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Chemical Kinetics Chemical kinetics, also known as reaction kinetics, the branch of physical chemistry that is concerned with understanding the rates of chemical reactions..

[Audio] Chemical transformations can be predicted to be spontaneous or non-spontaneous using the second law of thermodynamics. However, this law does not provide information about the speed or rate at which a reaction occurs. This is where chemical kinetics comes into play, examining the rates of chemical reactions and the factors that influence them..

[Audio] Chemical equilibrium is concerned with the composition of a reaction mixture at equilibrium. On the other hand, chemical kinetics deals with the composition of a reaction mixture that is far away from equilibrium. This means that kinetics plays a crucial role in real-life situations..

[Audio] Chemical reactions can occur over different time scales. Some reactions happen quickly, while others take longer. For example, some chemical reactions can complete within seconds, while others may take hours, days, or even years. This difference in reaction speed is crucial in understanding how chemicals interact with each other..

[Audio] Chemical kinetics is the study of reaction rates, which refers to the changes in concentrations of reactants or products as a function of time. This means we are examining how quickly the amounts of substances involved in a reaction change over time..

[Audio] The rate of a reaction can be defined quantitatively by measuring how fast reactants are consumed or products are formed over time. This is often done using the rate expression, which is a mathematical equation that describes the relationship between the concentration of reactants and the rate of the reaction. The rate expression for the decomposition of ozone might look something like this: d[O3]/dt = k [O3]^n, where d[O3]/dt is the rate of change of ozone concentration over time, k is a constant, and n is the order of the reaction. By rearranging this equation, we can solve for the rate of the reaction, which gives us a numerical value that represents how quickly the reaction occurs..

Rate of a reaction 7.

[Audio] Chemical kinetics deals with the study of rates of chemical reactions. There are two types of rates we can consider when looking at a reaction: average rate and instantaneous rate. The average rate is the rate of change over a given period of time, whereas the instantaneous rate is the rate of change at a specific point in time..

[Audio] At the start of a reaction, we initially measure the instantaneous rate, which is also known as the initial velocity. This is equivalent to the slope of the line that represents the reaction's progress over time. Interestingly, we find that the initial velocity of disappearance of a reactant is typically higher than the velocities measured later in the reaction. This phenomenon can be attributed to the fact that there is a high concentration of reactants present at the very beginning..

[Audio] The calculation of average rate reveals that the rate of change varies depending on the time period considered. Between the starting time and 10 seconds, the average rate is calculated, providing insight into how the reaction progresses over a longer period. In contrast, during the last 10 seconds, we examine the rate between 50 and 60 seconds, which helps us comprehend the rate of change in a shorter timeframe. The disparity between these two calculations underscores the significance of taking into account the time period when calculating the average rate of a reaction..

[Audio] The introduction of stoichiometric coefficients in the rate statement ensures that the same rate is obtained either by considering the formation of the product or the consumption of the reactants. This is crucial because it allows us to accurately describe the reaction mechanism and predict the outcome of the reaction. By including these coefficients, we can ensure that our calculations are consistent and reliable..

[Audio] The rate of disappearance of B compares to the rate of production of C as 3/2. This means that the rate of disappearance of B is three halves the rate of production of C..

[Audio] This graph shows the kinetics curves for the reaction of oxygen with hydrogen to form water. There are three curves here, one corresponding to the concentration of oxygen over time, another to the concentration of hydrogen over time, and the third to the concentration of water over time. The curve that represents the disappearance of hydrogen is the one where the concentration of hydrogen decreases over time. As we can see, this is exactly what happens in this curve. Therefore, the correct answer is this curve..

[Audio] The empirical rate law, also known as the rate equation, describes how the rate of a reaction changes with the concentrations of reactants. It's written in the form of a mathematical equation, where the rate of the reaction is proportional to the product of the concentrations of the reactants raised to the powers of their respective orders of reaction. The rate constant, k, is a measure of the rate of the reaction under certain conditions, and it's used to determine the rate of the reaction at different concentrations of the reactants. The order of reaction, m and n, refers to the powers to which the concentrations of the reactants are raised in the rate equation. These values must be determined experimentally, as they depend on the specific reaction being studied..

[Audio] The overall order of this reaction is one because there is only one reactant, O3, in the rate equation. In a first-order reaction, the rate depends on the concentration of a single reactant..

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[Audio] The reaction order can be determined by examining how the rate of a reaction changes when the concentrations of reactants are varied. If the rate of a reaction increases as the concentration of one reactant is doubled, but remains unchanged when the concentration of another reactant is doubled, then the reaction is first-order in the former reactant and zero-order in the latter. Similarly, if the rate of a reaction decreases as the concentration of one reactant is halved, but remains unchanged when the concentration of another reactant is halved, then the reaction is second-order in the former reactant and zero-order in the latter. In general, the reaction order can be any positive integer, including zero. The reaction order is often denoted by the symbol n, where n is the reaction order. For example, a reaction that is first-order in A and second-order in B would have a reaction order of (n_A, n_B) = (1, 2)..

[Audio] When deriving the units of rate constants, we need to consider the units of rate and concentration. The unit of rate is typically measured in moles per liter per second, or mol/L/s, which can also be written as M/s, where M represents molarity. The unit of concentration is typically measured in moles per liter, or mol/L, which can also be written as M, where M again represents molarity. Using these units, we can write the unit of rate constant, k, as follows: k = rate / [concentration]. Substituting our units, we get: k = (mol/L/s) / (M). Simplifying this expression, we find that the unit of rate constant, k, is indeed seconds to the minus one power, or s^-1. This makes sense, since rate constant is a measure of how quickly a reaction proceeds, and it's inversely related to the time it takes for the reaction to occur..

[Audio] We need to formulate an equation that tells us explicitly how the concentrations will change as a function of time. This new equation, called the integrated rate law, can be derived from the rate law itself..

[Audio] When we express the rate of a reaction as the rate of change of concentration as a function of time, we are talking about the integral rate law. This concept applies to zero-order reactions, where the rate of the reaction does not depend on the concentration of reactants. Instead, it is constant over time. We use this approach to describe the macroscopic change in concentration and the infinitesimal change in concentration over a small interval of time. By doing so, we can better understand how the concentrations will evolve over time..

[Audio] The integral rate law for zero-order reaction describes how the concentration of reactants changes over time. This type of reaction has no dependence on the concentration of reactants. Instead, it depends only on the initial conditions. We can express this rate as the rate of change of concentration as a function of time. For macroscopic changes, this rate is constant, meaning that the concentration of reactants decreases at a constant rate. For infinitesimal changes, the rate is also constant, but it's expressed in terms of the infinitesimal change in concentration..

[Audio] To estimate the rate constant for the decomposition of N2O on gold surface, we can use the Arrhenius equation. This equation relates the rate constant to the activation energy and the temperature. The Arrhenius equation is written as k = Ae^(-Ea/RT), where k is the rate constant, A is the frequency factor, Ea is the activation energy, R is the gas constant, and T is the temperature in Kelvin. By rearranging this equation, we can solve for the rate constant in terms of these variables..

[Audio] The integrated rate law for a first-order reaction reveals how the reactant's concentration evolves over time. This equation considers the initial reactant concentration, the rate constant k, and time. Using this equation, we can compute the reactant's concentration at any moment. For instance, knowing the initial reactant concentration, its rate constant, and the elapsed time since the reaction began, we can insert these values into the equation and determine the current reactant concentration. This information is vital in grasping the reaction's progression and predicting its outcome..

[Audio] The dissociation of ozone into oxygen molecules follows first-order kinetics, meaning that the rate of this reaction relies solely on the concentration of ozone, unaffected by the presence of other reactants. If the concentration of ozone doubles, so too does the rate of the reaction, a hallmark of first-order reactions where the rate is directly proportional to the concentration of one reactant..

[Audio] As we can see, the linear form of the integral rate expression for a first-order reaction is given by this equation. This equation reveals that plotting the natural logarithm of the concentration of O3 against time yields a straight line with a negative slope equal to minus k. This occurs because the rate constant, k, has a negative coefficient in front of it. Taking the natural logarithm of both sides of the rate law results in this simple and straightforward equation. Consequently, we anticipate a linear relationship between ln[O3] and time..

[Audio] When a first-order reaction proceeds for one half-life, the concentration of the substance must be equal to one-half of its original value. This means that if we start with a certain amount of reactant, after one half-life, we will have only half of that amount left..

[Audio] For second-order reactions, we have another integrated rate law. This one is given by the equation [A] = [A0]/(k[A0]t + 1), where [A] is the concentration of reactant A at time t, [A0] is its initial concentration, k is the rate constant, and t is time. This equation can be rearranged to give us a more useful form, namely [A] = [A0]/(kt + 1/A0). This shows that the concentration of reactant A decreases as time passes, and this decrease is proportional to the product of the rate constant and time..

[Audio] The unit for rate is given as mol L-1 s-1 or M s-1, which measures how quickly a certain amount of substance changes over a specific period of time. The rate law equation is written as rate equals k times the concentration of A, showing that the rate of a reaction depends on the concentration of the reactants. The unit for concentration is given as mol L-1 or M, measuring the amount of substance present in a given volume. The rate constant can be expressed as the rate divided by the concentration of A, giving the unit of M s-1/M, which represents the rate constant having units of inverse concentration and time..

[Audio] A thermodynamically allowed reaction may be kinetically forbidden, meaning that even though the reaction is feasible according to thermodynamic principles, it does not happen because there is no sufficient energy available to drive the reaction forward. In other words, the reaction requires activation energy to get started, and without this energy input, the reaction will not occur..

[Audio] Activation energy plays a crucial role in determining the rate of a chemical reaction. It is the minimum energy required for the molecules to react. In most cases, this energy is provided by heat, also known as thermal energy. This means that when we increase the temperature of a system, we're increasing the kinetic energy of the molecules, making it more likely for them to collide and react. The equation Ea(backward) = Ea(forward) + ∆H shows that the activation energy for the backward reaction is equal to the sum of the activation energy for the forward reaction and the change in enthalpy (∆H). This highlights the importance of considering both the forward and reverse reactions when analyzing the role of activation energy in a chemical reaction..

[Audio] Svante Arrhenius, a pioneer in the field of chemical kinetics, introduced the concept of collision theory in 1889. He combined the kinetic theories of gases with the Boltzmann distribution law of molecular speeds to develop a mathematical framework that links the rate constant with activation energy and temperature. This model was initially designed for gas-phase reactions. Four key assumptions underlie this theory: first, colliding molecules behave like hard spheres; second, molecules must collide with each other to react; third, these collisions must possess sufficient energy to break and re-form molecular bonds; and fourth, the reactant atoms must be aligned in a way that allows them to easily rearrange into product molecules..

[Audio] As the temperature increases, the rate constant, k, grows exponentially according to the Arrhenius equation. This means that the reaction rate also increases as the temperature rises. The Arrhenius constant, A, represents the likelihood of successful collisions between reacting molecules, taking into account their collision frequency and steric factor. The gas constant, R, helps convert temperatures from Kelvin to joules per mole. The average kinetic energy of molecules, RT, plays a key role in determining the rate constant. When the activation energy, Ea, is low or negligible compared to the average kinetic energy, the rate constant approaches its maximum value, A. In this scenario, the reaction rate is limited by the frequency and success of collisions between molecules..

[Audio] Molecules must collide with each other in order for a reaction to take place. For this collision to be successful, they need to have a certain minimum velocity, or kinetic energy. This distribution of molecular speeds is known as the Maxwell-Boltzmann distribution..

[Audio] The geometry of the collision between the reacting molecules plays a crucial role in determining the outcome of the reaction. When [O] and N2O collide to form N2 and O2, the steric factor refers to the orientation of these molecules as they collide. A non-reactive molecular collision occurs if the molecules do not meet the necessary conditions for reaction, such as the correct alignment of their atoms. This type of collision is unproductive, resulting in no product formation. Conversely, a reactive molecular collision occurs when the molecules possess the correct geometry, enabling them to react and produce the desired products..

[Audio] One of the four possible collisions between HCl and ethene may possibly lead on to a reaction. The geometry of this collision is such that the hydrogen atom of HCl approaches the double bond of ethene from the side opposite to the leaving group, resulting in the formation of a new bond between the hydrogen atom and the carbon atom of ethene. This is consistent with the Markovnikov rule, which states that in the presence of a catalyst, the hydrogen atom will add to the less substituted carbon atom..

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[Audio] Increasing the temperature can significantly increase the rate of a reaction because higher temperatures provide more energy for the reactants to collide and form products. Most chemical reactions speed up as temperature increases, which is described by the Arrhenius equation. The equation shows that the rate constant increases exponentially with temperature, leading to large increases in reaction rate even with small temperature increases. For example, a reaction with a rate constant of 1 x 10^(-3) s^-1 at room temperature might have a rate constant of 1 x 10^(-2) s^-1 at 50°C, resulting in a much faster reaction..

[Audio] The Arrhenius equation connects the rate constant k to the activation energy Ea. To find Ea from experimental data, we can utilize this equation. The equation is expressed as k = Ae^(-Ea/RT). By rearranging it, we can solve for Ea. This is achieved by taking the natural logarithm of both sides, yielding ln(k) = ln(A) - Ea/RT. Next, by plotting ln(k) versus 1/T, we can obtain a straight line with a slope equivalent to -Ea/R. From this graph, we can determine the value of Ea..

[Audio] The universal gas constant R is approximately 8.314 joules per mole kelvin. This value is used in the determination of activation energy from experimental measurements..

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[Audio] The activation energy, Ea, is often related to the average bond energies of different bond types involved in the reaction. This means that the energy required to break these bonds is similar to the activation energy..

[Audio] Many reactions in nature occur in multiple steps. These individual steps, known as elementary reactions, are characterized by their molecularity, which refers to the number of reactant particles involved in each step. There are three types of molecularity: unimolecular, bimolecular, and overall reaction with an empirical order one..

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[Audio] When a catalyst is added to a reaction, it forms a complex with one of the reactants, allowing the reaction to proceed faster. This is because the catalyst helps to lower the activation energy required for the reaction to occur. Without a catalyst, the reaction would take longer to happen, or may not even occur at all. With a catalyst present, the reaction can happen more quickly, resulting in a higher rate of reaction..

[Audio] A catalyst works by providing an alternative reaction path with a lower activation energy barrier, allowing the reaction to proceed faster. This means that the transition state, where the reactants are converted into products, has a lower energy requirement than the original reaction pathway. As a result, the reaction can proceed more quickly, but the overall thermodynamic properties of the reaction, such as enthalpy, Gibbs free energy, entropy, equilibrium constant, and product yield, remain unchanged..

[Audio] In this catalytic cycle, the representation of all elementary steps involved in a catalytic reaction is shown. The cycle begins with the reactant forming a complex with the catalyst, followed by the conversion of the reactant into the product. The product then forms another complex with the catalyst, and so on. Notice that the catalyst does not appear in the reactant or product sides of the sum of the elementary reactions. Instead, it appears only in the elementary steps, indicating that it is not consumed during the catalysis. This allows us to write the catalyst's name above the net reaction arrow, giving us a clear picture of the overall reaction mechanism..

[Audio] Catalysis can occur when reactants, products, and catalyst are all present in the same phase, such as in homogeneous catalysis. This type of catalysis is often seen in biological systems, where enzymes act as catalysts to speed up chemical reactions. On the other hand, heterogeneous catalysis occurs when reactants, products, and catalyst are present in different phases, such as in industrial processes where a solid catalyst is used to facilitate a reaction between gases or liquids..

[Audio] The catalytic destruction of ozone in the stratosphere is an example of gas phase homogeneous catalysis. Small amounts of chlorine radicals, formed from chlorofluorocarbons, act as catalysts to accelerate the breakdown of ozone into oxygen molecules..

[Audio] In heterogeneous catalysis, the reaction mechanism involves several key steps. The first step is when a reactant collides with the catalyst surface. This collision leads to adsorption, where the reactant binds to the surface. Next, the reactant dissociates into its constituent parts. Then, product formation occurs through various chemical pathways. Finally, the product desorbs from the catalyst surface, completing the reaction mechanism. These mechanistic steps take place on a solid surface, where the catalyst is supported by a thermally stable ceramic material known as a monolith..

[Audio] The decomposition of nitric oxide on a platinum surface is a complex process that involves the breaking down of two molecules of NO into oxygen and nitrogen gas. This reaction is an example of a heterogeneous catalytic reaction, where the catalyst, in this case, the platinum surface, plays a crucial role in facilitating the reaction. The reaction mechanism involves the adsorption of NO onto the platinum surface, followed by the formation of a transition state, and finally, the desorption of the products, oxygen and nitrogen gas. The rate of this reaction can be influenced by various factors such as the concentration of reactants, temperature, and pressure..