The pH of a solution of hydrochloric acid is 4. The molarity of this solution is

Options

A. `4.0`
B. `0.4`
C. `0.0001`
D. `0.04`

Explanation

To find the molarity of a hydrochloric acid (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:
\[ \text{pH} = -\log[\text{H}^+] \]
where \([\text{H}^+]\) is the concentration of hydrogen ions in moles per liter (M).

2. **Substitute the Given pH**:
We know the pH is 4. Therefore, we can substitute this value into the pH equation:
\[ 4 = -\log[\text{H}^+] \]

3. **Rearrange the Equation**:
To isolate \([\text{H}^+]\), we first multiply both sides by -1:
\[ -4 = \log[\text{H}^+] \]

4. **Convert Logarithmic to Exponential Form**:
To find \([\text{H}^+]\), we can rewrite the logarithmic equation in its exponential form:
\[ [\text{H}^+] = 10^{-4} \]

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

6. **Relate \([\text{H}^+]\) to HCl Concentration**:
Since HCl is a strong acid, it completely dissociates in solution. Thus, the concentration of HCl is equal to the concentration of \([\text{H}^+]\):
\[ \text{Molarity of HCl} = [\text{H}^+] = 0.0001 \, \text{M} \]

### Final Answer:
The molarity of the hydrochloric acid solution is \(0.0001 \, \text{M}\).

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