For which of the following pairs, the expression `pK_(a) + pK_(b) - 14 = 14 = 0` is true? (a) `KOH,HNO_(3)` (b) `CH_(2)COOH,CH_(3)COO^(-)`
(c ) `RNH_(2), RNH_(3)^(+)` (d) `RNH_(4)OH, HCI`
correct answer is :

Options

A. a,b
B. c,d
C. b,c
D. a,d

Answer

To solve the problem, we need to determine which pairs of compounds represent conjugate acid-base pairs, as the expression \( pK_a + pK_b = 14 \) holds true for such pairs.

### Step-by-Step Solution:

1. **Understanding the Expression**:
The expression \( pK_a + pK_b = 14 \) is valid for conjugate acid-base pairs. This means that if we have an acid (HA) and its conjugate base (A⁻), the relationship holds true.

2. **Analyzing Each Pair**:
- **(a) KOH, HNO₃**:
- KOH is a strong base, and HNO₃ is a strong acid. They do not form a conjugate acid-base pair.
- **Conclusion**: Not a conjugate pair.

- **(b) CH₃COOH, CH₃COO⁻**:
- CH₃COOH (acetic acid) is a weak acid, and CH₃COO⁻ (acetate ion) is its conjugate base.
- **Conclusion**: This is a conjugate acid-base pair.

- **(c) RNH₂, RNH₃⁺**:
- RNH₂ (a weak base) can accept a proton to form RNH₃⁺ (its conjugate acid).
- **Conclusion**: This is a conjugate acid-base pair.

- **(d) RNH₄OH, HCl**:
- RNH₄OH is not a typical acid-base pair with HCl. RNH₄OH is a salt that can dissociate into RNH₄⁺ and OH⁻, but HCl is a strong acid and does not form a conjugate pair with RNH₄OH.
- **Conclusion**: Not a conjugate pair.

3. **Final Conclusion**:
The pairs that satisfy the condition \( pK_a + pK_b = 14 \) are:
- (b) CH₃COOH, CH₃COO⁻
- (c) RNH₂, RNH₃⁺

### Answer:
The correct answer is (b) and (c).