Understanding the Rate Law for Chemical Reactions with Variable Exponents

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Discussion Overview

The discussion centers on the rate law for chemical reactions, specifically whether the exponents in the rate law must be whole numbers or if they can also be fractions or negative values. Participants explore examples and implications of different orders in the context of chemical kinetics.

Discussion Character

  • Debate/contested
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • Some participants propose that the rate law for a reaction can be expressed as rate = [a]^m * [b]^n, questioning whether m and n must be whole numbers.
  • One participant mentions their AP chemistry teacher asserting that m and n must be whole numbers, though they express uncertainty about this claim.
  • Another participant suggests that m and n can indeed be fractions, citing an example where the order of a reactant could be 0.5 if the rate doubles when the concentration of that reactant quadruples.
  • Another contribution supports the idea that fractional orders are possible, providing examples where the rate law includes non-integer exponents, such as 1.5 and -1.
  • Participants discuss the relationship between rate laws and experimental results, noting that while rate laws are useful models, they may not perfectly describe real-world dynamics.

Areas of Agreement / Disagreement

Participants express differing views on whether the exponents in rate laws must be whole numbers, with some asserting they can be fractions or negative, leading to an unresolved discussion on the topic.

Contextual Notes

Some assumptions about the applicability of rate laws and the conditions under which they hold may be missing, and the discussion does not resolve the mathematical implications of fractional or negative orders.

eax
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for
a + b -> c

the rate law would be
rate = [a]^m * ^n

Does m & n neccessarly have to be whole numbers? Could they be fractions?
 
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My ap chem teacher says that they have to be whole numbers, she didn't explain why but she did say that so I'm not 100% sure that this is the case but it kind of makes sense... maybe...
 
Yes.
Either 0, 1 or 2... and occassionally/rarely 3.
 
I think my teacher gave us one that came out to [itex][A]^{.5}[/itex]. If I find the example in my notes I will post it here.

Edit: Well I think I just thought of one (and I just remembered that I don't have my chemistry with me tonight).

Let's say that as A quadruples while B is held constant, the rate law only doubles. Wouldn't that give A an order of .5? Or is this just not physically possible?
 
Last edited:
pretty sure its possible, for simple cases such as this where you're given one rate equation, the rate law is related to the coefficients for the reactants or products. You're simply relating each of the reaction agents with each other. With weird molecules, you can also have strange rate laws, there may be one involving oxygen gas O2 which would has a coefficient of .5 for O2. Rate laws are more or less accurate in relating to experimental results, the're not actually laws, they're just used to model the dynamics...the equation itself may be adequate for some set of conditions but it is not the perfect description of it. That is real world does not comply to rate laws, at times it's fortunate that it can be used quite effectively.
 
eax said:
Does m & n neccessarly have to be whole numbers? Could they be fractions?

adding to what GCT said, they can be fractions or even negative.

For example, in
[tex]CH_3CHO \rightarrow CH_4 + CO[/tex]
the rate law is [tex]rate =k [CH_3CHO]^{1.5}[/tex]
And in
[tex]2O_3 \rightarrow 3O_2[/tex]
the rate law is [tex]rate=k [O_3]^2 [O_2]^{-1}[/tex]
 
yeah, rate laws can get pretty nasty
 

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