ \log(10^{-1}) = -1 \]
Substituting this back into the equation gives:
\[ \text{pOH} = \frac{1}{2} \times 4.744 + 1 \]

### Step 4: Calculate pOH
Now, calculate:
\[ \text{pOH} = 2.372 + 1 = 3.372 \]

### Step 5: Calculate pH
Finally, we can find the pH using the relationship:
\[ \text{pH} + \text{pOH} = 14 \]
Thus,
\[ \text{pH} = 14 - \text{pOH} = 14 - 3.372 = 10.628 \]

### Final Answer
The pH of the 0.1 M solution of NH₃ is approximately **10.63**.

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