Calculate the pH of a solution :
containing 20 gm of NaOH per litre water

Answer

To calculate the pH of a solution containing 20 g of NaOH per liter of water, follow these steps:

### Step 1: Calculate the number of moles of NaOH
To find the number of moles, we use the formula:
\[ \text{Number of moles} = \frac{\text{Given mass}}{\text{Molar mass}} \]
The molar mass of NaOH is calculated as follows:
- Sodium (Na) = 23 g/mol
- Oxygen (O) = 16 g/mol
- Hydrogen (H) = 1 g/mol

So, the molar mass of NaOH = 23 + 16 + 1 = 40 g/mol.

Now, substituting the values:
\[ \text{Number of moles} = \frac{20 \text{ g}}{40 \text{ g/mol}} = 0.5 \text{ moles} \]

### Step 2: Calculate the molarity of the NaOH solution
Since the solution is prepared in 1 liter of water, the molarity (M) is:
\[ \text{Molarity} = \frac{\text{Number of moles}}{\text{Volume in liters}} = \frac{0.5 \text{ moles}}{1 \text{ L}} = 0.5 \text{ M} \]

### Step 3: Determine the concentration of hydroxide ions (OH⁻)
Since NaOH is a strong base, it completely dissociates in solution:
\[ \text{NaOH} \rightarrow \text{Na}^+ + \text{OH}^- \]
Thus, the concentration of OH⁻ ions is equal to the molarity of NaOH:
\[ [\text{OH}^-] = 0.5 \text{ M} \]

### Step 4: Calculate the pOH of the solution
The pOH is calculated using the formula:
\[ \text{pOH} = -\log[\text{OH}^-] \]
Substituting the concentration of OH⁻:
\[ \text{pOH} = -\log(0.5) \approx 0.301 \]

### Step 5: Calculate the pH of the solution
Using the relationship between pH and pOH:
\[ \text{pH} + \text{pOH} = 14 \]
We can find the pH:
\[ \text{pH} = 14 - \text{pOH} = 14 - 0.301 \approx 13.699 \]

### Final Answer
The pH of the solution is approximately **13.7**.

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