The Question is from neet-chemistry chemical-kinetics , and it was created by the author Mr. S M HUSSAIN

Question

For a reaction with the rate law: Rate = k[A]^[1/2][B], if the concentration of B is doubled while keeping [A] constant, how does the half-life change?

Mr. S M HUSSAIN · Accepted Answer

## CORE INFORMATION
✓ **Answer**: C
## CONCEPT FRAMEWORK
	**Primary Concept**: Half-life and Rate Law
	**Related Topics**: Reaction Order, Integrated Rate Laws
	**Prerequisites**: Understanding of rate laws and half-life.
## SOLUTION PATHWAY
**Given Information**:
	Rate = k[A]^[1/2][B]
	[B] is doubled, [A] is constant.
**Method & Steps**:
	1. **Determine the overall order with respect to B:**
		Reasoning: The order with respect to B is 1, as the exponent of [B] in the rate law is 1. This means the rate is directly proportional to [B].
	2. **Relate the change in concentration of B to the rate:**
		Working: Doubling [B] doubles the rate.
		Key Point: For reactions with fractional orders with respect to other reactants (like A in this case), the half-life depends on the initial concentration of those reactants.  However, changes in the concentration of a first-order reactant do *not* affect the half-life related to its own consumption.
	3. **Analyze the effect on half-life:**
		Result: Since the half-life for a first-order reactant (or overall first-order reaction) is independent of its concentration, doubling [B] (and hence doubling the rate) will not change the half-life.
		Verification: The half-life of a first-order reaction is given by $t_{1/2} = \frac{0.693}{k'}$, where $k' = k[A]^{1/2}$. Since [A] is constant, $k'$ is constant, and thus, the half-life is constant.
## OPTION ANALYSIS
[A] :x: The half-life doubles: This would be true if the overall order of the reaction with respect to B was -1, which it isn't. 
[B] :x: The half-life is halved: This would be true if [B] was involved in a second-order reaction where increasing [B] would decrease $t_{1/2}$.
[C] ✓: The half-life remains unchanged: This is correct because changing the concentration of a first-order reactant doesn't change its half-life.
[D] :x: The half-life is quadrupled: This is incorrect and generally not observed with simple reaction orders.
## LEARNING AIDS
	**Common Mistakes**:
		1. Confusing the effect of changing the concentration of a reactant on the *rate* versus the *half-life*.: Remember that rate and half-life are related but distinct concepts.
		2. Not recognizing the order of the reaction with respect to each reactant.: Carefully examine the exponents in the rate law.
	**Quick Tips**:
		1. For first-order reactions, $t_{1/2}$ is independent of concentration.
		2. For zero-order reactions, $t_{1/2}$ is directly proportional to concentration.
		3. For second-order reactions, $t_{1/2}$ is inversely proportional to concentration.

Mr. S M HUSSAIN · Answer

The half-life doubles.

Mr. S M HUSSAIN · Answer

The half-life is halved.

Mr. S M HUSSAIN · Answer

The correct Option is "The half-life remains unchanged."

Mr. S M HUSSAIN · Answer

The half-life is quadrupled.

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