At a given temperature, When an acid is added to water then the value of `K_(w)`

Options

A. Decreases
B. Increases
C. Remains same
D. First decreases then increases.

Answer

To solve the question regarding the effect of adding an acid to water on the value of \( K_w \), we can follow these steps:

### Step-by-Step Solution:

1. **Understanding \( K_w \)**:
- \( K_w \) is the ionization constant of water, defined as:
\[ K_w = [H^+][OH^-] \]
- Here, \([H^+]\) is the concentration of hydrogen ions, and \([OH^-]\) is the concentration of hydroxide ions in pure water.

2. **Dissociation of Water**:
- Water dissociates into hydrogen ions and hydroxide ions:
\[ H_2O \rightleftharpoons H^+ + OH^- \]
- In pure water, the concentrations of \([H^+]\) and \([OH^-]\) are equal, and at 25°C, \( K_w \) is \( 1.0 \times 10^{-14} \).

3. **Adding Acid to Water**:
- When an acid is added to water, it dissociates completely (if it is a strong acid) to produce additional \( H^+ \) ions:
\[ HA \rightarrow H^+ + A^- \]
- This increases the concentration of \( H^+ \) ions in the solution.

4. **Effect on \( K_w \)**:
- The addition of acid increases the concentration of \( H^+ \) ions, which in turn affects the equilibrium of the water dissociation reaction.
- According to Le Chatelier's principle, the increase in \( H^+ \) concentration will shift the equilibrium to the right, resulting in an increase in \( OH^- \) concentration as well.

5. **Conclusion**:
- Therefore, when an acid is added to water, the value of \( K_w \) increases due to the increase in both \([H^+]\) and \([OH^-]\) concentrations.

### Final Answer:
The value of \( K_w \) increases when an acid is added to water.

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