For a reaction that follows first-order kinetics, what is the relationship betwe

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Question: For a reaction that follows first-order kinetics, what is the relationship between the rate constant and the half-life?

Options:

Correct Answer: Half-life is inversely proportional to k

Solution:

For first-order reactions, the half-life is inversely proportional to the rate constant (t1/2 = 0.693/k).

For a reaction that follows first-order kinetics, what is the relationship between the rate constant and the half-life?

For a reaction that follows first-order kinetics, what is the relationship between the rate constant and the half-life?

Step 1: Understand what first-order kinetics means. It refers to a reaction where the rate depends on the concentration of one reactant.
Step 2: Learn about the rate constant (k). It is a number that indicates how fast a reaction occurs.
Step 3: Know what half-life (t1/2) means. It is the time required for the concentration of a reactant to decrease to half of its initial value.
Step 4: Recognize the formula for half-life in first-order reactions: t1/2 = 0.693/k.
Step 5: Analyze the relationship: As the rate constant (k) increases, the half-life (t1/2) decreases, meaning they are inversely proportional.

First-Order Kinetics – In first-order reactions, the rate of reaction is directly proportional to the concentration of one reactant.
Half-Life – The half-life of a reaction is the time required for the concentration of a reactant to decrease to half its initial value.
Rate Constant – The rate constant (k) is a proportionality factor in the rate equation that is specific to a given reaction at a specific temperature.
Relationship Between Half-Life and Rate Constant – For first-order reactions, the half-life is constant and inversely related to the rate constant, expressed as t1/2 = 0.693/k.