In a solution of acid `H^(+)` concentration is `10^(-10)M`. The pH of this solution will be

Options

A. 8
B. 6
C. Between 6 and 7
D. Between 3 and 6

Explanation

To find the pH of a solution with an \( H^+ \) concentration of \( 10^{-10} \, M \), we need to follow these steps:

### Step 1: Understand 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 liter.

### Step 2: Substitute the Given Concentration
In this case, the concentration of \( H^+ \) ions is \( 10^{-10} \, M \). Plugging this value into the pH formula gives:
\[ \text{pH} = -\log(10^{-10}) \]

### Step 3: Calculate the Logarithm
Using the properties of logarithms:
\[ \text{pH} = -(-10) = 10 \]

### Step 4: Consider the Nature of the Solution
However, we need to consider that a solution with a \( H^+ \) concentration of \( 10^{-10} \, M \) is very dilute. Pure water has a \( H^+ \) concentration of \( 10^{-7} \, M \). Therefore, the total \( H^+ \) concentration in this solution is the sum of the \( H^+ \) from the acid and that from water:
\[ \text{Total } [H^+] = 10^{-10} + 10^{-7} = 10^{-7} + 10^{-10} \]

### Step 5: Approximate the Total Concentration
Since \( 10^{-10} \) is much smaller than \( 10^{-7} \), we can approximate:
\[ \text{Total } [H^+] \approx 10^{-7} \, M \]

### Step 6: Recalculate the pH
Now, substituting this total concentration back into the pH formula:
\[ \text{pH} = -\log(10^{-7}) = 7 \]

### Conclusion
Thus, the pH of the solution is approximately 7, indicating that the solution is neutral.