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

Answer

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

### Step 1: Calculate the number of moles of NaOH
To find the number of moles, use the formula:
\[ \text{Number of moles} = \frac{\text{Given weight}}{\text{Molar mass}} \]
The given weight of NaOH is 20 grams, and the molar mass of NaOH (sodium + oxygen + hydrogen) is:
- Sodium (Na) = 23 g/mol
- Oxygen (O) = 16 g/mol
- Hydrogen (H) = 1 g/mol

Thus, the molar mass of NaOH is:
\[ 23 + 16 + 1 = 40 \text{ g/mol} \]
Now, calculate the number of moles:
\[ \text{Number of moles} = \frac{20 \text{ g}}{40 \text{ g/mol}} = 0.5 \text{ moles} \]

### Step 2: Calculate the molarity of the NaOH solution
Molarity (M) is defined as the number of moles of solute per liter of solution:
\[ \text{Molarity} = \frac{\text{Number of moles}}{\text{Volume in liters}} \]
Since the volume of the solution is 1 liter:
\[ \text{Molarity} = \frac{0.5 \text{ moles}}{1 \text{ L}} = 0.5 \text{ M} \]

### Step 3: Determine the concentration of OH⁻ ions
NaOH is a strong base and completely dissociates in water:
\[ \text{NaOH} \rightarrow \text{Na}^+ + \text{OH}^- \]
This means that the concentration of OH⁻ ions is also 0.5 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⁻:
\[ \text{pOH} = -\log(0.5) \]
To calculate this, note that:
\[ 0.5 = 5 \times 10^{-1} \]
Using logarithmic properties:
\[ \text{pOH} = -\log(5) + 1 \]
Calculating \(-\log(5)\) gives approximately 0.301, so:
\[ \text{pOH} \approx 0.301 + 1 = 0.301 \]

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

### Final Answer
Thus, the pH of the solution is approximately:
\[ \text{pH} \approx 13.70 \]

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