Chapter 17 Study Guide: 1/2 Exam 1 -Chemistry 2

Know that the temperature dependence of reaction rate is modeled by the Arrhenius equation, an equation that describes the rate constant k in terms of temperature, a frequency factor, andan activation energy.

It provides a mathematical model of the temperature dependence of reaction rates. Here's the equation: k=Ae−RTEa​ Where: k is the rate constant of the reaction, A is the pre-exponential factor or frequency factor, which represents the rate of reaction when there are no energy barriers to the reaction, Ea is the activation energy of the reaction, which is the minimum energy required for the reaction to occur, R is the universal gas constant, and T is the absolute temperature. The term e−RTEa​ represents the fraction of molecules that have energy equal to or greater than the activation energy Ea at a given temperature T. This equation shows that the rate of a reaction increases with increasing temperature, as more molecules have the necessary energy to overcome the activation barrier.

Use the method of initial rates to determine the order of a reaction from a table of concentration and initial rates.

1. Conduct Experiments: Conduct several experiments where you change the initial concentration of one reactant while keeping the others constant. Measure the initial rate of reaction for each experiment. 2. Calculate Rate Ratios: Choose two experiments and calculate the ratio of the initial rates. 3. Calculate Concentration Ratios: Calculate the ratio of the initial concentrations for the same two experiments. 4. Determine Reaction Order: The reaction order with respect to that reactant is determined by the exponent n in the equation (Rate 2/Rate 1) = (Concentration 2/Concentration 1)^n. If doubling the concentration doubles the rate, the reaction is first order with respect to that reactant. If doubling the concentration quadruples the rate, the reaction is second order, and so on. 5. Repeat for Other Reactants: Repeat steps 1-4 for all other reactants. 6. Determine Overall Reaction Order: The overall reaction order is the sum of the orders with respect to each reactant.

Determine and identify the order of a reaction with multiple reactants by observing the effect of a concentration change on the rate of reaction for each independent reactant.

1. Isolate one reactant: Change the concentration of one reactant while keeping the concentrations of all other reactants constant. This allows you to study the effect of the isolated reactant on the rate of reaction. 2. Measure the rate of reaction: Conduct the reaction and measure the rate of reaction for each different concentration of the isolated reactant. 3. Analyze the data: Compare the changes in the rate of reaction to the changes in the concentration of the isolated reactant. - If the rate of reaction changes proportionally with the concentration, the reaction is first order with respect to that reactant. - If the rate of reaction changes with the square of the concentration, the reaction is second order with respect to that reactant. - If the rate of reaction does not change with the concentration, the reaction is zero order with respect to that reactant. 4. Repeat for all reactants: Repeat steps 1-3 for each reactant in the reaction. The overall order of the reaction is the sum of the orders of all the reactants. Remember, the order of a reaction is an experimental quantity. It cannot be predicted from the stoichiometric equation of the reaction and must be determined empirically. Let's consider a general reaction: aA+bB→products The rate law for this reaction can be written as: rate=k[A]m[B]n Where: k is the rate constant, [A] and [B] are the concentrations of the reactants A and B, m and n are the orders of the reaction with respect to A and B. The values of m and n (which can be 0, 1, 2, ...) are determined experimentally by observing how the rate of reaction changes as the concentrations of A and B change. The overall order of the reaction is m+n.

Define activation energy and frequency factor.

Activation energy is the minimum amount of energy required for a chemical reaction to occur. It is denoted by Ea and is expressed in joules per mole. Frequency factor, also known as pre-exponential factor, is a constant that takes into account the frequency of collisions and likelihood of correct molecular orientation. It is denoted by A and has units of L mol −1 s −1. The Arrhenius equation relates the rate constant k of a chemical reaction to the temperature T, activation energy Ea, and frequency factor A as follows: k = A e^(-Ea/RT) where R is the gas constant and T is the temperature expressed in Kelvin

Know that atoms and molecules contain a distribution of energy that depends on temperature and that those exceeding the activation energy can undergo reaction

Atoms and molecules in a system do not all possess the same energy, but rather a distribution of energies that is influenced by the temperature of the system. This distribution is described by the Boltzmann distribution law, which states that the probability of a particle having a certain energy is proportional to the exponential of negative that energy divided by the product of the Boltzmann constant (k) and the absolute temperature (T). In the context of a chemical reaction, only those molecules whose energy exceeds the activation energy (Ea) can undergo a reaction. The activation energy is the minimum energy that reactants must possess in order to convert into products. As the temperature increases, the fraction of molecules with energies equal to or greater than the activation energy also increases, leading to an increase in the rate of reaction. This is why reactions generally proceed faster at higher temperatures.

Know that catalysts lower the activation energy of a reaction, often by changing the mechanism or the nature of the transition state.

Catalysts are defined as substances that participate in a chemical reaction but are not changed or consumed. Instead, they provide a new mechanism for a reaction, which has a lower activation energy than the reaction without the catalyst.

Know that a catalyst increases the rate of a reaction without being consumed by the reaction.

Catalysts typically speed up a reaction by reducing the activation energy or changing the reaction mechanism. Enzymes are proteins that act as catalysts in biochemical reactions.

Determine the rate constant from the slope of a plot of natural logarithm of reactant concentration versus time for a first-order reaction.

For a first-order reaction, the rate of reaction is directly proportional to the concentration of one reactant. The rate law for a first-order reaction is: Rate = k[A] where: rate is the rate of reaction, k is the rate constant, [A] is the concentration of the reactant. If we rearrange this equation and integrate it from the initial concentration [A]₀ to the concentration [A] at time t, we get: In ([A] / [A]0) = -kt or equivalently, ln([A]) =−kt+ ln([A]0​) This equation is in the form of a straight line equation y = mx + c, where: y = ln([A]) (the natural logarithm of the reactant concentration), m = -k (the slope of the line, which is the negative of the rate constant), x = t (the time), c = ln([A]₀) (the y-intercept, which is the natural logarithm of the initial reactant concentration). So, if you plot ln([A]) versus t for a first-order reaction, the slope of the line will be -k. Therefore, you can determine the rate constant k from the slope of this plot by taking the negative of the slope

Use the second-order integrated rate law to find the reactant concentration at a given time or the time elapsed for a given concentration change.

For a second-order reaction, the integrated rate law is: [A]t​1​=kt+[A]0​ where: [A]t​ is the concentration of the reactant at time t, k is the rate constant, [A]0​ is the initial concentration of the reactant. If you want to find the reactant concentration at a given time ([A]t​), you can rearrange the equation to solve for [A]t​: [A]t​=kt+[A]0​1​1​ You would need to know the rate constant k, the initial concentration [A]0​, and the time t. If you want to find the time elapsed for a given concentration change (t), you can rearrange the equation to solve for t: t=k[A]t​1​−[A]0​1​​ You would need to know the rate constant k, the initial concentration [A]0​, and the final concentration [A]t​. Remember, this method is only valid for second-order reactions where the reaction is second order with respect to a single reactant. If the reaction is second order overall but involves two first-order reactants, a different method would be needed.

Determine the rate constant from the slope of a plot inverse reactant concentration versus time for a second-order reaction.

For a second-order reaction, the integrated rate law is: [A]t​1​=kt+[A]0​1​ If you plot [A]t​1​ (the inverse of the reactant concentration) on the y-axis and t (time) on the x-axis, the slope of the line will be equal to the rate constant k. Here's how you can determine the rate constant: 1. Plot the data: Plot your data with [A]t​1​ on the y-axis and t on the x-axis. 2. Determine the slope: Use a line of best fit to determine the slope of the line. The slope of the line is the rate constant k. 3. Calculate k: The value of the slope is your rate constant k. Remember, this method is only valid for second-order reactions where the reaction is second order with respect to a single reactant. If the reaction is second order overall but involves two first-order reactants, a different method would be needed.

Determine the rate constant from the slope of a plot of reactant concentration versus time for a zero-order reaction.

For a zero-order reaction, the integrated rate law is: [A]t​=−kt+[A]0​ If you plot [A]t​ (the reactant concentration) on the y-axis and t (time) on the x-axis, the slope of the line will be equal to the negative of the rate constant −k. Here's how you can determine the rate constant: 1. Plot the data: Plot your data with [A]t​ on the y-axis and t on the x-axis 2. Determine the slope: Use a line of best fit to determine the slope of the line. The slope of the line is the negative of the rate constant −k. 3. Calculate k: The absolute value of the slope is your rate constant k. Remember, this method is only valid for zero-order reactions. If the reaction is not zero order, a different method would be needed.

Know the general definition of a rate law and the meaning and significance of the rate order and rate constant.

Rate laws or rate equations are mathematical expressions that describe the relationship between the rate of a chemical reaction and the concentration of its reactants. In general, a rate law (or differential rate law, as it is sometimes called) takes this form: rate=k[A]m[B]n[C]p A rate law shows how the rate of a chemical reaction depends on reactant concentration. For a reaction such as aA → products, the rate law generally has the form rate = k[A]ⁿ, where k is a proportionality constant called the rate constant and n is the order of the reaction with respect to A.

Know and understand that the rate of a chemical reaction is a change in concentration measured during a change in time

The reaction rate is the change in the concentration of either the reactant or the product over a period of time. The concentration of A decreases with time, while the concentration of B increases with time. rate = Δ[B] Δt = − Δ[A] Δt Square brackets indicate molar concentrations, and the capital Greek delta (Δ) means "change in."

Use the first-order integrated rate law to find the reactant concentration at a given time or the time elapsed for a given concentration change.

Sure, let's use the first-order integrated rate law. The equation is: ln([A])=−kt + ln([A]0​) where: [A] is the concentration of the reactant at time t, k is the rate constant, t is the time, [A]₀ is the initial concentration of the reactant. If you want to find the reactant concentration [A] at a given time t, you can rearrange the equation to solve for [A]: [A]=[A]0​⋅e−kt If you want to find the time t elapsed for a given concentration change, you can rearrange the equation to solve for t: t=−kln([A]/[A]0​)​ Please note that the rate constant k and the initial concentration [A]₀ need to be known or determined from experimental data to use these equations. Also, the concentration [A] should be in the same units as [A]₀, and the time t should be in the same units as the inverse of the rate constant k.

Calculate the activation energy from a plot of the natural logarithm of the rate constant versus inverse temperature, ln k versus 1/T

The Arrhenius equation can be rearranged into a linear form that allows us to calculate the activation energy (Ea) from a plot of ln(k) versus 1/T. The linear form of the Arrhenius equation is: ln k = - Ea / R * 1 / T + ln A This equation is in the form of a straight line (y = mx + b), where: y = ln k m = -Ea/R x = 1/T b = ln A If you plot ln(k) versus 1/T, the slope of the line will be -Ea/R. Therefore, you can calculate Ea using the equation: Ea = - slope * R Where: Ea is the activation energy, slope is the slope of the line from the plot, and R is the universal gas constant. Please note that the temperature T should be in Kelvin, and the value of R should be consistent with the units of Ea and k. Typically, R = 8.314 J/(mol·K) is used when Ea is in joules per mole and k is in s^-1. Remember to convert the slope to the correct units before calculating Ea. For example, if the slope is in K^-1 and you want Ea in kJ/mol, you should convert R to kJ/(mol·K) before calculating.

Know the difference between average and instantaneous rates, and understand how each can be measured or estimated from a plot of concentration versus time (or from a table of data used to produce such a plot).

The average rate and instantaneous rate are two different ways to measure the rate of change of a quantity. The average rate of change represents the total change in one variable in relation to the total change of another variable1. It is calculated by taking the difference in the dependent variable (e.g., concentration) divided by the difference in the independent variable (e.g., time) over a certain interval. Average Rate: ΔY/ΔX = Y2 - Y1 / X2 - X1 where Δy and Δx are the changes in y and x, respectively, The instantaneous rate of change, on the other hand, measures the specific rate of change of one variable in relation to a specific, infinitesimally small change in the other variable1. It is the rate of change at a particular instant or point and can be thought of as the rate of change as the interval approaches zero. This is essentially the derivative of the function at a particular point. It can be estimated from a graph by drawing a tangent to the curve at the point of interest and calculating its slope. Mathematically, it is expressed as: Instantaneous Rate: dy/dx where dy and dx represent infinitesimally small changes in y and x, respectively.

Calculate an average rate of reaction and predict a change in concentration from a plot of concentration versus time (or from a table of data used to produce such a plot).

The average rate of a reaction can be calculated using the formula: Average Rate: Δ[concentration]/ΔT where: Δ[Concentration] is the change in concentration of the reactant or product. Δt is the change in time. To predict a change in concentration from a plot of concentration versus time, you can use the slope of the line at a specific point. The slope of the line on a concentration vs. time graph represents the reaction rate. Rate Law: It's a mathematical equation that links the rate of a reaction to the concentrations of its reactants. It's usually in the form: rate = k[A]^m[B]^n[C]^p.... Rate Order: It's the exponent in the rate law for each reactant, indicating how the rate is affected by the concentration of that reactant. The total order is the sum of all individual orders. Rate Constant (k): It's a factor in the rate law that connects the concentrations of reactants to the reaction rate. It's specific to a particular reaction at a specific temperature.

Know and understand the collision model: atoms or molecules need to come in contact or collide in order to react.

The collision model is a fundamental concept in chemical kinetics. It states that for a reaction to occur, it's not enough for reactants to be present in a system; they must also collide with each other. However, not all collisions result in a reaction. According to the collision model, an effective collision that leads to a reaction must satisfy two conditions: 1. Sufficient Energy: The particles must collide with energy equal to or greater than the activation energy of the reaction. This is the minimum energy required to overcome the energy barrier and transform reactants into products. 2. Proper Orientation: The particles must collide in a way that allows the bonds to break and new ones to form. This means that the atoms involved in the breaking and forming of bonds need to be suitably aligned at the moment of impact. So, in essence, the collision model helps us understand why reactions occur at different rates under different conditions.

Know that the collision model accounts for the frequency factor in the Arrhenition and that effective collisions require the proper orientation between two reacting molecules.us equation and that effective collisions require the proper orientation between two reacting molecules.

The collision model is a theory that explains the frequency factor (A) in the Arrhenius equation. It postulates that for a reaction to occur, not only must particles collide, but they must also do so with sufficient energy and an appropriate orientation. The frequency factor, A, is a measure of the number of collisions that could lead to a reaction. It's influenced by factors such as the concentration of reactants and their relative velocities. However, not all collisions lead to a reaction. For a collision to be effective and result in a reaction, two conditions must be met: 1. The colliding molecules must have a combined kinetic energy equal to or greater than the activation energy (Ea) of the reaction. This is the minimum energy required to overcome the energy barrier and transform reactants into products. 2. The molecules must collide with the proper orientation. This means that the atoms involved in the breaking and forming of bonds need to be suitably aligned at the moment of impact. This is why the collision model is so important in understanding reaction rates and the factors that influence them. It provides a microscopic perspective on the processes that govern chemical reactions.

Understand the difference between rate law and integrated rate law.

The differential rate law tells you how the rate of a reaction depends on the concentration of reactant (s). The integrated rate law tells you how the concentration of reactant (s) depends on time.

Understand that the order of a reaction must be determined experimentally and not from a balanced reaction

The exponents (y and z) must be experimentally determined and do not necessarily correspond to the coefficients in the balanced chemical equation. Reaction Order, The sum of the concentration term exponents in a rate law equation is known as its reaction order.

Calculate the half-life or predict the concentration of a reactant using the mathematical expressions for first- and second-order reactions.

The half-life and concentration of a reactant can be calculated using different formulas depending on the order of the reaction. First-Order Reactions: For a first-order reaction, the rate of the reaction is directly proportional to the concentration of one reactant. The mathematical expression for the concentration of the reactant A is: [A]=[A]0​e−kt where: [A] is the concentration of the reactant at time t, [A]0​ is the initial concentration of the reactant, k is the rate constant, t is the time. The half-life (t1/2​) of a first-order reaction is given by: t1/2 = 0.693 /k Second-Order Reactions: For a second-order reaction, the rate of the reaction is proportional to the square of the concentration of one reactant or to the product of the concentrations of two reactants. The mathematical expression for the concentration of the reactant A is: 1 /[A] =kt + 1/[A]0 where: [A] is the concentration of the reactant at time t, [A]0​ is the initial concentration of the reactant, k is the rate constant, t is the time. The half-life (t1/2​) of a second-order reaction is given by: t1/2 = 1/k[A]0 Please note that these formulas assume that the reaction is only first-order or second-order and does not change order during the reaction. Also, the rate constant k and the concentrations need to be in consistent units in order for the equations to work correctly.

Define half-life and understand how it can be identified from a plot of reactant concentration versus time.

The half-life of a reaction, often denoted as t1/2​, is the time required for the concentration of a reactant to decrease to half of its initial concentration. It is a characteristic property of each radioactive isotope. For a zero-order reaction, the half-life is given by: t1/2​=2k[A]0​​ where: [A]0​ is the initial concentration of the reactant, k is the rate constant. In a plot of reactant concentration ([A]) versus time (t), the half-life can be identified as the time at which the reactant concentration has decreased to half of its initial value. For a zero-order reaction, this plot is a straight line with a negative slope, and the half-life is the time at which the concentration is half of the y-intercept (which represents the initial concentration [A]0​). Please note that the half-life depends on the order of the reaction and the rate constant, and it can vary significantly for different reactions or under different conditions.

Know and understand the first-order integrated rate law and that a plot of the natural logarithm of the reactant concentration versus time is linear

The natural log of the concentration of A at a given time t --> Ln [A]ₜ is basically Y, and is equal to the natural log of the initial concentration of A --> Ln [A]₀ which is basically b, minus the rate constant -->k (basically m, aka the slope of the line) multiplied by time (basically x). So we get a linear graph of the form Y=mx+b ii.

Know that a rate is the change of a particular property with respect to time

The rate at which a reactant is consumed in a first-order process is proportional to its concentration at that time. This general relationship, in which a quantity changes at a rate that depends on its instantaneous value, is said to follow an - exponential law.

Know and understand the second-order integrated rate law and that a plot of the inverse reactant concentration versus time is linear.

The second-order integrated rate law is used to describe the behavior of reactions that are second order. This means that the rate of the reaction depends on the concentration of one reactant raised to the second power, or the product of the concentrations of two reactants. The general form of the second-order rate law is: [A]t​1​=kt+[A]0​1​ where: [A]t​ is the concentration of the reactant at time t, k is the rate constant, [A]0​ is the initial concentration of the reactant. This equation shows that a plot of the inverse of the reactant concentration (1/[A]t​) versus time (t) will be a straight line. The slope of this line is equal to the rate constant k, and the y-intercept is equal to 1/[A]0​. This linear relationship is a characteristic feature of second-order reactions and can be used to determine the rate constant from experimental data. It's important to note that this form of the rate law is valid only for reactions that are second order in a single reactant. If a reaction is second order overall, but not second order in a single reactant, this form of the rate law does not apply. In such cases, the reaction rate may depend on the concentrations of two different reactants, each raised to the first power. The integrated rate law for such reactions would be different.

Know that a transition state or activated complex represents a transient arrangement of atoms that occurs as reactants form products

The transition state, also known as the activated complex, is a high-energy state that is intermediate between the reactants and the products in a chemical reaction. It represents a transient arrangement of atoms at the peak of the reaction's energy profile. At this point, the system has enough energy to overcome the activation barrier, but it has not yet formed the products. The transition state is very unstable and exists for an extremely short period of time before the reaction proceeds to form products. It's important to note that the transition state cannot be isolated or observed directly because of its fleeting existence. The concept of the transition state is crucial in understanding the kinetics of chemical reactions, as it's directly related to the activation energy in the Arrhenius equation. The lower the energy of the transition state, the faster the reaction will proceed. This is the principle behind the use of catalysts, which provide an alternative reaction pathway with a lower activation energy, thereby increasing the reaction rate.

Draw and interpret a potential energy diagram, a plot of energy versus reaction progress, including the energy levels of the reactants, transition state, and products.

The y-axis represents the potential energy of the system. A higher position on the axis indicates a higher energy level. The x-axis represents the progress of the reaction, from reactants to products. The reactants and products are represented by plateaus on the diagram. The energy level of the reactants is shown at the start of the reaction, and the energy level of the products is shown at the end. The transition state, or the highest energy point along the reaction path, represents the point at which the system is in its most unstable state. This is also known as the activation energy for the reaction. The difference in energy between the reactants and products is the change in enthalpy (ΔH) for the reaction. If the products have a lower energy than the reactants, the reaction is exothermic (ΔH < 0). If the products have a higher energy, the reaction is endothermic (ΔH > 0).

Know and understand the zero-order integrated rate law and that a plot of the reactant concentration versus time is linear.

The zero-order integrated rate law is used to describe the behavior of reactions that are zero order. This means that the rate of the reaction does not depend on the concentration of the reactant. The general form of the zero-order rate law is: [A]t​=−kt+[A]0​ where: [A]t​ is the concentration of the reactant at time t, k is the rate constant, [A]0​ is the initial concentration of the reactant. This equation shows that a plot of the reactant concentration ([A]t​) versus time (t) will be a straight line. The slope of this line is equal to the negative of the rate constant −k, and the y-intercept is equal to the initial concentration [A]0​. This linear relationship is a characteristic feature of zero-order reactions and can be used to determine the rate constant from experimental data. It's important to note that this form of the rate law is valid only for reactions that are zero order. If a reaction is not zero order, this form of the rate law does not apply.

Know that the reaction rate is measured experimentally and that instruments like aspectrometer or gas chromatograph are used to measure concentrations.

Two common instruments used for this purpose are: spectrometers and gas chromatographs. A spectrometer measures the intensity of different wavelengths of light. It's often used in colorimetry or spectrophotometry to measure the concentration of a substance in a solution, based on how much light it absorbs. A gas chromatograph, on the other hand, is used to analyze the composition of a volatile substance or separate different components of a mixture. In the context of reaction rates, it can be used to measure the concentrations of reactants and products over time.

Know that the order of the reaction predicts the dependence of concentration on time.

What does the reaction order tell us: We need to know the order of a reaction because it tells us the functional relationship between concentration and rate. It determines how the amount of a compound speeds up or retards a reaction. For example, a reaction order of three means the rate of reaction increases as the cube of the concentration.

Know that the plot of rate (often in units of M/s) versus concentration produces a straight horizontal line for zero-order reactions, a straight line with a positive slope for first-order reactions, and a curved line with a positive slope for higher-order reactions.

Zero-order reactions: The rate of reaction is independent of the concentration of the reactants. Hence, the rate remains constant over time, leading to a straight horizontal line when the rate is plotted against concentration. First-order reactions: The rate of reaction is directly proportional to the concentration of one reactant. This results in a straight line with a positive slope when the rate is plotted against concentration. Second-order or higher reactions: The rate of reaction depends on the concentration of two or more reactants or the square of the concentration of a reactant. This leads to a curved line with a positive slope when the rate is plotted against concentration.

Use the zero-order integrated rate law to find the reactant concentration at a given time or the time elapsed for a given concentration change.

the zero-order integrated rate law is used when the rate of reaction is independent of the concentration of the reactants. It is given by: [A]=−kt+[A]0​ where: [A] is the concentration of the reactant at time t, k is the rate constant, t is the time elapsed, [A]0​ is the initial concentration of the reactant. To find the reactant concentration at a given time, you can rearrange the equation to: [A]=−kt+[A]0​ And to find the time elapsed for a given concentration change, you can rearrange the equation to: t=k[A]0​−[A]​ Please note that the units of the rate constant k in zero-order reactions are typically M/s (molarity per second) or similar, depending on the units used for concentration and time. Also, this law is applicable under the assumption that the reaction is zero-order, which may not always be the case in real-world scenarios. Always make sure to verify the order of the reaction when using integrated rate laws.