Average Rate of Reaction: Videos & Practice Problems

The rate of a chemical reaction is the change in concentration of reactants or products over time. For reactants, this rate is negative as they are consumed, while for products, it is positive since they are formed. The rate equation,

$\mathrm{rate}=\frac{\mathrm{change} \mathrm{in} \mathrm{concentration}}{\mathrm{change} \mathrm{in} \mathrm{time}}$

is further defined by the stoichiometric coefficients from a balanced chemical equation. This means the rate of disappearance of reactants is equal to the rate of appearance of products when adjusted for their respective stoichiometric coefficients. Understanding this relationship is crucial when analyzing reaction rates and how the concentration of substances varies with time during a chemical reaction.

Average Rate of Reaction

Now average or general rate is the change in concentration in terms of molarity of a reactant or product over a period of time. Now here when we say change in concentrations, realize that the change in concentrations for reactants will be negative in terms of their sign and for products positive. The reason for this is remember as a reaction proceeds reactants are lost or broken down so that we can make product. So products are made overtime with our average or general rate.

We have our average or general rate expression. Here we'd say that rate equals changing concentration over change in time. But if we're applying it to a balanced chemical equation it takes on a little bit more meaning to it. So here we have change in concentration of reactants. Remember change in concentration. Concentration is shown by brackets equals final concentration minus initial concentration divided by A times change in time. Here A represents the stoichiometric coefficients for the reactants.

In a balanced chemical equation this rate would equal the rate of the product formation. Here it equals positive because remember products are being made. Change in product concentration divided by B times change in time. Again, change in product concentration is the same idea, it's final concentration minus initial concentration. Here B would represent again the stoichiometric coefficient, this time in terms of the products and change in time again would be your final time minus your initial time.

We're going to be utilizing these general average rate expressions when looking at a balanced chemical equation and being asked to discuss the relationship in rates between your reactants and your products, right. So keep these ideas in mind as we progress more and more into this idea of changes in concentration of our reactant molecules to produce products.

Rate Expressions Example

Provide the expressions for rate of disappearance of reactants and rate of appearance of products for the following reaction. All right. So here we're going to say that our average rate, so we're going to say our reactants are these two here. So it'd be change in the concentration of C₃H₇-O divided by. Remember here the coefficient for reactants is represented by the variable A. So for this first reactant, it's a two, so it'd be two times change in time.

Since it's a reactant, it's disappearing, so it would be a negative sign here that equals negative for the other reactant. So change in O₂ / 9 because the coefficient is 9 times change in time and these all equal the products because their products are being made. So this is plus change in concentration of CO₂ divided by coefficient of 6. So that's six times.

Change in time equals plus for the other product being formed. Change in H₂O water divided by 8 times. Change in time so this would represent each one of their average or general rate expressions and how they be equal to one another. So this would be your final answer.

Average Rate Calculation Example

Now when dealing with average rate calculations, just remember that knowing how to write expressions for the rate of reaction will help to determine calculations for various time intervals. Remember when we say rate of reaction, that's not tying it to a product or reactant. So in this case, rate would just equal change in concentration over change in time. It's once we react, we combine it to reactives or products that the not negative and positive signs come up in. The coefficients play a role.

So here we're going to say, calculate the average rate of change in concentration of nitrogen monoxide in the 1st 5 seconds of the reaction if the concentration dropped from 1.3 molar to 1.09 molar. All right. So now we're not talking about the rate of reaction. We're talking specifically about this reactant. So now because it's a reactant, it's disappearing, so it has a negative sign. We're talking about exchanging concentration over its change in time. But remember its coefficient has to be included.

So here times change in time, so now that becomes negative. So change in concentration is final minus initial. So that's 1.09 molar - 1.3 molar / 2 × 5 seconds. Remember to set the 1st 5 seconds. So here when we do that, that comes out to be 0.021 molarity per second. Because remember, the top units are molarity, the bottom is seconds.

Here we're not going to look at the five seconds for our number of sig figs. Better to use the concentrations. 1.3 has two, 1.09 has three. You go with the least number of sig figs. So that's why it's 0.021. Notice here that the answer at the end is a positive value. That's because when we subtract, these two get a negative value. Negative times a negative gives me a positive. So although reactants are decreasing over time, their rate is still a positive value. Rate is always positive.

OK, so here the rate of decrease or rate of disappearance for nitrogen monoxide would be 0.021 molar of this reactant disappearing per second.

Consider the following reaction:2 H₂O₂ (aq) → 2 H₂O (l) + O₂ (g)
Calculate the rate of the reaction between 25 sec and 65 sec.

• A. 0.018 M/s
• B. 9.0×10^–3 M/s
• C. 0.036 M/s
• D. 0.041 M/s
• E. 0.083 M/s

Answer: (B)

Here’s what students ask on this topic:

How do you find the average rate of reaction?

To find the average rate of reaction, you need to measure the change in concentration of a reactant or product over a specific time period. Here’s the step-by-step process:

1. Choose which reactant or product you will monitor for the reaction. The choice may depend on which substance is easier to measure or more relevant to the reaction's context.
2. Measure the initial concentration of the chosen substance. This is often denoted as $A_0$, where "A" represents the substance and "$0$" indicates the initial measurement.
3. After a certain period, measure the concentration of the substance again. This is your final concentration, $A_1$.
4. Calculate the change in concentration by subtracting the initial concentration from the final concentration: $\Delta A_1-A_0$. If you're measuring a reactant, the change will be negative, as reactants are consumed.
5. Determine the time interval ($\Delta t$) during which the change occurred. This is the difference between the final time and the initial time.
6. Divide the change in concentration by the time interval to find the average rate of reaction:

How do you calculate the average rate of reaction?

To calculate the average rate of reaction, you need to measure the change in concentration of a reactant or product over a specific time period. Here's a step-by-step method:

1. Identify the reactant or product you'll be focusing on.
2. Measure its concentration at two different times during the reaction. Concentration can be in moles per liter (M).
3. Calculate the change in concentration (Δ[Concentration]) by subtracting the initial concentration from the final concentration.
4. Determine the change in time (ΔTime) by subtracting the initial time from the final time.
5. Divide the change in concentration by the change in time to find the average rate of reaction.

The formula looks like this:

$\text{Average Rate of Reaction =}\frac{\Delta \left[\text{Concentration}\right]}{\Delta \text{Time}}$

If the concentration decreases over time (for a reactant), the change in concentration will be negative, indicating the rate at which the reactant is being consumed. If you're measuring a product, the change in concentration will be positive, showing the rate at which the product is being formed. Remember to keep your units consistent when performing these calculations.

What is needed to calculate the average reaction rate of a system?

To calculate the average reaction rate of a chemical system, you'll need to know a few key pieces of information:

1. Concentration Change of Reactants or Products: You must measure the change in concentration of one of the reactants or products over a specific time period. This can be in moles per liter (M) for solutions or in pressure (atm) for gases.
2. Time Interval: The time over which the concentration change occurs is crucial. It should be recorded in seconds, minutes, or hours, depending on the reaction's speed.
3. Balanced Chemical Equation: Having the balanced equation for the reaction allows you to relate the changes in concentration of one reactant or product to the others involved in the reaction.
4. Stoichiometry of the Reaction: The stoichiometry from the balanced equation will tell you the ratio in which reactants are consumed and products are formed. This is necessary to calculate the rate for each reactant and product.

The average reaction rate is then calculated by taking the change in concentration (Δ[Concentration]) of the reactant or product and dividing it by the change in time (ΔTime) over which the change occurred. Remember to account for the stoichiometry and to express the rate in terms of the decrease in concentration of reactants or the increase in concentration of products.

How do you write a rate expression?

To write a rate expression, also known as the rate law, for a chemical reaction, you need to know the reaction's rate and the concentrations of the reactants. The general form of a rate expression is:

Rate = k [A]^m [B]ⁿ ...

Here, 'Rate' is the rate of the reaction, 'k' is the rate constant, and [A] and [B] represent the molar concentrations of reactants A and B, respectively. The exponents 'm' and 'n' are the reaction orders with respect to each reactant, indicating how the rate is affected by changes in the concentration of that reactant.

To determine the specific rate expression for a reaction, you typically need to conduct experiments to measure the reaction rate under various concentrations of reactants. From the data, you can deduce the order of the reaction with respect to each reactant (the exponents 'm' and 'n') and calculate the rate constant 'k'. Remember that the reaction order is not necessarily related to the stoichiometric coefficients of the reactants in the balanced equation; it must be determined experimentally.

What is the rate law expression for this reaction if the second step is rate determining?

To provide you with a rate law expression for a reaction where the second step is rate-determining, I would need the specific reaction steps, including the reactants, products, and intermediates. The rate law is determined by the slowest (rate-determining) step in a reaction mechanism, assuming that the reaction proceeds through a series of elementary steps.

However, I can give you a general approach to finding the rate law for such a scenario:

1. Identify the rate-determining step (the slowest step) in the mechanism.
2. Write the rate law based on the reactants involved in that step. Only species that are part of the rate-determining step will appear in the rate law.
3. If the rate-determining step involves intermediates (species formed in an earlier step that do not appear in the overall balanced equation), you need to express these intermediates in terms of the initial reactants using the equilibrium conditions from the fast steps.

For example, if the second step of a two-step reaction is rate-determining and involves reactants A and B, the rate law might look like this:

$\mathrm{rate}=k\left[A\right]\left[B\right]$

Here, 'k' is the rate constant, and the concentrations of A and B are raised to the power of their stoichiometric coefficients in the rate-determining step.