Rate Law 

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Rate laws are equations that relate reaction rate to the concentration of reactants. The generic form of the rate law is the rate constant “k” of a reaction multiplied by the concentration of reactants raised to an exponent.
Rate constants, discussed in another video, are proportional to the temperature of a reaction and inversely proportional to the activation energy of a reaction. The exponent of reactant concentration, “x”, is the reaction order, a number which specifies how the reaction rate responds to a change in reactant concentration. The rate order can be one, two, or any number. If the rate order is 1, doubling reactant concentration will double the rate (21 = 2). If the rate order is 2, doubling reactant concentration will quadruple the rate (22 = 4). The rate order of a reactant can be determined in one of two ways: either via experimental data or by analyzing the elementary steps of a reaction.
Determining Rate Order with Experimental Data
An example reaction from which to determine rate order experimentally is shown.
Experimenters will run a number of trials of the reaction, in each trial varying the concentration of a subset of the reactants, while measuring the rate of product formation. For instance, see the data below:
1. Step one of determining the rate law is remembering that rate is equal to the rate constant, k, multiplied by the concentration of the reactants, A, B, and C. The experimental data is used to find the exponent of each reactant.
2. Step 2 is to analyze the experimental data. The best approach is to determine the exponents one at a time. Pick two trials where the concentration of all but one of the reactants stays the same. By manipulating only the concentration of one reactant over two trials, we know that any differences in product formation are due to that one change. For instance, note that over trials 1 and 2, only the concentration of reactant B changes, from 0.2 to 0.1.
3. Step 3 is to analyze how the rate of product formation changes between the two selected trials. We can see that the rate of product formation didn’t change from trial 1 to 2. Therefore, the term [B]y did not change from trial 1 to 2. The only way this could be possible is if changing the concentration of [B] has no effect on rate. The term [B]y has no effect on rate if and only if it’s exponent is 0, because any number raised to the zeroth power is one. Therefore, y = 1. Similarly, by comparing trials 2 and 3, the value of x can be determined to be 1. Comparing trials 3 and 4, the value of z can be determined to be 2. The final rate law is therefore:
Rate Law from Elementary Steps
The rate law of a reaction can also be found by using elementary steps. Elementary steps describe the individual steps that are actually occurring during the reaction. You are only able to tell if a step is elementary if the MCAT provides each step of the reaction mechanism. Elementary steps cannot be determined if you’re given only the overall reaction for a multistep reaction. For instance, see the reaction below, broken down into two steps.
The step indicated as the slowest step is the rate determining step. However, a rate law can be written for each step of the reaction. For each step, the rate law is written as k multiplied by reactant concentration raised to some exponent. Here’s what’s different: using elementary steps, stoichiometric coefficients become exponents. For step 1, the coefficient of A is 1 so it’s exponent in the rate law is 1. The coefficient of C is 2 so it’s exponent in the rate law is 2:
Looking at the rate law for the second step, keep in mind that only aqueous and gaseous substances are included in the rate law, which means solids and liquids are excluded. The molecule I, a solid, is not included in the rate law for the second step.
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