To make a solution of `pH=12`, the amount of `NaOH` dissolved in one litre of the solution should be

Options

A. `0.1g`
B. `0.2g`
C. `0.4g`
D. `1.2g`

Explanation

To determine the amount of NaOH needed to make a solution with a pH of 12, we can follow these steps:

### Step 1: Calculate the concentration of H⁺ ions
The pH of a solution is defined as:
\[ \text{pH} = -\log[H^+] \]
Given that the pH is 12, we can find the concentration of H⁺ ions:
\[ [H^+] = 10^{-\text{pH}} = 10^{-12} \, \text{M} \]

### Step 2: Calculate the concentration of OH⁻ ions
We know that the product of the concentrations of H⁺ and OH⁻ ions in water at 25°C is:
\[ K_w = [H^+][OH^-] = 10^{-14} \]
Using the concentration of H⁺ ions calculated in Step 1, we can find the concentration of OH⁻ ions:
\[ [OH^-] = \frac{K_w}{[H^+]} = \frac{10^{-14}}{10^{-12}} = 10^{-2} \, \text{M} \]

### Step 3: Relate the concentration of OH⁻ to the concentration of NaOH
Since NaOH dissociates completely in solution:
\[ \text{NaOH} \rightarrow \text{Na}^+ + \text{OH}^- \]
The concentration of NaOH will be equal to the concentration of OH⁻:
\[ [\text{NaOH}] = [OH^-] = 10^{-2} \, \text{M} \]

### Step 4: Calculate the number of moles of NaOH
The number of moles of NaOH in 1 liter of solution can be calculated using the formula:
\[ \text{Number of moles} = \text{Concentration} \times \text{Volume} \]
Substituting the values we have:
\[ \text{Number of moles} = 10^{-2} \, \text{mol/L} \times 1 \, \text{L} = 10^{-2} \, \text{mol} \]

### Step 5: Calculate the mass of NaOH
To find the mass of NaOH required, we use the formula:
\[ \text{Mass} = \text{Number of moles} \times \text{Molar mass} \]
The molar mass of NaOH (sodium = 23, oxygen = 16, hydrogen = 1) is:
\[ \text{Molar mass of NaOH} = 23 + 16 + 1 = 40 \, \text{g/mol} \]
Now substituting the values:
\[ \text{Mass} = 10^{-2} \, \text{mol} \times 40 \, \text{g/mol} = 0.4 \, \text{g} \]

### Final Answer
To make a solution of pH 12, the amount of NaOH dissolved in one liter of the solution should be **0.4 grams**.

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