How many grams of NaOH must be dissolved in 1 L of the solution to give it a pH value of 12?

Answer

To determine how many grams of sodium hydroxide (NaOH) must be dissolved in 1 liter of solution to achieve a pH of 12, we can follow these steps:

### Step 1: Understand the relationship between pH and pOH
The pH of a solution is related to the concentration of hydrogen ions \([H^+]\) in the solution. The relationship is given by:
\[ \text{pH} = -\log[H^+] \]
Additionally, we know that:
\[ \text{pH} + \text{pOH} = 14 \]

### Step 2: Calculate pOH
Given that the pH is 12, we can find the pOH:
\[ \text{pOH} = 14 - \text{pH} = 14 - 12 = 2 \]

### Step 3: Calculate the concentration of hydroxide ions \([OH^-]\)
Using the pOH value, we can find the concentration of hydroxide ions:
\[ \text{pOH} = -\log[OH^-] \]
Substituting the pOH value:
\[ 2 = -\log[OH^-] \]
To find \([OH^-]\), we can rewrite the equation:
\[ [OH^-] = 10^{-\text{pOH}} = 10^{-2} = 0.01 \, \text{M} \]

### Step 4: Relate the concentration of NaOH to its molarity
Sodium hydroxide (NaOH) dissociates completely in solution:
\[ \text{NaOH} \rightarrow \text{Na}^+ + \text{OH}^- \]
This means that the concentration of NaOH will be equal to the concentration of hydroxide ions:
\[ [\text{NaOH}] = [OH^-] = 0.01 \, \text{M} \]

### Step 5: Calculate the number of moles of NaOH needed
Since we want a 1-liter solution:
\[ \text{Moles of NaOH} = \text{Concentration} \times \text{Volume} = 0.01 \, \text{mol/L} \times 1 \, \text{L} = 0.01 \, \text{mol} \]

### Step 6: Calculate the mass of NaOH required
To find the mass of NaOH, we use the molar mass of NaOH, which is approximately 40 g/mol:
\[ \text{Mass of NaOH} = \text{Moles} \times \text{Molar Mass} = 0.01 \, \text{mol} \times 40 \, \text{g/mol} = 0.40 \, \text{g} \]

### Final Answer
To achieve a pH of 12, you must dissolve **0.40 grams of NaOH** in 1 liter of solution.

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