Aqueous solution of HCl has pH = 4 . Its molarity would be

Options

A. `4 M`
B. `0.4 M`
C. `0.0001 M`
D. `10 M`

Answer

To find the molarity of an aqueous solution of HCl with a given pH of 4, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Relationship Between pH and [H⁺]:**
The pH of a solution is defined by the formula:
\[ \text{pH} = -\log[H^+] \]
where \([H^+]\) is the concentration of hydrogen ions in moles per liter (Molarity).

2. **Substitute the Given pH Value:**
We know from the problem that the pH is 4. Therefore, we can write:
\[ 4 = -\log[H^+] \]

3. **Rearranging the Equation:**
To find \([H^+]\), we can rearrange the equation:
\[ -4 = \log[H^+] \]
This can be rewritten using the properties of logarithms:
\[ [H^+] = 10^{-4} \text{ M} \]

4. **Determine the Molarity of HCl:**
Since HCl is a strong acid, it completely dissociates in solution:
\[ \text{HCl} \rightarrow \text{H}^+ + \text{Cl}^- \]
This means that the concentration of HCl is equal to the concentration of \([H^+]\):
\[ \text{Molarity of HCl} = [H^+] = 10^{-4} \text{ M} \]

### Final Answer:
The molarity of the aqueous solution of HCl is \(10^{-4} \text{ M}\).

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