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 question, we need to determine which of the given pairs of compounds satisfies the equation:

\[ pK_a + pK_b - 14 = 0 \]

This can be rearranged to:

\[ pK_a + pK_b = 14 \]

This equation holds true for conjugate acid-base pairs. Let's analyze each option:

### Step 1: Analyze Each Pair

**(a) KOH, HNO₃**

- KOH is a strong base and HNO₃ is a strong acid.
- Strong acids and bases do not have conjugate pairs that satisfy the equation since their \( pK_a \) and \( pK_b \) values are not related in this way.
- **Conclusion:** This pair does not satisfy the equation.

**(b) CH₃COOH, CH₃COO⁻**

- CH₃COOH (acetic acid) is a weak acid and CH₃COO⁻ (acetate ion) is its conjugate base.
- For a conjugate acid-base pair, the relationship \( pK_a + pK_b = 14 \) holds true.
- **Conclusion:** This pair satisfies the equation.

**(c) RNH₂, RNH₃⁺**

- RNH₂ (a primary amine) acts as a weak base and RNH₃⁺ (the conjugate acid) is formed when RNH₂ accepts a proton.
- This is a conjugate acid-base pair, so the relationship \( pK_a + pK_b = 14 \) holds true.
- **Conclusion:** This pair satisfies the equation.

**(d) RNH₄OH, HCl**

- RNH₄OH is a weak base (ammonium hydroxide) and HCl is a strong acid.
- Similar to option (a), this pair does not represent a conjugate acid-base pair.
- **Conclusion:** This pair does not satisfy the equation.

### Final Answer

The pairs that satisfy the equation \( pK_a + pK_b = 14 \) are:

- **(b) CH₃COOH, CH₃COO⁻**
- **(c) RNH₂, RNH₃⁺**