10. Consider the following chemical reaction in which forward rate constant (K₁) is 1/sec and
backward rate constant is 10⁷/sec

What will equilibrium rate constant?
(1) 1                                                               (2) 10⁷
(3) 10^-7                                                          (4) 10⁶

The correct answer is (3) 10−710−7. The equilibrium constant (KeqKeq) for the reaction is calculated as the ratio of the forward rate constant K1=1 s−1K1=1s−1 to the backward rate constant K2=107 s−1K2=107s−1, so Keq=K1K2=1107=10−7Keq=K2K1=1071=10−7.

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Introduction

The equilibrium constant is a fundamental concept in chemistry and biochemistry, representing the ratio of product to reactant concentrations at equilibrium in reversible reactions. Understanding how to calculate the equilibrium constant using the rate constants for the forward and backward reactions is essential for students, researchers, and those preparing for competitive exams such as CSIR NET and GATE. This article provides a step-by-step explanation for calculating equilibrium rate constants from provided kinetic data.

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Theoretical Background: Rate Constants and Equilibrium

A reversible chemical reaction can be represented as:

A⇌K1K2BAK2⇌K1B

• Forward rate constant (K1K1): Rate at which A converts to B.

• Reverse (backward) rate constant (K2K2): Rate at which B converts back to A.

At equilibrium, the rates of forward and reverse reactions equalize, and the equilibrium constant (KeqKeq) links the two:

Keq=K1K2Keq=K2K1

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Problem Breakdown

Given:

• Forward rate constant (K1K1) = 1 s−11s−1

• Backward rate constant (K2K2) = 107 s−1107s−1

To find:
Equilibrium constant (KeqKeq)

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Mathematical Calculation

Plugging the numbers into the equation:

Keq=K1K2=1107=10−7Keq=K2K1=1071=10−7

Thus, the equilibrium rate constant for this reaction is 10−710−7.

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Conceptual Explanation

• Low Equilibrium Constant (Keq<1Keq<1): Indicates that at equilibrium, the concentration of reactant A is much higher than product B. The reverse reaction dominates.

• High Equilibrium Constant (Keq>1Keq>1): Favors product formation—most reactant is converted into product at equilibrium.

• In this scenario, K2K2 (backward rate) is much larger than K1K1, meaning the system heavily favors the reactant side (A) at equilibrium.

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Importance in Life Sciences

Equilibrium constants dictate the direction and extent of biological and chemical reactions:

• Enzyme kinetics: Understanding how enzymes drive reactions toward products or substrates.

• Metabolic control: Pathways with low equilibrium constants limit the conversion of substrates to products unless coupled with favorable reactions.

• Drug design: Binding affinities, reaction reversibility, and metabolic flux control are all governed by kinetic and equilibrium principles.

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Real-World Applications

• Clinical Chemistry: Drug binding, metabolic transformations, enzymatic assays use equilibrium constants for quantitation.

• Biochemical Research: Protein folding, ligand interactions, nucleic acid hybridization all rely on these calculations.

• Environmental Chemistry: Predicting the fate of pollutants based on kinetic and equilibrium data.

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Examples and Practice for Students

1. If a reaction has K1=100 s−1K1=100s−1 and K2=50 s−1K2=50s−1, calculate KeqKeq:

   Keq=10050=2Keq=50100=2

   The product (B) is favored at equilibrium.

2. For K1=5 s−1K1=5s−1 and K2=20 s−1K2=20s−1:

   Keq=520=0.25Keq=205=0.25

   The reactant (A) is favored.

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Common Pitfalls and Misconceptions

• Units: Equilibrium constants are typically dimensionless for concentration-based equilibria, but kinetic units (s⁻¹) must be consistent for proper calculations.

• Directionality: Always use the forward and backward rate constants according to the direction specified in the question.

• Reaction Type: Applies only to simple, reversible reactions. Complex mechanisms may require more advanced treatment.

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Summary Table

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Conclusion

The equilibrium rate constant for the reaction, given the kinetic parameters, is 10−710−7. This calculation confirms that the reaction heavily favors the reactant side at equilibrium. Knowledge of equilibrium constants and their calculation from rate constants is crucial for mastering biochemistry, enzyme kinetics, and many fields in life sciences.