KAE_Measuring Reaction Rate Lesson

Measuring Reaction Rate

All rates are expressed as some change over time. Chemical reaction rates are usually expressed as a change in concentration of one of the components of the reaction over time. Since concentration is expressed in molarity, the unit for rate is moles/L per second.

REACTION RATE rate=Δconcentration/time = (moles/ L )/s = M/s

A reaction rate is not constant. As reactants are used up, the reaction slows down. The rate at a particular moment in called the instantaneous rate.  

Consider this reaction: 2 HI(g) → H2(g) +  I2(g)    

The reaction rate could be measured by the rate of disappearance of HI. The instantaneous rate would be determined by:

LaTeX: \text{rate with respect to HI}=\frac{\text{([HI] at time t}_2-\text{[HI] at time t}_1)}{t_2-t_1}= \frac{\Delta [HI]}{\Delta t}rate with respect to HI=([HI] at time t2−[HI] at time t1)t2−t1=Δ[HI]Δt

Below, you will see a plot of [HI] vs. time. The slope is negative because we are measuring the disappearance of HI. The graph is a curve because the reaction rate changes. But you can find the instantaneous reaction rate by drawing a tangent to the curve at any point and determining its slope.

Rate Graph: indicating at point in graph: At this instant in time Slope = -0.027 mol/L / 110s rate=0.00025 mol L^-1 s^-1 rate=2.5 x 10^-4 mol L^-1 s^-1

Even though the slope is negative, reaction rates are always expressed as positive numbers.

Rate Laws

Calculating reaction rates, as shown above, only focuses on one reactant or product at a time. In order to get a complete picture of the rate of the overall reaction, we must determine something called the rate law. Rate laws are written from the perspective of the reactants as follows.

For the following equation:          

A + B → products

The rate is expressed as                  

rate ∝ [A]m[B]n

 A rate constant converts the proportionality into an equation.  

rate = k[A]m[B]n

The values for the exponents (m and n above) must be determined experimentally. They are NOT found from the coefficients of the balanced equations. This is because the slowest step in a reaction determines the rate law, not the overall reaction. As we mentioned on the previous page, this step is known as the rate determining step. Once the exponents are determined experimentally, the value of the rate constant, k, can be determined. Although you will calculate the value of k for a specific reaction at a certain temperature, know that the value of k does change with temperature. The temperature dependence of reaction rates is contained in the temperature dependence of the rate constant.

Watch the presentation below to see how a rate law is determined from experimental data. Work along with the video, as you will need to be able to do this on your own using experimental data.

Rate Laws and Reaction Mechanisms

Another way to determine a rate law is by considering the reaction mechanism. Recall that the reaction mechanism is a theoretical series of elementary processes that are more probable to occur than a reaction happening in just one step. If a reaction mechanism has been established and the rate determining step proposed, we can predict the rate law from the coefficients of the balanced equation of that rate determining step. Always make sure that an equation has been specifically identified as the likely rate determining step before using the coefficients to determine the rate law. Otherwise, you must use experimental data (as above) to determine the rate law.

Consider that each of the following reactions has been determined to be the rate determining step of another reaction and are therefore elementary reactions. We can use the stoichiometric coefficients to determine the rate law as shown below.

AB+C rate = k[A] unimolecular reaction 2A → B rate = k[A]² bimolecular reaction A+B⇒C rate = k[A][B] bimolecular reaction

Remember that reaction mechanisms are theoretical. A proposed reaction mechanism must be consistent with an experimentally determined rate law. You should be able to look at a given rate law and a proposed reaction mechanism and discuss the reasonableness of that reaction mechanism. An example of this is shown below.

The reaction of nitrogen dioxide and carbon monoxide is: NO₂+ CO NO + CO2 The rate law for this reaction found experimentally is: rate = k[NO₂]² The proposed reaction mechanism is: Step 1: 2NO → NO + NO₃ slow Step 2: NO3 + CO→ NO₂+ CO2 fast Is this reaction mechanism reasonable? In order for a reaction mechanism to be reasonable: The individual steps must add up to the overall reaction. • The rate determining step must agree with the experimentally determined rate law. Let's look at each of these one at a time. The individual steps must add up to the overall reaction. 2NO₂ → NO + NO₂ slow NO₂+ CO→NO + CO₂ fast NO₂+ CO NO + CO₂ overall When the two elementary processes are added together, the overall equation is obtained. The rate determining step must agree with the experimentally determined rate law. rate = k[NO2]2 2NO2 NO+ NO3 Both the rate law and the slow step (the rate determining step) involve a collision of two NO2 molecules. So, these are consistent. Since both criteria for a reasonable mechanism have been met, this is a valid mechanism for this reaction. In addition to checking these criteria, also keep in mind that the individual steps in the proposed mechanism must themselves be reasonable. It would not be reasonable to have a step with multiple molecules colliding at once.

Keep in mind that a number of reaction mechanisms may be proposed for a given reaction. It is important to be able to distinguish the likely mechanisms from the unlikely based on the experimental evidence. In addition to using the experimentally determined rate law, experimental detection of a reaction intermediate is a common way to build evidence in support of one reaction mechanism over an alternative mechanism. A reaction intermediate is produced by some elementary steps and consumed by others, such that it is present only while a reaction is occurring. Links to an external site.

Order of Reaction

Once a rate law is determined, we can describe the reaction further by describing what we call the order of the reaction. The order with respect to one reactant is just the exponent from the rate law. Consider the following the rate law:

rate = k[A][B]2

The reaction is 1st order with respect to A and 2nd order with respect to B.  

The overall order of a reaction is obtained by adding the orders with respect to each reactant in the rate law. In the above example, the overall order of the reaction is 3.

Recall unimolecular reactions, A → B + C, and bimolecular reactions, 2A → B or A + B → C, from before. Unimolecular reactions are first order and bimolecular collisions are second order, etc. While an overall reaction can certainly be a higher order, elementary reactions involving the simultaneous collision of three particles are rare.

Remember to work on the module practice problems as you complete each section of content.

[CC BY-NC-SA 4.0 Links to an external site.] UNLESS OTHERWISE NOTED | IMAGES: LICENSED AND USED ACCORDING TO TERMS OF SUBSCRIPTION - INTENDED ONLY FOR USE WITHIN LESSON.