This question involves comparing reaction rates (a and b) based on a reaction energy diagram. The diagram shows the activation energy barriers for two competing pathways.

Step 1: Understanding the Diagram

The image shows a reaction coordinate diagram with two possible pathways from reactants to products. Pathway "a" has a lower activation energy barrier than pathway "b".

Step 2: Recall the Arrhenius Equation

Reaction rate is governed by the Arrhenius equation:

$k = A e^{- \frac{E_{a}}{R T}}$

where $k$ is the rate constant, $E_{a}$ is the activation energy, and $R$ and $T$ are the gas constant and temperature respectively.

Step 3: Compare Activation Energies

Since pathway "a" has lower activation energy than pathway "b" ( $E_{a (a)} < E_{a (b)}$ ), and the exponential term makes rate extremely sensitive to activation energy differences, the reaction rate through pathway "a" will be significantly faster.

Step 4: Final Answer

Therefore, the correct relationship is: a > b

Related Topics

Chemical Kinetics
Reaction Mechanisms
Activation Energy
Reaction Coordinate Diagrams
Competing Reactions

Key Formulae

Arrhenius Equation: $k = A e^{- \frac{E_{a}}{R T}}$

Rate Law: $Rate = k [reactants]^{n}$

Theory

The pathway with the lowest activation energy is typically the fastest reaction pathway because fewer molecules have sufficient energy to overcome a smaller energy barrier. This principle explains why some reactions proceed through specific mechanisms even when multiple pathways are theoretically possible.