The pH of a solution obtained by dissolving 0.4 g of solid NaOH in one litre of water will be

To calculate the pH of the solution obtained by dissolving 0.4 g of solid NaOH in one liter of water, follow these steps:

### Step 1: Calculate the number of moles of NaOH
First, determine the molar mass of NaOH:

- Sodium (Na): \( 22.99 \, \text{g/mol} \)
- Oxygen (O): \( 16.00 \, \text{g/mol} \)
- Hydrogen (H): \( 1.01 \, \text{g/mol} \)

So, the molar mass of NaOH is:

\[ \text{Molar mass of NaOH} = 22.99 + 16.00 + 1.01 = 40.00 \, \text{g/mol} \]

Now, calculate the number of moles of NaOH:

\[ \text{Number of moles} = \frac{\text{Mass of NaOH}}{\text{Molar mass of NaOH}} = \frac{0.4 \, \text{g}}{40.00 \, \text{g/mol}} = 0.01 \, \text{moles} \]

### Step 2: Determine the concentration of NaOH
Since the NaOH is dissolved in one liter of water, the concentration of NaOH (and thus \(\text{OH}^-\) ions) is:

\[ [\text{OH}^-] = \frac{0.01 \, \text{moles}}{1 \, \text{liter}} = 0.01 \, \text{M} \]

### Step 3: Calculate the pOH of the solution
The pOH is calculated using the formula:

\[ \text{pOH} = -\log[\text{OH}^-] = -\log(0.01) = -\log(10^{-2}) = 2 \]

### Step 4: Calculate the pH of the solution
Use the relationship between pH and pOH:

\[ \text{pH} = 14 - \text{pOH} = 14 - 2 = 12 \]

So, the pH of the solution is **12**.

Would you like more details or have any questions? Here are some related questions:

1. How does the concentration of a base affect the pH of the solution?
2. What is the difference between a strong base and a weak base in terms of dissociation?
3. How can you prepare a buffer solution with a specific pH?
4. How does temperature affect the value of \(K_w\) and consequently the pH of pure water?
5. What is the significance of the pH scale in everyday chemistry?

**Tip:** For strong bases like NaOH, the concentration of the base directly equals the concentration of \(\text{OH}^-\) ions since they dissociate completely in water.

Learn how to calculate the pH of a solution obtained by dissolving 0.4 g of solid NaOH in one liter of water. Step-by-step guide including the calculation of moles, concentration of NaOH, pOH, and pH. Suitable for undergraduate-level chemistry students.

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