The half-life of a first-order reaction is independent of the initial concentrat

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Question: The half-life of a first-order reaction is independent of the initial concentration. What is the expression for the half-life?

Options:

Correct Answer: t₁/₂ = 0.693/k

Solution:

The half-life of a first-order reaction is given by t₁/₂ = 0.693/k.

The half-life of a first-order reaction is independent of the initial concentration. What is the expression for the half-life?

The half-life of a first-order reaction is independent of the initial concentration. What is the expression for the half-life?

Step 1: Understand what half-life means. Half-life is the time it takes for half of a substance to react or decay.
Step 2: Know that a first-order reaction is a type of chemical reaction where the rate depends on the concentration of one reactant.
Step 3: Recognize that for first-order reactions, the half-life does not change with different starting amounts of the reactant.
Step 4: Learn the formula for the half-life of a first-order reaction, which is t₁/₂ = 0.693/k, where k is the rate constant.
Step 5: Remember that 0.693 is a constant that comes from the natural logarithm of 2, which is used in this formula.

First-Order Reactions – Reactions where the rate is directly proportional to the concentration of one reactant.
Half-Life – The time required for the concentration of a reactant to decrease to half its initial value.
Independence from Initial Concentration – In first-order reactions, the half-life does not depend on the starting concentration of the reactant.