Is independent of the concentration of the reactant. 0th order and 2nd order depend on concentration of reactant.
How comes?
How comes?
Half life of 1st order
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That's just how the math works out. 😕
One way to explain it to yourself is that 1st order depends in the right "amount" to the concentration that the half-time stays constant. As the concentration goes down, the reaction slows down but the half that needs to be lost also decreases.
0th order become too fast and get too fast through that half and 2nd order and higher are too dependent on concentration and slow down too fast to keep constant half-time.
One way to explain it to yourself is that 1st order depends in the right "amount" to the concentration that the half-time stays constant. As the concentration goes down, the reaction slows down but the half that needs to be lost also decreases.
0th order become too fast and get too fast through that half and 2nd order and higher are too dependent on concentration and slow down too fast to keep constant half-time.
No wait! I lied. I thought I understood. Writing down in notebook, realized not sure how to explain it to myself.
Can you please explain.
edit 1:OH 0th progresses too fast to keep a constant half life. 2nd order too slow to keep a constant half life. 1st order is just right?
lol goldilocks & 3 bears
edit 2: screw it. they're not going to ask "why".
thanks anyway.
Can you please explain.
edit 1:OH 0th progresses too fast to keep a constant half life. 2nd order too slow to keep a constant half life. 1st order is just right?
lol goldilocks & 3 bears
edit 2: screw it. they're not going to ask "why".
thanks anyway.
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I'm not having the easiest time explaining it myself. 😀
Let's say that we look at the first half-life.
0th order: Does not care about concentration at all. Concentration drops but the reaction does not slow down so by that time it has progressed further than half-life. And it gets worse from there since the rate stays constant.
1st order: Life's great! As the concentration decreases, the rate slows down too. So from 1 to 1/2 you go fairly quickly. From 1/2 to 1/4 you have to react away only 1/4 but the reaction has slowed down just enough so that it takes the same time as from 1 to 1/2. And so on...
2nd+ order: It starts to get too touchy. The reaction slows down fairly quickly so by half-time you have not reacted nearly enough. It also gets worse after that since it's slowing down even more.
And yes, "why" is probably not a great question. It is feasible to have something in the lines of comparing concentrations between 0th, 1st and 2nd order reactions after the same time.
Let's say that we look at the first half-life.
0th order: Does not care about concentration at all. Concentration drops but the reaction does not slow down so by that time it has progressed further than half-life. And it gets worse from there since the rate stays constant.
1st order: Life's great! As the concentration decreases, the rate slows down too. So from 1 to 1/2 you go fairly quickly. From 1/2 to 1/4 you have to react away only 1/4 but the reaction has slowed down just enough so that it takes the same time as from 1 to 1/2. And so on...
2nd+ order: It starts to get too touchy. The reaction slows down fairly quickly so by half-time you have not reacted nearly enough. It also gets worse after that since it's slowing down even more.
And yes, "why" is probably not a great question. It is feasible to have something in the lines of comparing concentrations between 0th, 1st and 2nd order reactions after the same time.
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Did you see what TBR had to say about this? I thought it was pretty helpful and in depth enough to get it right on the mcat.
In a 0-order reaction the rate of rxn is constant, so initially when you are saturated with reactants, the half-life is pretty slow because it takes longer to consume, say, 50 reactants than 5 reactants. So it makes sense that, since 0-order reactions continue at the exact same rate no matter what, the first half life (say from 100 to 50) will take much much longer than the fifth half life (from 6.25 to 3.125). It's easiest to quantify it than to think about it qualitatively. Sorry if this is rambling on, but it's how I made sense of it. So say your reaction rate for 0-order is 1 reactant per second and you start with 100 reactant molecules. It takes you 1 second to consume 1 reactant, so your first half-life takes 50 seconds. Then your second half-life (from 50 to 25) only takes 25 seconds, your third half life then only takes 12.5 seconds, etc. Obviously this isn't exactly correct as there are other things affecting the reaction, but it works for understanding half-life.
First-order reactions half constant half-life because your reaction slows down as reactants are consumed, but the number of reactants to be consumed before a half-life is reached decreases as well.
In a 2nd order reaction, the rxn rate is initially very fast and slows down pretty quickly because you consume the reactants faster relative to a first order reaction. So initially the half-life time is going to be very short, then progressively get longer and longer because your reaction is getting slower and slower.
In a 0-order reaction the rate of rxn is constant, so initially when you are saturated with reactants, the half-life is pretty slow because it takes longer to consume, say, 50 reactants than 5 reactants. So it makes sense that, since 0-order reactions continue at the exact same rate no matter what, the first half life (say from 100 to 50) will take much much longer than the fifth half life (from 6.25 to 3.125). It's easiest to quantify it than to think about it qualitatively. Sorry if this is rambling on, but it's how I made sense of it. So say your reaction rate for 0-order is 1 reactant per second and you start with 100 reactant molecules. It takes you 1 second to consume 1 reactant, so your first half-life takes 50 seconds. Then your second half-life (from 50 to 25) only takes 25 seconds, your third half life then only takes 12.5 seconds, etc. Obviously this isn't exactly correct as there are other things affecting the reaction, but it works for understanding half-life.
First-order reactions half constant half-life because your reaction slows down as reactants are consumed, but the number of reactants to be consumed before a half-life is reached decreases as well.
In a 2nd order reaction, the rxn rate is initially very fast and slows down pretty quickly because you consume the reactants faster relative to a first order reaction. So initially the half-life time is going to be very short, then progressively get longer and longer because your reaction is getting slower and slower.
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On thing that might help with second-order is to recognize that the half-life keeps doubling every time the concentration gets cut in half.
If 100% to 50% takes 10 minutes, then 50% to 25% is going to take 20 minutes and 25% to 12.5% is going to take 40 minutes.
If 100% to 50% takes 10 minutes, then 50% to 25% is going to take 20 minutes and 25% to 12.5% is going to take 40 minutes.
I haven't encountered anything that relates reaction order and half life in EK nor Kaplan. I don't know what you guys are talking about. Can someone please shed some light on where should I look for this material?
Thank you!!
