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# Worked example: Determining a rate law using initial rates data

The rate law for a chemical reaction can be determined using the method of initial rates, which involves measuring the initial reaction rate at several different initial reactant concentrations. In this video, we'll use initial rates data to determine the rate law, overall order, and rate constant for the reaction between nitrogen dioxide and hydrogen gas. Created by Jay.

## Want to join the conversation?

• When we talk about initial rate of a reaction, is that a INSTANTANEOUS RATE of a product or sum of all the products or sum of all reactant ? I have an practice question in my AP Chemistry book by Pearson and they dont have answer key.
Given a reaction C2H5Br + OH- ---> C2H5OH + Br- , has rate law has rate= k[C2H5Br][OH] . When [C2H5Br}= 0.0477 and [OH-]=0.100 M , the rate of disappearance of ethyl bromide is 1.7 x 10^-7 M/s. What is the value of k, rate constant?
If it is a sum of all reactants, I got k= 7.12 x 10^-5 • An instantaneous rate is the slope of a tangent to the graph at that point.
An average rate is the slope of a line joining two points on a graph.
If the two points are very close together, then the instantaneous rate is almost the same as the average rate.
So the initial rate is the average rate during the very early stage of the reaction and is almost exactly the same as the instantaneous rate at t = 0.
If rate = k[C₂H₅Br][OH⁻], then
k = rate/([C₂H₅Br][OH⁻]) = 1.7 × 10⁻⁷mol·L⁻¹s⁻¹/(0.0477 mol·L⁻¹ × 0.100 mol·L⁻¹) =
3.6 x 10⁻⁵ L·mol⁻¹s⁻¹
• You've mentioned in every video, the unit of concentration of any reactant is (M) that is (Mol) and the unit of rate of reaction to be (M/s). But what we've been taught is that the unit of concentration of any reactant is (mol.dm^-3) and unit of rate of reaction is (mol.dm^-3.s^-1) . Can you please explain that?
Thank you. • how can you raise a concentration of a certain substance without changing the concentration of the other substances? • One of the reagents concentrations is doubled while the other is kept constant in order to first determine the order of reaction for that particular reagent. This is done because in the equation for the rate law, the rate equals the concentrations of the reagents raised to a particular power. The order of reaction with respect to a particular reagent gives us the power it is raised to
• In our book, they want us to tell the order of reaction by just looking at the equation, without concentration given! How would you decide the order in that case?
Thanks. • Late, but maybe someone will still find this useful.
Sometimes you can tell the reaction order from stoichiometry, but ONLY if the reaction is elementary - that means that it happens in one step, with no intermediates. I'm assuming that's what your textbook meant. In that case, the reaction order with respect to a reactant is equal to its stoichiometric coefficient, and the overall reaction order is the sum of those. For example:
A + B -> C
The stoichoimetric coefficient of A is 1, so the reaction is 1st order in A. It's also 1 for B, so the reaction is 1st order in B as well. Then you add their orders together and find that the reaction is 2nd order overall.

In practice, reaction order is only determined experimentally, and it's actually what helps us determine the reaction mechanism. For example, if reaction orders line up with stoichiometric coefficients in the equation, you know it's a one-step mechanism. If it doesn't, you can tell there are more steps, and you have to devise a mechanism that agrees with the experimentally determined rate. It only really works the other way around in, yeah, textbook problems ("assuming xyz is an elementary reaction, determine reaction order").
• I get k constant as 25 not 250 - could you check? • is it possible to find the reaction order ,if concentration of both reactant is changing .

is there anyway to cancel out the effect of other reactant ?? • Yes. To the first part, the changing concentrations have nothing to do with the order, and in fact, the way in which they change is in fact the order. So, if they were not changing, then we cannot determine the order.

As to the second part, yes. In fact, cancelling out the effect of all but one reactant is the standard method of finding the order. The method used is called flooding. In this, all but one are taken in very high concentrations (excess) such that even if the entire reaction were to take place and our reactant (in small amount) were to be entirely consumed, the net change in the concentrations of the remaining would be negligible, and hence can be taken as zero (constant concentration). Hence all their concentration along with the actual rate constant now form a new constant which can be computed while measuring the rate with respect to one reactant only. By doing this for every reactant, the original constant can be determined. To note, although we are taking the concentrations to be constant, it is just a mathematical step (the change being closed to zero) and not in reality, since their concentrations need to change for the reaction to occur (or at least, they need to be used up).
• at so we have to use the experiment/trial that have a constant concentration when we want to determine the order of reaction? • What if i was solving for y (order) of a specific concentration and found that 2^y=1.41? I know that y has to be an integer so what would i round 1.41 to in order to find y?   