What is the `pH 10^(-3)` M HCl solution ?

Options

A. 1
B. 11
C. 3
D. 14

Answer

To find the pH of a \(10^{-3}\) M HCl solution, we can follow these steps:

### Step 1: Understand the nature of HCl
HCl is a strong acid, which means it completely dissociates in water. Therefore, a \(10^{-3}\) M HCl solution will dissociate into \(H^+\) ions and \(Cl^-\) ions in equal concentrations.

### Step 2: Write the dissociation equation
The dissociation of HCl can be represented as:
\[ \text{HCl} \rightarrow \text{H}^+ + \text{Cl}^- \]

### Step 3: Determine the concentration of \(H^+\) ions
Since the concentration of HCl is \(10^{-3}\) M, the concentration of \(H^+\) ions will also be \(10^{-3}\) M because it dissociates completely.

### Step 4: Use 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.

### Step 5: Substitute the concentration into the pH formula
Substituting the concentration of \(H^+\):
\[ \text{pH} = -\log(10^{-3}) \]

### Step 6: Apply logarithmic properties
Using the property of logarithms:
\[ -\log(10^{-3}) = -(-3) \cdot \log(10) \]
Since \(\log(10) = 1\), we have:
\[ \text{pH} = 3 \]

### Final Answer
Thus, the pH of the \(10^{-3}\) M HCl solution is:
\[ \text{pH} = 3 \]

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