The `K_(a)` of monobasic acid `P, Q` and R are `10^(-6),10^(-8)` and `10^(-10)` respectively. The concentrations of P, Q and R are respectively
0.1M, 0.01 M and 0.001 M .
Q. Which acid has the minimum pH?

Options

A. P
B. Q
C. R
D. All have equal pH

Answer

To determine which acid (P, Q, or R) has the minimum pH, we need to analyze the given information about their dissociation constants (K_a) and concentrations.

### Step-by-Step Solution:

1. **Identify the given values**:
- For acid P: \( K_a = 10^{-6} \) and concentration = 0.1 M
- For acid Q: \( K_a = 10^{-8} \) and concentration = 0.01 M
- For acid R: \( K_a = 10^{-10} \) and concentration = 0.001 M

2. **Understand the relationship between \( K_a \) and acidity**:
- The larger the \( K_a \), the stronger the acid, which means it dissociates more in solution and produces more hydrogen ions (\( H^+ \)).
- Therefore, the acid with the highest \( K_a \) will have the lowest pH.

3. **Calculate the concentration of \( H^+ \) ions for each acid**:
- For a weak acid, the dissociation can be represented as:
\[ HA \rightleftharpoons H^+ + A^- \]
The expression for \( K_a \) is:
\[ K_a = \frac{[H^+][A^-]}{[HA]} \]
- Assuming \( x \) is the concentration of \( H^+ \) produced, we can write:
\[ K_a = \frac{x^2}{[HA] - x} \approx \frac{x^2}{[HA]} \quad \text{(for weak acids, where } x \text{ is small compared to } [HA]) \]

4. **Calculate \( H^+ \) concentration for each acid**:
- For acid P:
\[ K_a = 10^{-6} = \frac{x^2}{0.1} \implies x^2 = 10^{-6} \times 0.1 = 10^{-7} \implies x = 10^{-3} \, \text{M} \]
- For acid Q:
\[ K_a = 10^{-8} = \frac{x^2}{0.01} \implies x^2 = 10^{-8} \times 0.01 = 10^{-10} \implies x = 10^{-5} \, \text{M} \]
- For acid R:
\[ K_a = 10^{-10} = \frac{x^2}{0.001} \implies x^2 = 10^{-10} \times 0.001 = 10^{-13} \implies x = 10^{-6.5} \, \text{M} \]

5. **Determine the pH for each acid**:
- pH is calculated using the formula:
\[ \text{pH} = -\log[H^+] \]
- For acid P:
\[ \text{pH} = -\log(10^{-3}) = 3 \]
- For acid Q:
\[ \text{pH} = -\log(10^{-5}) = 5 \]
- For acid R:
\[ \text{pH} = -\log(10^{-6.5}) \approx 6.5 \]

6. **Compare the pH values**:
- pH of P = 3
- pH of Q = 5
- pH of R ≈ 6.5

7. **Conclusion**:
- The acid with the minimum pH is acid P, which has the highest \( K_a \) value.

### Final Answer:
**Acid P has the minimum pH.**