<< Chapter < Page Chapter >> Page >
2NO + Cl 2 2 NOCl rate = k [NO] 2 [ Cl 2 ]

Relating reaction mechanisms to rate laws

It's often the case that one step in a multistep reaction mechanism is significantly slower than the others. Because a reaction cannot proceed faster than its slowest step, this step will limit the rate at which the overall reaction occurs. The slowest step is therefore called the rate-limiting step (or rate-determining step) of the reaction [link] .

A photo is shown of cattle passing through a narrow chute into a holding pen. A person directs them through the gate with a long white and red pole.
A cattle chute is a nonchemical example of a rate-determining step. Cattle can only be moved from one holding pen to another as quickly as one animal can make its way through the chute. (credit: Loren Kerns)

As described earlier, rate laws may be derived directly from the chemical equations for elementary reactions. This is not the case, however, for ordinary chemical reactions. The balanced equations most often encountered represent the overall change for some chemical system, and very often this is the result of some multistep reaction mechanisms. In every case, we must determine the overall rate law from experimental data and deduce the mechanism from the rate law (and sometimes from other data). The reaction of NO 2 and CO provides an illustrative example:

NO 2 ( g ) + CO ( g ) CO 2 ( g ) + NO ( g )

For temperatures above 225 °C, the rate law has been found to be:

rate = k [ NO 2 ] [ CO ]

The reaction is first order with respect to NO 2 and first-order with respect to CO. This is consistent with a single-step bimolecular mechanism and it is possible that this is the mechanism for this reaction at high temperatures.

At temperatures below 225 °C , the reaction is described by a rate law that is second order with respect to NO 2 :

rate = k [ NO 2 ] 2

This is consistent with a mechanism that involves the following two elementary reactions, the first of which is slower and is therefore the rate-determining step:

NO 2 ( g ) + NO 2 ( g ) NO 3 ( g ) + NO ( g ) ( slow ) NO 3 ( g ) + CO ( g ) NO 2 ( g ) + CO 2 ( g ) ( fast )

The rate-determining step gives a rate law showing second-order dependence on the NO 2 concentration, and the sum of the two equations gives the net overall reaction.

In general, when the rate-determining (slower) step is the first step in a mechanism, the rate law for the overall reaction is the same as the rate law for this step. However, when the rate-determining step is preceded by a step involving an equilibrium reaction, the rate law for the overall reaction may be more difficult to derive.

An elementary reaction is at equilibrium when it proceeds in both the forward and reverse directions at equal rates. Consider the dimerization of NO to N 2 O 2 , with k 1 used to represent the rate constant of the forward reaction and k -1 used to represent the rate constant of the reverse reaction:

NO + NO N 2 O 2 rate forward = rate reverse k 1 [ NO ] 2 = k −1 [ N 2 O 2 ]

If N 2 O 2 was an intermediate in a mechanism, this expression could be rearranged to represent the concentration of N 2 O 2 in the overall rate law expression using algebraic manipulation:

( k 1 [ NO ] 2 k −1 ) = [ N 2 O 2 ]

However, once again, intermediates cannot be listed as part of the overall rate law expression, though they can be included in an individual elementary reaction of a mechanism. [link] will illustrate how to derive overall rate laws from mechanisms involving equilibrium steps preceding the rate-determining step.

Questions & Answers

what is coordination number
YERUMAKULA Reply
coordination number is the number of atoms or ions immediately surrounding a central atom in a complex or crystal
Chidera
what is isotope
Bukar
who is the father of chemistry
Roland Reply
Antoine Lavoisier. Father of modern chemistry
Yapi
What is geometric isomerism
Imoh Reply
jo
Lakshmi
pls I don't really know teach me
Joel
geometric isomerism are molecules that are locked into their spatial position with respect to one another due to a double Bond or ring structure
Chidera
Chromatography is a physical method of seperation where by mixtures that are in two phrases are separated
Lexzzy Reply
What is chromatography?
Chukwudi Reply
meaning of electrode
DJKRANKY Reply
is ion exchange and ion chromatography the same process?
Vivian
define boyes law and give the formula
Esther Reply
define chemistry and it's properties
Esther
Boyle's law state that at a constant temperature, the pressure of a fixed mass of gas is inversely proportionally to it's volume. P=k/v P1v1=p2v2
MAUREE
Chemistry is the study of matter and it's properties..... It's deals with the composition that governors d use of matter..... Chemistry is also d study of chemical reaction of a substance and it's matter. Properties of chemistry Atom Elements Compound Molecules
MAUREE
chemistry seems more accurately defined as the measurement and study of the interaction / behavior that occurs between any given person place or thing or unit of measure, ie time and energy correlation
Elaine
Reactive metals are extracted by _______?
Joseph Reply
electrolytic reduction
Amisu
what is ionxide
Wisdom Reply
What is isometrics
Kamaluddeen Reply
Molar mass of aluminum
Victor Reply
why an equation should balanced?
Kwanele Reply
in order to obey the law of conservation of mass
Ibrahim
why does the atomic radius increase across the period
Timothy Reply
preparation of hydrogen in the laboratory
Emmanuel Reply
state the dual nature of an electron
Celine Reply
no you PunOko
Practice Key Terms 8

Get the best Chemistry course in your pocket!





Source:  OpenStax, Chemistry. OpenStax CNX. May 20, 2015 Download for free at http://legacy.cnx.org/content/col11760/1.9
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Chemistry' conversation and receive update notifications?

Ask