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 the HCl solution given that its pH is 4, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the pH Definition**:
The pH of a solution is defined as the negative logarithm (base 10) of the hydrogen ion concentration \([H^+]\) in moles per liter (M):
\[ \text{pH} = -\log[H^+] \]

2. **Substitute the Given pH Value**:
Given that the pH is 4, we can substitute this value into the pH equation:
\[ 4 = -\log[H^+] \]

3. **Rearrange to Find \([H^+]\)**:
To find the concentration of hydrogen ions, we need to solve for \([H^+]\):
\[ -4 = \log[H^+] \]
Taking the antilogarithm (base 10) of both sides gives:
\[ [H^+] = 10^{-4} \]

4. **Calculate the Concentration**:
Evaluating \(10^{-4}\):
\[ [H^+] = 0.0001 \, \text{M} \]

5. **Relate \([H^+]\) to HCl Molarity**:
Since HCl is a strong acid, it completely dissociates in solution:
\[ \text{HCl} \rightarrow \text{H}^+ + \text{Cl}^- \]
Therefore, the molarity of the HCl solution is equal to the concentration of hydrogen ions:
\[ \text{Molarity of HCl} = [H^+] = 0.0001 \, \text{M} \]

### Final Answer:
The molarity of the HCl solution is **0.0001 M**.

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