Concentration Dependence
Chemical Kinetics and the Reaction Rate Law
Chemical kinetics refers to the rate or speed of a chemical reaction. The rate depends on the mechanism, c…
The measure of how fast a reaction proceeds is called the reaction rate. For a single-step reaction, the rate is equal to the change in concentration of each reactant or product over time multiplied by the inverse of the corresponding stoichiometric coefficient. You can think of the change in concentration over time as the concentration at time t minus the starting concentration divided by t. Reaction rates are always positive, so the reactant expressions have negative signs. These rates may not be equal in multi-step reactions, but we can still use this relationship as an estimate for the overall reaction.
The rate law, or rate equation, describes the relationship between the speed of the reaction and the reactant concentrations. In this equation, k is the rate constant, A and B are the two reactants, and m and n are their respective reaction orders. Reaction order describes the relationship between the concentration of a reactant and the rate and is not related to stoichiometry. It is vital to remember that the reaction order is not the same as the coefficient of the reactant in the balanced equation.
When a reaction involves two or more reactants, we must consider the reaction order for each reactant. The overall reaction order is equal to the sum of the reactants' reaction orders. For example, if reactant A is first-order and reactant B is zero-order, the overall reaction order is one. The most common reaction orders in simple reactions are zero-order, first-order, and second-order. Let's go through them using a unimolecular reaction as an example.
If the reaction is zero order, the reactant concentration has no effect on the reaction rate. Thus, the reaction rate is equal to k, the rate constant. A graph of the reaction rate with respect to concentration is a horizontal line.
In first order relationships, the reactant concentration is linearly related to the reaction rate. Thus, the rate is equal to the rate constant times the reactant concentration. A graph of the reaction rate with respect to concentration will be linear, with k as the slope.
If the reaction is second order, there is a quadratic relationship between the concentration and the rate. Thus, the rate is equal to the rate constant times the concentration squared. A graph of the rate with respect to concentration will be parabolic, with k as the slope.
The rate constant, k, is a temperature-dependent value that relates the activation energy of the reaction to the reaction rate. You will explore this in the next lab experiment.
Reaction rates are typically given in moles per liter per second. The rate has the same units, regardless of the reaction order. Thus, the rate constant has different units, depending on the reaction order. For example, if A is first order and B is zero order, then we have one instance of moles per liter in the rate equation. Therefore, the rate constant must be in inverse seconds.
So how do we determine reaction order? The reaction order must be determined experimentally using a series of tests. If you have two reactants, one method is to hold the concentration of one reactant constant, vary the other, and time how long it takes to make a certain amount of product. The same process is repeated for the second reactant. You can then estimate the order for each reactant by plotting rate versus the reactants' varying concentration, and seeing whether it looks like a zero, first, or second-order graph. Matching your data to the corresponding rate equation will also let you calculate k.
In this lab, you will determine the reaction orders of two reactants by varying their concentrations and timing how long it takes the reaction to progress to turning the solution opaque.
The measure of how fast a reaction proceeds is called the reaction rate. For a single-step reaction, the rate is equal to the change in concentration of each reactant or product over time multiplied by the inverse of the corresponding stoichiometric coefficient. You can think of the change in concentration over time as the concentration at time t minus the starting concentration divided by t. Reaction rates are always positive, so the reactant expressions have negative signs. These rates may not be equal in multi-step reactions, but we can still use this relationship as an estimate for the overall reaction.
The rate law, or rate equation, describes the relationship between the speed of the reaction and the reactant concentrations. In this equation, k is the rate constant, A and B are the two reactants, and m and n are their respective reaction orders. Reaction order describes the relationship between the concentration of a reactant and the rate and is not related to stoichiometry. It is vital to remember that the reaction order is not the same as the coefficient of the reactant in the balanced equation.
When a reaction involves two or more reactants, we must consider the reaction order for each reactant. The overall reaction order is equal to the sum of the reactants' reaction orders. For example, if reactant A is first-order and reactant B is zero-order, the overall reaction order is one. The most common reaction orders in simple reactions are zero-order, first-order, and second-order. Let's go through them using a unimolecular reaction as an example.
If the reaction is zero order, the reactant concentration has no effect on the reaction rate. Thus, the reaction rate is equal to k, the rate constant. A graph of the reaction rate with respect to concentration is a horizontal line.
In first order relationships, the reactant concentration is linearly related to the reaction rate. Thus, the rate is equal to the rate constant times the reactant concentration. A graph of the reaction rate with respect to concentration will be linear, with k as the slope.
If the reaction is second order, there is a quadratic relationship between the concentration and the rate. Thus, the rate is equal to the rate constant times the concentration squared. A graph of the rate with respect to concentration will be parabolic, with k as the slope.
The rate constant, k, is a temperature-dependent value that relates the activation energy of the reaction to the reaction rate. You will explore this in the next lab experiment.
Reaction rates are typically given in moles per liter per second. The rate has the same units, regardless of the reaction order. Thus, the rate constant has different units, depending on the reaction order. For example, if A is first order and B is zero order, then we have one instance of moles per liter in the rate equation. Therefore, the rate constant must be in inverse seconds.
So how do we determine reaction order? The reaction order must be determined experimentally using a series of tests. If you have two reactants, one method is to hold the concentration of one reactant constant, vary the other, and time how long it takes to make a certain amount of product. The same process is repeated for the second reactant. You can then estimate the order for each reactant by plotting rate versus the reactants' varying concentration, and seeing whether it looks like a zero, first, or second-order graph. Matching your data to the corresponding rate equation will also let you calculate k.
In this lab, you will determine the reaction orders of two reactants by varying their concentrations and timing how long it takes the reaction to progress to turning the solution opaque.
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Q1: What is the difference between reaction order and stoichiometric coefficients?
Reaction order describes how reactant concentration affects reaction rate and must be determined experimentally. Stoichiometric coefficients are the numbers in the balanced chemical equation and do not determine reaction order. For example, a reactant with a coefficient of 2 could be zero-order, first-order, or second-order depending on its actual relationship to the reaction rate.
Q2: How does concentration affect the reaction rate in a zero-order reaction?
In a zero-order reaction, reactant concentration has no effect on the reaction rate. The rate equals only the rate constant k, making the reaction rate independent of how much reactant is present. A graph of reaction rate versus concentration appears as a horizontal line.
Q3: What is the mathematical relationship between concentration and rate in first-order reactions?
In first-order reactions, reactant concentration is linearly related to the reaction rate. The rate equation is rate = k[A], where k is the rate constant and [A] is the reactant concentration. Doubling the concentration doubles the reaction rate, and the graph is linear with slope k.
Q4: How does doubling a reactant's concentration affect a second-order reaction?
In second-order reactions, there is a quadratic relationship between concentration and rate. When you double the reactant concentration, the reaction rate increases by a factor of four. The rate equation is rate = k[A]², and the concentration-versus-rate graph appears parabolic.
Q5: Why does the rate constant have different units depending on reaction order?
The rate constant k must have units that make the overall rate expression equal moles per liter per second. For zero-order reactions, k has units M/s. For first-order, k is 1/s. For second-order, k is 1/(M·s). The units adjust so the rate always has consistent dimensions regardless of reaction order.
Q6: What experimental method is used to determine the reaction order of each reactant?
To determine reaction order, hold one reactant's concentration constant while varying the other, then measure the time for the reaction to progress to a visible endpoint. Repeat for each reactant. Compare how reaction time changes with concentration: constant time indicates zero-order, linear changes indicate first-order, and a factor-of-four change when concentration doubles indicates second-order.
Q7: How is the overall reaction order calculated when a reaction has multiple reactants?
The overall reaction order is the sum of the individual reaction orders for each reactant. For example, if reactant A is first-order (m = 1) and reactant B is zero-order (n = 0), the overall reaction order is one. This sum determines how the combined concentrations of all reactants affect the total reaction rate.