Chapter 6: Rates, kinetics (C5723760)

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1 Reaction rates

Reaction kinetics is the study of reaction rates. Reaction rate is the change in concentration of reactants per unit time. The reaction rate does not consider the effects of the reverse reaction, but only the rate of reaction of a reactant in either the forward or backward direction.

“As an example, burning fire is a fast reaction, and corrosion is a slow reaction,” Mandy remarked.

Collision theory states that chemical reactions occur when particles successfully collide with one another. Successful collision means that sufficient energy, known as activation energy, has been generated as a result of the collision, to break preexisting bonds, and form new bonds. Remember from that in ideal gases (which can be applied more liberally to particles), kinetic energy is dependent on temperature. Remember also that kinetic energy is related to velocity. Therefore, temperature is related to velocity. Thus, raising temperature increases velocity of particles, which increases collision energy, thus successful collisions, thereby increasing rate of reaction. Reaction rate constant quantifies the speed of a chemical reaction. Therefore, raising temperature increases both rate of reaction, and the rate constant. The collision theory however, assuming perfectly spherical particles, fails to consider special shapes of particles, which can cause a reaction with sufficient energy not to proceed (as expected).

Arrhenius equation states that the rate constant ($k$) is proportional to the frequency of collisions [leading to a reaction or not] [factored into $A$]  [, fraction of collisions with the correct orientation [factored into $A$], and fraction of collisions with sufficient activation energy ($e^{-\dfrac{E_{a}}{RT}}$), or alternatively, $k=A.e^{-\dfrac{E_{a}}{RT}}$.

2 Rate law

Rate law states that reaction rate is dependent on the concentration of reactants, given by $r=k[A]^x [B]^y$, where $k$ is rate constant, $[A],[B]$ is the concentration of reactants A and B respectively, and $x, y$ is the stoichiometric coefficient. For elementary reactions, the exponent is directly the stoichiometric coefficients of the respective reactants in the balanced equation. Elementary reactions are reactions which directly form products in a single step. Therefore, [coefficients in a balanced equation for] elementary reactions describe the [exact] number of colliding molecules, as there is only a single reaction step. The number of colliding molecules creating a reaction is known as molecularity. Multi-step reactions can be broken down into a series of elementary reactions. For example, $\ce{NO2+CO -> NO+CO2}$ can be broken down into the first step, $\ce{NO2+NO2 -> NO3+NO}$; and the second step, $\ce{NO3+CO -> NO2+CO2}$. Thus, the overall reaction is $\ce{NO2+NO2+NO3+CO -> NO3+NO+NO2+CO2}$, which can be reduced to $\ce{NO2+CO -> NO+CO2}$, quod erat demonstrandum. Now with the substituent elementary reactions, noting just the term $[A]^x$ where $A$ is $\ce{NO2}$, the number of reactants with this form is 2, meaning the exponent $x=2$.

3 Rate-determining step

It should be noted that in the reaction $\ce{NO2+CO -> NO+CO2}$, the 1st step is slower than the 2nd step. This means that the 1st step is the bottleneck, slowing the reaction to this slowest step, known as the rate-determining step.

Commonly however, it may be unknown whether the reaction is elementary or otherwise. Thus, experimental data showing a same reaction undergoing over several trials, each time with different concentrations of reactants, can be used, in the form of a table:

 Trial [A] [B] Rate 1 0.5 0.5 1.2 2 1.0 0.5 4.8 3 2.0 1.0 38.4

Two trials can be compared, where only one [of the two] reactants were altered. Reaction order can include:

• If the rate is unchanged for either trial, the respective reactant is not in the slow step, as reaction rate is unchanged. As increasing reactant concentration will not speed up the reaction rate (the concentration of the reactant is irrelevant), $r=k$, meaning the exponent of that reactant is 0. This reaction is known as zero-order
• If the rate is doubled [and one of the reactants was doubled too], reaction rate is directly related to the reactant concentration, meaning $r=k[A]$, meaning the exponent of that reactant is 1. This reaction is known as first-order
• If the rate quadrupled [and one of the reactants was only doubled], reaction rate is related to the square of the concentration, meaning $r=k[A]^2$, meaning the exponent of that reactant is 2. This reaction is known as second-order
• If the rate is $\times 8$ [and one of the reactants was only doubled], reaction rate is related to the cubed of that concentration, meaning $r=[A]^3$, meaning the exponent of that reactant is 3. This reaction is known as third-order

Because the exponent describes the order of that reactant, the order of a reaction is equal to the sum of the order of its reactants, therefore, the sum of the exponents of that reaction. The experimental method is useful, because the stoichiometric coefficients (exponents) determined for a particular reaction, applies for subsequent experiments for that reaction.

4 Reaction rate, temperature

(See reaction rate, )

5 Kinetic, thermodynamic control

6 Catalysts and enzymes

Catalysts lower the activation energy [required for the reaction to occur], thereby increasing reaction rate. Catalysts are not altered or consumed by the reaction. As discussed , as the Arrhenius equation links activation energy and rate constant, and the rate law utilizes the rate constant; a catalyst thus alters the rate constant, and thus the rate law. Catalysts work by providing an alternative reaction pathway, meaning a lower activation energy can be used to initiate a reaction. An example of a catalyst is an enzyme.

 Learning activity What is a catalyst? What is an enzyme?

7 Equilibrium in reversible chemical reactions

As the reaction moves forward, reactants are converted into products, thereby increasing the reverse reaction rate. Where the forward reaction proceeds at the same rate as the reverse reaction, is known as equilibrium. Note that even though at equilibrium, the forward and reverse reaction rates are equal, the concentration of products and reactants are not necessarily equal. The law of mass action describes the ratio of concentrations when an equilibrium is reached, where $K=\dfrac{[S]^{\sigma}.[T]^{\tau}}{[A]^{\alpha}.[B]^{\beta}}$, where $K$ is the [concentration] equilibrium constant, $A, B$ are the reactants and $S, T$ are the products, $[]$ refers to the concentration of the constituents at equilibrium, and $\alpha, \beta$ are the stoichiometric coefficients of the reactants and $\sigma, \tau$ are the stoichiometric coefficients of the products. The law of mass action is distinct from the rate law, because it utilizes the stoichiometric coefficients directly irrespective of whether the reaction is elementary or otherwise. Also, pure liquids or solids are not included in the law of mass action, because the concentration can be regarded as constant. In [all] gas reactions, gas equilibrium constant can be used in lieu of the equilibrium constant [on the left hand side of the equation], and partial pressure can be used in lieu of concentration. Note also that unlike the rate law, there is no reaction rate constant; only stoichiometry and concentration. Thus, the presence of molecules outside the chemical equation [such as catalysts, or even molecules which react with the products or reactants] doesn’t alter the equilibrium constant. Evidently, molecules present can alter the concentration of reactants and products in equilibrium; however, the ratio of concentrations that constitutes equilibrium (known as the equilibrium concentration) is unchanged. The equilibrium constant only changed by temperature, but not by catalyst, or concentration.

Le Chatelier’s principle predicts the effect of changes on a chemical equilibrium, stating that if a system at equilibrium is disturbed by a change in temperature, concentration, or pressure [of one of its constituents], the equilibrium position will shift to counteract the effects of the disturbance. For example, if heat is removed from a reaction which produces heat [in the forward direction], the equilibrium will shift [to the right] to produce more heat. In contrast, if heat is added in the analogous circumstances, the equilibrium will shift [to the left] to remove heat. Note therefore, that unlike the Arrhenius equation where the rate constant always increases as a result of heat, the equilibrium constant [which is determined by Le Chatelier’s principle] depends on whether the reaction produces or absorbs (removes) heat. Another example, if reactants are added, the equilibrium will shift to the right to reduce reactants. In contrast, if products are added, the equilibrium will shift to the left to reduce products. Another example, noting from that partial pressure is the concentration of gas, if pressure is increased, the equilibrium will shift to reduce the concentration of gas molecules added.

Reaction quotient can be used to predict the direction a chemical reaction will move to reach equilibrium. Reaction quotient ($Q$) is determined like equilibrium constant, with products on top and reactants on bottom, but utilizes instantaneous concentration, rather than equilibrium concentration. This means that $Q$ wishes to become more like $K$. If $Q=K$, the reaction is at equilibrium. If $Q$ products must increase and reactants must decrease, meaning the reaction moves forward. Thus, if $Q$ reaction moves forward. In converse, if $Q>K$, the reaction moves backward.

8 Relationship of the equilibrium constant and [latex]I^{GA\circ}

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