Calculate the pH of a solution containing 2.0 g of NaOH per litre of the solution.

Explanation

To calculate the pH of a solution containing 2.0 g of NaOH per liter, follow these steps:

### Step 1: Calculate the Molar Mass of NaOH
- The molar mass of sodium hydroxide (NaOH) can be calculated as follows:
- Sodium (Na) = 23 g/mol
- Oxygen (O) = 16 g/mol
- Hydrogen (H) = 1 g/mol
- Therefore, the molar mass of NaOH = 23 + 16 + 1 = 40 g/mol.

### Step 2: Calculate the Number of Moles of NaOH
- Use the formula:
\[ \text{Number of moles} = \frac{\text{mass (g)}}{\text{molar mass (g/mol)}} \]
- Here, the mass of NaOH = 2.0 g.
- Therefore, the number of moles of NaOH:
\[ \text{Number of moles} = \frac{2.0 \, \text{g}}{40 \, \text{g/mol}} = 0.05 \, \text{mol} \]

### Step 3: Determine the Concentration of OH⁻ Ions
- Since NaOH is a strong base, it dissociates completely in water:
\[ \text{NaOH} \rightarrow \text{Na}^+ + \text{OH}^- \]
- Therefore, the concentration of OH⁻ ions is equal to the number of moles of NaOH in 1 liter:
\[ [\text{OH}^-] = 0.05 \, \text{mol/L} \]

### Step 4: Calculate the pOH
- The pOH is calculated using the formula:
\[ \text{pOH} = -\log[\text{OH}^-] \]
- Substituting the concentration of OH⁻:
\[ \text{pOH} = -\log(0.05) \approx 1.30 \]

### Step 5: Calculate the pH
- The relationship between pH and pOH is given by:
\[ \text{pH} + \text{pOH} = 14 \]
- Therefore, we can calculate pH:
\[ \text{pH} = 14 - \text{pOH} = 14 - 1.30 = 12.70 \]

### Final Answer
The pH of the solution is approximately **12.7**.

---