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

The average or general rate of a chemical reaction is defined as the change in concentration, measured in molarity, of a reactant or product over a specified period of time. It is important to note that the change in concentration for reactants is represented as a negative value, while for products, it is positive. This distinction arises because, during a reaction, reactants are consumed to form products, leading to a decrease in reactant concentration and an increase in product concentration over time.

The average rate can be expressed mathematically as:

Rate = \(\frac{\Delta [C]}{\Delta t}\)

In this equation, \(\Delta [C]\) represents the change in concentration, and \(\Delta t\) denotes the change in time. When applying this concept to a balanced chemical equation, the expression becomes more specific. For reactants, the change in concentration is calculated as:

\(\Delta [A] = \frac{[A]_{final} - [A]_{initial}}{a \cdot \Delta t}\)

Here, \([A]\) denotes the concentration of the reactant, and \(a\) is the stoichiometric coefficient from the balanced equation. Conversely, for products, the rate of formation is expressed as:

Rate = \(\frac{\Delta [B]}{b \cdot \Delta t}\)

In this case, \([B]\) represents the concentration of the product, and \(b\) is the corresponding stoichiometric coefficient. The change in product concentration is similarly calculated as:

\(\Delta [B] = \frac{[B]_{final} - [B]_{initial}}{b \cdot \Delta t}\)

Understanding these average rate expressions is crucial when analyzing the relationship between the rates of reactants and products in a balanced chemical equation. As we delve deeper into the topic, these concepts will help clarify how changes in the concentration of reactant molecules lead to the formation of products.

Rate Expressions Example

In a chemical reaction, the rates of disappearance of reactants and appearance of products can be expressed using their respective changes in concentration over time. For the reaction involving the reactants and products, the average rate can be formulated as follows:

Let the reactants be represented as C₃H₇OH and O₂, and the products as CO₂ and H₂O. The rate expressions are:

For the first reactant, the rate of disappearance is given by:

Rate = -\frac{1}{2} \frac{\Delta [C_3H_7OH]}{\Delta t}

For the second reactant, the rate of disappearance is:

Rate = -\frac{1}{9} \frac{\Delta [O_2]}{\Delta t}

For the products, the rate of appearance for CO₂ is:

Rate = \frac{1}{6} \frac{\Delta [CO_2]}{\Delta t}

And for H₂O, the rate of appearance is:

Rate = \frac{1}{8} \frac{\Delta [H_2O]}{\Delta t}

These expressions illustrate how the rates of disappearance of the reactants relate to the rates of appearance of the products, maintaining a balance in the reaction kinetics.

Average Rate Calculation Example

Understanding average rate calculations is crucial in reaction kinetics, particularly when determining the change in concentration of reactants or products over time. The rate of reaction is defined as the change in concentration divided by the change in time, expressed mathematically as:

\[ \text{Rate} = \frac{\Delta [C]}{\Delta t} \]

Where \(\Delta [C]\) represents the change in concentration and \(\Delta t\) represents the change in time. When focusing on a specific reactant, such as nitrogen monoxide (NO), it is important to note that the concentration of reactants decreases over time, which is indicated by a negative sign in the calculation. However, the rate itself is always expressed as a positive value.

For example, to calculate the average rate of change in concentration of nitrogen monoxide over the first five seconds of a reaction where the concentration drops from 1.3 M to 1.09 M, we can follow these steps:

1. Determine the change in concentration:

\[ \Delta [NO] = [NO]_{\text{final}} - [NO]_{\text{initial}} = 1.09 \, \text{M} - 1.3 \, \text{M} = -0.21 \, \text{M} \]

2. Calculate the change in time, which is 5 seconds.

3. Incorporate the stoichiometric coefficient of the reactant, which in this case is 2 (for the reaction involving 2 moles of NO). The average rate of disappearance can be calculated as:

\[ \text{Rate} = -\frac{\Delta [NO]}{2 \Delta t} = -\frac{-0.21 \, \text{M}}{2 \times 5 \, \text{s}} = \frac{0.21 \, \text{M}}{10 \, \text{s}} = 0.021 \, \text{M/s} \]

4. When considering significant figures, the concentration values dictate the precision of the final answer. The concentration of 1.3 M has 2 significant figures, while 1.09 M has 3. Therefore, the final answer should be reported as:

\[ \text{Rate} = 0.021 \, \text{M/s} \]

In summary, while the concentration of nitrogen monoxide decreases over time, the calculated rate of disappearance remains a positive value, reflecting the convention that rates are always expressed positively, even when reactants are consumed.

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.