Calculate the pH of a solution made by mixing 50 mL of `0.01 Mba(OH)_(2)` with 50 mL water. (Assume complete ionisation)

Answer

To calculate the pH of a solution made by mixing 50 mL of 0.01 M Ba(OH)₂ with 50 mL of water, we can follow these steps:

### Step 1: Calculate the number of moles of Ba(OH)₂
To find the number of moles of Ba(OH)₂ in the solution, we can use the formula:

\[ \text{Number of moles} = \text{Molarity} \times \text{Volume (in L)} \]

Given:
- Molarity of Ba(OH)₂ = 0.01 M
- Volume = 50 mL = 0.050 L

Calculating the number of moles:

\[ \text{Number of moles} = 0.01 \, \text{mol/L} \times 0.050 \, \text{L} = 0.0005 \, \text{mol} \]

### Step 2: Convert moles to millimoles
Since we are dealing with milliliters, we can convert moles to millimoles:

\[ \text{Millimoles} = \text{Number of moles} \times 1000 = 0.0005 \, \text{mol} \times 1000 = 0.5 \, \text{mmol} \]

### Step 3: Calculate the total volume of the solution
The total volume after mixing Ba(OH)₂ with water is:

\[ \text{Total Volume} = 50 \, \text{mL} + 50 \, \text{mL} = 100 \, \text{mL} \]

### Step 4: Calculate the concentration of Ba(OH)₂ in the mixed solution
Now, we can find the concentration of Ba(OH)₂ in the total volume:

\[ \text{Concentration} = \frac{\text{Millimoles}}{\text{Total Volume (in mL)}} = \frac{0.5 \, \text{mmol}}{100 \, \text{mL}} = 0.005 \, \text{M} \]

### Step 5: Determine the concentration of OH⁻ ions
Ba(OH)₂ dissociates completely in water as follows:

\[ \text{Ba(OH)}_2 \rightarrow \text{Ba}^{2+} + 2 \text{OH}^- \]

From the stoichiometry of the reaction, for every 1 mole of Ba(OH)₂, we get 2 moles of OH⁻. Therefore, the concentration of OH⁻ ions will be:

\[ \text{[OH⁻]} = 2 \times \text{[Ba(OH)₂]} = 2 \times 0.005 \, \text{M} = 0.010 \, \text{M} \]

### Step 6: Calculate the pOH of the solution
Using the concentration of OH⁻ ions, we can calculate the pOH:

\[ \text{pOH} = -\log[\text{OH}^-] = -\log(0.010) = 2 \]

### Step 7: Calculate the pH of the solution
Finally, we can find the pH using the relationship:

\[ \text{pH} + \text{pOH} = 14 \]

Thus,

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

### Final Answer:
The pH of the solution is **12**.

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