What is the pH of a solution whose `H^(+)` ion concentration is `2xx10^(-5)g` ions/litre ?

Answer

To find the pH of a solution with a given concentration of hydrogen ions \((H^+)\), we can follow these steps:

### Step-by-Step Solution:

1. **Identify the given concentration**:
The concentration of hydrogen ions is given as \(2 \times 10^{-5}\) gram ions/litre.

2. **Convert gram ions to moles**:
Since the concentration is given in gram ions, we need to convert it to moles. The molar mass of hydrogen ions \((H^+)\) is approximately 1 g/mol. Therefore, the concentration in moles is:
\[ \text{Concentration in moles} = 2 \times 10^{-5} \text{ g ions/L} = 2 \times 10^{-5} \text{ moles/L} \]

3. **Use the pH formula**:
The pH of a solution is calculated using the formula:
\[ \text{pH} = -\log[H^+] \]
where \([H^+]\) is the concentration of hydrogen ions in moles per litre.

4. **Substitute the concentration into the pH formula**:
\[ \text{pH} = -\log(2 \times 10^{-5}) \]

5. **Break down the logarithm**:
Using the properties of logarithms:
\[ \text{pH} = -\log(2) - \log(10^{-5}) \]
\[ \text{pH} = -\log(2) + 5 \]

6. **Calculate \(-\log(2)\)**:
The value of \(-\log(2)\) is approximately \(-0.301\). Therefore:
\[ \text{pH} = 5 - 0.301 = 4.699 \]

7. **Final answer**:
The pH of the solution is approximately \(4.699\).