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The half-life of a given reaction is doubled if the initial concentration of the reactant is doubled. What is the order of the reaction?
- a)0
- b)1
- c)2
- d)3
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
The half-life of a given reaction is doubled if the initial concentrat...
Half-life (t1⁄2) is the time required for a quantity to reduce to half of its initial value. The half-life of a zero-order reaction is directly proportional to its initial concentration. They are related as:
t1/2 = [R]0/2k.
t1/2 = [R]0/2k.
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The half-life of a given reaction is doubled if the initial concentrat...
The order of a reaction determines how the concentration of the reactant affects the rate of the reaction.
The half-life of a reaction is the time taken for the concentration of a reactant to decrease by half. It is a useful measure to understand the rate of a reaction.
According to the given information, when the initial concentration of the reactant is doubled, the half-life of the reaction is also doubled. This implies that the rate of the reaction is independent of the initial concentration.
The order of a reaction can be determined by examining the relationship between the concentration of the reactant and the rate of the reaction. In this case, since the rate of the reaction is not affected by the initial concentration, the order of the reaction is zero.
Let's assume the initial concentration of the reactant is [A]₀ and the half-life of the reaction is t₁/₂.
If the initial concentration is doubled, the new concentration becomes 2[A]₀. According to the given information, the new half-life is 2t₁/₂. This implies that the new concentration decreases to half in 2t₁/₂, which is the same as the original half-life.
This behavior is characteristic of zero-order reactions, where the rate of the reaction is independent of the concentration of the reactant. In zero-order reactions, the reactant is consumed at a constant rate, regardless of its concentration.
Therefore, the correct answer is option 'A' - zero order.
Half-life of a reaction
The half-life of a reaction is the time taken for the concentration of a reactant to decrease by half. It is a useful measure to understand the rate of a reaction.
Effect of initial concentration on half-life
According to the given information, when the initial concentration of the reactant is doubled, the half-life of the reaction is also doubled. This implies that the rate of the reaction is independent of the initial concentration.
Order of the reaction
The order of a reaction can be determined by examining the relationship between the concentration of the reactant and the rate of the reaction. In this case, since the rate of the reaction is not affected by the initial concentration, the order of the reaction is zero.
Explanation
Let's assume the initial concentration of the reactant is [A]₀ and the half-life of the reaction is t₁/₂.
If the initial concentration is doubled, the new concentration becomes 2[A]₀. According to the given information, the new half-life is 2t₁/₂. This implies that the new concentration decreases to half in 2t₁/₂, which is the same as the original half-life.
This behavior is characteristic of zero-order reactions, where the rate of the reaction is independent of the concentration of the reactant. In zero-order reactions, the reactant is consumed at a constant rate, regardless of its concentration.
Therefore, the correct answer is option 'A' - zero order.
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The half-life of a given reaction is doubled if the initial concentrat...
Half-life (t1⁄2) is the time required for a quantity to reduce to half of its initial value. The half-life of a zero-order reaction is directly proportional to its initial concentration. They are related as:
t1/2 = [R]0/2k.
t1/2 = [R]0/2k.
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The half-life of a given reaction is doubled if the initial concentration of the reactant is doubled. What is the order of the reaction?a)0b)1c)2d)3Correct answer is option 'A'. Can you explain this answer?
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