NEET 2024 Q5: Manipulating K: Reverse, Multiply, Divide — Full solution + Why they asked this

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1. TITLE

NEET 2024 Q5: Manipulating K: Reverse, Multiply, Divide — Full solution + Why they asked this

2. THE ACTUAL NEET QUESTION

NEET 2024 Re — Question
At a given temperature and pressure, the equilibrium constant values for the equilibria are given below:
$3A_{2} + B_{2} \rightleftharpoons 2A_{3}B, K_{1}$
$A_{3}B \rightleftharpoons \frac{3}{2}A_{2} + \frac{1}{2}B_{2}, K_{2}$

The relation between $K_{1}$ and $K_{2}$ is :
A) $K_{1}^{2} = 2K_{2}$
B) $K_{2} = \frac{K_{1}}{2}$
C) $K_{1} = \frac{1}{\sqrt{K_{2}}}$
D) $K_{2} = \frac{1}{\sqrt{K_{1}}}$

3. OFFICIAL ANSWER

NEET Answer Key: (D)

4. COMPLETE SOLUTION

Step-by-step calculation:
1. Analyze the Initial Equation:
$3A_{2} + B_{2} \rightleftharpoons 2A_{3}B$ (Equilibrium constant = $K_{1}$)
2. Reverse the Equation:
To match the product/reactant sides of the target equation, we first reverse the initial equation. When you reverse a chemical equation, the new equilibrium constant is the inverse of the original.
$2A_{3}B \rightleftharpoons 3A_{2} + B_{2}$ (New constant $K' = \frac{1}{K_{1}}$)
3. Multiply by a Coefficient:
The target equation has 1 mole of $A_{3}B$, but our reversed equation has 2 moles. We must multiply the entire reversed equation by $\frac{1}{2}$ (or divide by 2). When you multiply an equation by a factor 'n', the new constant must be raised to the power of 'n'.
$\frac{1}{2} \times [2A_{3}B \rightleftharpoons 3A_{2} + B_{2}]$
$A_{3}B \rightleftharpoons \frac{3}{2}A_{2} + \frac{1}{2}B_{2}$
4. Calculate Final K:
New constant $K_{2} = (K')^{1/2} = \left(\frac{1}{K_{1}}\right)^{1/2} = \frac{1}{\sqrt{K_{1}}}$.

Formula used:
* Reversing reaction: $K_{new} = \frac{1}{K_{old}}$
* Multiplying stoichiometry by $n$: $K_{new} = (K_{old})^{n}$

Why this approach:
The Law of Chemical Equilibrium dictates that the numerical value of $K_{c}$ changes specifically based on the form of the balanced chemical equation. By tracking stoichiometric changes step-by-step (reverse, then halve), we avoid mathematical errors.

5. WHY NEET ASKED THIS

Explain the examiner's intent:
* What concept were they testing? The examiner is testing your ability to apply the Law of Mass Action rules mathematically when modifying chemical equations.
* What's the common mistake they expected students to make? Students frequently confuse the rules for equilibrium constants with basic algebra. When halving the coefficients of a reaction, many students mistakenly divide the equilibrium constant by 2 instead of taking the square root.
* Which option was the "trap"? Option B ($K_{2} = \frac{K_{1}}{2}$) is the classic trap for students who just divide the constant by 2. Option C is a trap for students who incorrectly apply the square root to the wrong constant in the equation.

6. COMPARISION TABLE

Year	How they asked	Twist
2024	Find relation between two equations ($A_2$ and $B_2$)	Simultaneous reversing and halving variables.
2015	Halving the reaction coefficients ($N_2 + O_2$)	Asked to find the new $K$ as $K^{1/2}$ exactly without reversing.
2012	Reversing and dividing by 2 ($SO_2 + O_2$)	Required actually calculating the numerical square root ($1/\sqrt{278}$).
2011	Adding two reactions and reversing ($N_2 + O_2$)	Required multiplying $K_1$ and $K_2$ first, then taking the square root.

Prediction for NEET 2026:
Expect a multi-step variation where three equations are given, and you must combine them (adding equations $\rightarrow$ multiplying $K$ values) and reverse/multiply coefficients to find the $K$ of a fourth target equation.

7. SIMILAR QUESTIONS TO PRACTICE

"If you understood this, you can solve:"
* NEET 2012 Q56: $2SO_2(g) + O_2(g) \rightleftharpoons 2SO_3(g)$ with $K=278$. Find $K$ for $SO_3(g) \rightleftharpoons SO_2(g) + \frac{1}{2}O_2(g)$.
* NEET 2015 Q41: $N_2(g) + O_2(g) \rightleftharpoons 2NO(g)$ is $K$. Find $K$ for $\frac{1}{2}N_2(g) + \frac{1}{2}O_2(g) \rightleftharpoons NO(g)$.
* NEET 2011 Q60: Manipulating K by combining equations to form $NO_2 \rightleftharpoons \frac{1}{2}N_2 + O_2$.

8. QUICK REVISION FOR THIS TYPE

For Manipulating K questions, always:

[First check] How the target equation differs from the parent equation visually. Did the products become reactants? Did the stoichiometric numbers change?
[Then apply] The golden rules of $K$:
Reverse reaction $\rightarrow$ $K' = \frac{1}{K}$
Multiply by '$n$' $\rightarrow$ $K' = K^n$
Add two reactions $\rightarrow$ $K_{net} = K_1 \times K_2$
[Watch out for] Halving an equation! Remember, multiplying coefficients by $\frac{1}{2}$ means you take the square root of the equilibrium constant ($K^{1/2}$), you DO NOT divide it by 2!

9. NCERT BASE

This question tests: NCERT Class 11, Chapter 6 (Equilibrium), Page 177 (Table 6.4: Relations between Equilibrium Constants for a General Reaction and its Multiples).

10. CTA

All PYQs from this chapter → Equilibrium Guide
Practice similar questions → [PYQ Test: Equilibrium]