Half life `(t_(1/2))` of first order reaction is

Options

A. dependent of concentration
B. independent of concentration
C. dependent of time
D. dependent of molecularity

Answer

To find the half-life \( t_{1/2} \) of a first-order reaction, we can follow these steps:

### Step 1: Understand the Definition of Half-Life
The half-life of a reaction is the time required for the concentration of a reactant to decrease to half of its initial concentration.

### Step 2: Identify the Order of the Reaction
In this case, we are dealing with a first-order reaction. For first-order reactions, the rate of reaction is directly proportional to the concentration of the reactant.

### Step 3: Use the Formula for Half-Life of First-Order Reactions
The half-life \( t_{1/2} \) for a first-order reaction is given by the formula:
\[ t_{1/2} = \frac{0.693}{k} \]
where \( k \) is the rate constant of the reaction.

### Step 4: Analyze the Dependence of Half-Life
For first-order reactions, the half-life is independent of the initial concentration of the reactant. This means that regardless of how much reactant you start with, the half-life remains constant as long as the rate constant \( k \) does not change.

### Step 5: Conclusion
Thus, the half-life \( t_{1/2} \) of a first-order reaction is a constant value that only depends on the rate constant \( k \) and is independent of the concentration of the reactant.

### Final Answer
The half-life \( t_{1/2} \) of a first-order reaction is given by:
\[ t_{1/2} = \frac{0.693}{k} \]
and it is independent of the initial concentration of the reactant.

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