How many grams of NaOH must be dissolved in one litre of the solution to give it a pH value of 10.6 at `25^@C`.

Answer

To determine how many grams of NaOH must be dissolved in one liter of solution to achieve a pH of 10.6 at 25°C, we can follow these steps:

### Step 1: Calculate pOH
Since pH and pOH are related by the equation:
\[ \text{pH} + \text{pOH} = 14 \]

We can rearrange this to find pOH:
\[ \text{pOH} = 14 - \text{pH} \]
Substituting the given pH value:
\[ \text{pOH} = 14 - 10.6 = 3.4 \]

### Step 2: Calculate the concentration of OH⁻ ions
The relationship between pOH and the concentration of hydroxide ions [OH⁻] is given by:
\[ \text{pOH} = -\log[\text{OH}^-] \]

To find [OH⁻], we can rearrange this equation:
\[ [\text{OH}^-] = 10^{-\text{pOH}} \]
Substituting the value of pOH:
\[ [\text{OH}^-] = 10^{-3.4} \]

Calculating this gives:
\[ [\text{OH}^-] \approx 3.98 \times 10^{-4} \, \text{mol/L} \]

### Step 3: Relate [OH⁻] to moles of NaOH
Since NaOH is a strong base and dissociates completely in solution:
\[ \text{NaOH} \rightarrow \text{Na}^+ + \text{OH}^- \]

The concentration of NaOH will be equal to the concentration of OH⁻ ions. Therefore:
\[ [\text{NaOH}] = [\text{OH}^-] = 3.98 \times 10^{-4} \, \text{mol/L} \]

### Step 4: Calculate the number of moles of NaOH
For a 1-liter solution, the number of moles of NaOH is:
\[ \text{Number of moles} = [\text{NaOH}] \times \text{Volume (L)} \]
\[ \text{Number of moles} = 3.98 \times 10^{-4} \, \text{mol} \]

### Step 5: Calculate the mass of NaOH required
To find the mass of NaOH, we use the formula:
\[ \text{Mass} = \text{Number of moles} \times \text{Molar mass} \]

The molar mass of NaOH is approximately 40 g/mol. Thus:
\[ \text{Mass} = 3.98 \times 10^{-4} \, \text{mol} \times 40 \, \text{g/mol} \]
\[ \text{Mass} \approx 0.01592 \, \text{g} \]

### Final Answer
Therefore, to achieve a pH of 10.6 in one liter of solution, you need to dissolve approximately **0.01592 grams of NaOH**.

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