How many grams of sodium hydroxide must be dissolved in one litre of water to prepare its N/10 solution ? What will be its pH value ?

Explanation

To solve the question of how many grams of sodium hydroxide (NaOH) must be dissolved in one liter of water to prepare a N/10 solution, and to find the pH value of that solution, we can follow these steps:

### Step 1: Understand the concept of Normality
Normality (N) is defined as the number of equivalents of solute per liter of solution. For NaOH, which is a strong base, the normality is equal to its molarity because it provides one hydroxide ion (OH⁻) per molecule.

### Step 2: Determine the required Normality
The question specifies a N/10 solution, which means:
- N = 1 (for NaOH, as it is a monoacidic base)
- Therefore, N/10 = 1/10 = 0.1 N

### Step 3: Use the formula for Normality
The formula for Normality is given by:
\[ \text{Normality (N)} = \frac{\text{Weight of solute (g)}}{\text{Molecular weight (g/mol)} \times \text{Volume (L)} \times \text{n factor}} \]

For NaOH:
- Molecular weight of NaOH = 40 g/mol
- Volume = 1 L
- n factor = 1 (since NaOH releases one OH⁻ ion)

### Step 4: Set up the equation
Substituting the known values into the Normality equation:
\[ \frac{1}{10} = \frac{\text{Weight of NaOH}}{40 \times 1 \times 1} \]

### Step 5: Solve for the weight of NaOH
Rearranging the equation to find the weight of NaOH:
\[ \text{Weight of NaOH} = \frac{1}{10} \times 40 \times 1 \]
\[ \text{Weight of NaOH} = 4 \text{ grams} \]

### Step 6: Calculate the pH of the solution
To find the pH, we first need to determine the concentration of OH⁻ ions in the solution:
- Since it is a 0.1 N solution of NaOH, the concentration of OH⁻ ions is also 0.1 M.

### Step 7: Calculate the pOH
Using the formula for pOH:
\[ \text{pOH} = -\log[\text{OH}^-] \]
\[ \text{pOH} = -\log(0.1) = 1 \]

### Step 8: Calculate the pH
Using the relationship between pH and pOH:
\[ \text{pH} + \text{pOH} = 14 \]
\[ \text{pH} = 14 - \text{pOH} = 14 - 1 = 13 \]

### Final Answer
- The weight of sodium hydroxide needed is **4 grams**.
- The pH of the solution is **13**.