Can anyone help me out with this question please?

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Farhan01
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"Half life of a first-order reaction is independent of the initial concentration of the reactant". Is this only applicable for first-order reaction? And if not, then what effect does, changing the initial concentration of the reactant, have on zero-order and second-order reactions? Can anyone kindly help me out, please???
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Pigster
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(Original post by Farhan01)
"Half life of a first-order reaction is independent of the initial concentration of the reactant". Is this only applicable for first-order reaction? And if not, then what effect does, changing the initial concentration of the reactant, have on zero-order and second-order reactions? Can anyone kindly help me out, please???
Half life is not constant. That should do it.

The time it takes to half the conc increases for zero order reactions and decreases for second order reactions.
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Farhan01
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(Original post by Pigster)
Half life is not constant. That should do it.

The time it takes to half the conc increases for zero order reactions and decreases for second order reactions.
This effect that you are talking about, is it when I change the initial concentration or in general? Because I know the half-lives for zero and second order are not constant. I learned that the half life, in general, decreases for zero order and increases for second order reactions.
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Pigster
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(Original post by Farhan01)
I learned that the half life, in general, decreases for zero order and increases for second order reactions.
Sorry about that, I didn't have my thinking head on.

If you look at a conc. v time graph for a first order reaction, then the graph will look the same regardless of scale. i.e. if you double the x and y-axes scales and extend the curve, it will look identical to the smaller-scale graph. Having a constant half-life just means that if you start at x on the conc. scale and find the time needed to go to x/2 then it will be the same time as needed to go from x/2 to x/4, or from x/4 to x/8 or x/8 to x/16 OR from x/3 to x/6 etc. etc. i.e. it is in general, rather than from an initial conc. (which surely is just whatever you pick).
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Farhan01
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(Original post by Pigster)
Sorry about that, I didn't have my thinking head on.

If you look at a conc. v time graph for a first order reaction, then the graph will look the same regardless of scale. i.e. if you double the x and y-axes scales and extend the curve, it will look identical to the smaller-scale graph. Having a constant half-life just means that if you start at x on the conc. scale and find the time needed to go to x/2 then it will be the same time as needed to go from x/2 to x/4, or from x/4 to x/8 or x/8 to x/16 OR from x/3 to x/6 etc. etc. i.e. it is in general, rather than from an initial conc. (which surely is just whatever you pick).
I understand but my question wasn't regarding that. Let me just give you a scenario of what I'm trying to enquire here.

Ok so, let's say I have two conc vs time graphs of compound P decomposing. The first graph shows zero-order reaction and the second graph shows second-order reaction and both graphs start from a particular initial concentration of 6 units. In part (a) of the question, I've been told to prove that they are zero order and second order respectively, which I do so by showing them that the half life for zero order is decreasing and half life for second order is increasing. Now, in part (b), the question asks me :-
i) For the zero order graph, explain the effect on the half-life of doubling the initial concentration of P.
ii) For the second order graph, explain the effect on the half-life of doubling the initial concentration of P.

These are the two questions I want the answers to. The actual question in the textbook involved just the first order and it said there will be no change because half-life of a first-order reaction is independent of the initial concentration of the reactant.

I hope you got what I'm exactly asking about. Sorry for the hassle, but it'd be really nice if you could answer them.
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charco
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(Original post by Farhan01)
Now, in part (b), the question asks me :-
i) For the zero order graph, explain the effect on the half-life of doubling the initial concentration of P.
ii) For the second order graph, explain the effect on the half-life of doubling the initial concentration of P.
For zero order kinetics:

Rate = k

d[A]/dt = k

This integrates to [A]=[A0]–kt

So, at the half-life [A]/2 = [A0] - kt1/2

Therefore [A0] - [A]/2 = kt1/2
So, [A0]/2 = kt1/2

and therefore:

t1/2 = [A0]/2k

So the half-life depends on both the rate constant and the initial concentration.

For second order kinetics:

rate = d[A]/dt = k[A]2

Integrating

1/[A] - 1/ [A0] = kt

at the half-life

1/[A0]/2 - 1/ [A0] = kt1/2

Rearranges to:

t1/2 = 1/k[A0]

So the half-life is inversely proportional to both the concentration and the rate constant
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Farhan01
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(Original post by charco)
For zero order kinetics:

t1/2 = [A0]/2k

So the half-life depends on both the rate constant and the initial concentration.
Do you mean it is directly proportional for zero-order reaction? Like you said it is inversely proportional for second-order and for first order there is no effect so I'm guessing for zero-order it is directly proportional?
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