The exact concentration of `H^(+)` ion in `10^(-3)` molar HCl aq solution at 298 K is

Options

A. `10^(-3)+10^(-7)`
B. `10^(-3)+(K_(w))/([H^(+)])`
C. `10^(-3)+(K_(w))/([OH^(-)])`
D. `10^(-3)`

Answer

To determine the exact concentration of \( H^+ \) ions in a \( 10^{-3} \) molar HCl aqueous solution at 298 K, we need to consider the dissociation of HCl in water.

### Step-by-Step Solution:

1. **Understand the Dissociation of HCl**:
HCl is a strong acid, which means it completely dissociates in aqueous solution. The dissociation reaction can be written as:
\[ \text{HCl} \rightarrow \text{H}^+ + \text{Cl}^- \]
This means that for every mole of HCl that dissociates, one mole of \( H^+ \) ions and one mole of \( Cl^- \) ions are produced.

2. **Calculate the Concentration of \( H^+ \) Ions**:
Since HCl completely dissociates, the concentration of \( H^+ \) ions in the solution will be equal to the concentration of HCl. Therefore, if we have a \( 10^{-3} \) molar HCl solution:
\[ [H^+] = [\text{HCl}] = 10^{-3} \text{ M} \]

3. **Consider the Effect of Water's Autoionization**:
In pure water at 298 K, the concentration of \( H^+ \) ions is \( 10^{-7} \) M due to the autoionization of water. However, since \( 10^{-3} \) M HCl is much greater than \( 10^{-7} \) M, we can ignore the contribution of \( H^+ \) from water in this case.

4. **Final Calculation**:
Thus, the exact concentration of \( H^+ \) ions in the \( 10^{-3} \) M HCl solution is:
\[ [H^+] = 10^{-3} \text{ M} \]

### Final Answer:
The exact concentration of \( H^+ \) ions in a \( 10^{-3} \) molar HCl aqueous solution at 298 K is \( 10^{-3} \text{ M} \).

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