If the pH value is 4.5 for a solution then what is the value of `H^(+)` concentration?

Options

A. `3.162 xx 10^(-5)` mol/L
B. `31.62 xx 10^(-5)` mol/L
C. `0.316 xx 10^(-5)` mol/L
D. `3.162 xx 10^(-8)` mol/L

Answer

To find the concentration of hydrogen ions \([H^+]\) from the given pH value of 4.5, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding pH and its Relationship to \([H^+]\)**:
The pH of a solution is defined as the negative logarithm (base 10) of the hydrogen ion concentration:
\[ \text{pH} = -\log[H^+] \]

2. **Rearranging the pH Formula**:
To find the concentration of hydrogen ions \([H^+]\), we can rearrange the formula:
\[ [H^+] = 10^{-\text{pH}} \]

3. **Substituting the Given pH Value**:
Now, substitute the given pH value (4.5) into the equation:
\[ [H^+] = 10^{-4.5} \]

4. **Calculating \(10^{-4.5}\)**:
We can break down \(10^{-4.5}\) into two parts:
\[ 10^{-4.5} = 10^{-4} \times 10^{-0.5} \]
Here, \(10^{-4} = 0.0001\) and \(10^{-0.5} = \frac{1}{\sqrt{10}} \approx 0.3162\).

5. **Final Calculation**:
Now, multiply the two results:
\[ [H^+] = 0.0001 \times 0.3162 \approx 0.00003162 \]
This can also be expressed in scientific notation:
\[ [H^+] \approx 3.162 \times 10^{-5} \, \text{mol/L} \]

### Final Answer:
The concentration of hydrogen ions \([H^+]\) in the solution is approximately:
\[ [H^+] \approx 3.162 \times 10^{-5} \, \text{mol/L} \]