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For example,for the reaction $\ce{A + B \longrightarrow C}$,If rate law expression is: $$\mathrm{Rate=k \times [A]^{(0.5)}\times [B]^{(-0.5)}}$$ It is a zero order reaction but whether it is independent of concentrations of reactants?

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    $\begingroup$ It is not zero order; moreover, reaction order in general is not a thing at all. It is order 0.5 in A, and order -0.5 in B, period. $\endgroup$ – Ivan Neretin Sep 19 '18 at 15:05
  • $\begingroup$ But overall order is sum of exponents of concentrations and here it is 0 $\endgroup$ – kanishkan senthil Sep 19 '18 at 15:18
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    $\begingroup$ @kanishkansenthil Yes, and the product of exponents is -0.25, but that doesn't mean it's a number that means anything useful. $\endgroup$ – Zhe Sep 19 '18 at 15:25
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    $\begingroup$ There is no such thing as overall order. $\endgroup$ – Ivan Neretin Sep 19 '18 at 15:33
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    $\begingroup$ Rate=[A]^x[B]^y. [A] and [B] express the concentration of the species A and B (usually in moles per liter (molarity, M)). The exponents x and y are the partial orders of reaction for A and B and the overall reaction order is the sum of the exponents. {From Wikipedia} $\endgroup$ – kanishkan senthil Sep 19 '18 at 17:07
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I think the issue is not that you can't define overall order, but that it isn't a meaningful quantity. This gets at the point that Zhe was making that while we can define the total order of a reaction as the sum of the exponents, it doesn't tell us anything about how the reaction occurs.

Your question gives a very good example of why it isn't a useful quantity: you might expect a zeroth order reaction to have no dependence on the concentration of reactants, but your reaction clearly depends on the concentration of $\ce{A} \text{ and } \ce{B}$, so the total reaction order isn't actually telling us anything about the kinetics of the reaction.

If the order of a particular reactant is zero however, you can say that its concentration won't affect the rate of reaction (within certain limits, as no reaction can be entirely independent of the concentration of an involved reactant).

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  • $\begingroup$ @kanishkansenthil Not a problem. If you like the answer, consider upvoting and accepting it. $\endgroup$ – Tyberius Sep 20 '18 at 18:01
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The overall order of reaction helps to determine to some extent how to proceed with the mechanism of a particular reaction. For example, in the question you asked, the overall order zero for sure implies that the reaction is complex, it can never be in a single step. Also suppose there is a particular rate with overall order 3, it signifies that the reaction can be both single as well as multi step.

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