CHEM191 Module 2 - Energetics, Rates & Driving Forces of Chemical Reactions (Notes) PDF

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CHEM191 Module 2Energetics, Rates & Driving Forces of Chemical ReactionsLecture 1EnthalpyFirst Law Of ThermodynamicsThe first law of thermodynamics tells us that energy is always conserved. But, energy can be changed from one type to another (for example, gravitational potential energy turns int...

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CHEM191 Module 2 Energetics, Rates & Driving Forces of Chemical Reactions

Lecture 1 Enthalpy First Law Of Thermodynamics The first law of thermodynamics tells us that energy is always conserved. But, energy can be changed from one type to another (for example, gravitational potential energy turns into kinetic energy). In chemistry, we are interested in changes in potential energy and heat. In a chemical reaction:

Δr E = Eproducts − Ereactants Heat (q) is the most readily measurable type of energy to study in chemistry: - If the products of a reaction have a lower heat content than the reactants, the reaction will release heat when it occurs, an exothermic reaction. - If the products of a reaction have a higher heat content than the reactants, the reaction will absorb heat when it occurs, an endothermic reaction.

Enthalpy This heat energy (at a constant pressure) is called the enthalpy. Many chemical reactions, and all biochemical reactions, occur with no change in the pressures of the reactants or products (they stay at atmospheric pressure). Under these conditions, we describe heat changes as enthalpy changes:

Δr H = Hproducts − Hreactants Enthalpy change is measured in kilojoules per mole (kJ mol-1). For exothermic reactions, enthalpy change is negative. For endothermic reactions, enthalpy change is positive. Enthalpy changes take stoichiometry into account. For example, a reaction will have a certain enthalpy change. If you double the number of moles of all the products and reactants, the enthalpy change will double. Note that we cannot measure absolute values of enthalpy for substances, only changes.

Hess’s Law Enthalpy is a state function, which means that the change in enthalpy upon the conversion of A to B will be the same, regardless of whether it occurs in one step or a number of steps. This can provide us with a way to calculate enthalpy change values which are difficult to measure experimentally. The law tells us that if a reaction is conducted in a series of steps, enthalpy change for the overall reaction will equal the sum of the enthalpy changes for the individual steps. For example, the reaction of solid carbon with oxygen to make carbon monoxide is difficult. However, we can easily measure enthalpy change for converting solid carbon to carbon dioxide, and the enthalpy change for converting carbon monoxide into carbon dioxide. We can use the enthalpy change values of these reactions to calculate the enthalpy change value for the conversion we want:

In this example, one of the equations was reversed, and when this was done, the sign of the enthalpy change value was also reversed. This is one way we can manipulate the reactions to make everything cancel out, in order to get the reaction we want. Another way to do it is to multiply an equation by some number (for example, double everything). When we do this, we must multiply the enthalpy change value by the same number.

Enthalpies Of Formation Hess’s law allows for the calculation of enthalpy changes for various sorts of chemical reactions: - ΔcomH for combustion reactions (adding oxygen). - ΔfusH for fusion reactions (melting). - ΔvapH for vaporisation reactions (boiling). - ΔfH for formation reactions. A formation reaction describes the formation of 1 mole of a compound from its constituent elements in their standard states. Standard states are the most stable form of the element under normal conditions (atmospheric pressure). We also define ΔfH° as the standard enthalpy of formation. This refers to the formation reaction occurring under standard conditions. Tables of ΔfH° values can be found in data books and online, and enable the calculation of ΔrH for almost any reaction: ∘ ∘ Δr H ∘ = Σ[Δf H products ] − Σ[Δf Hreactants ]

This equation states that the standard enthalpy change for a reaction equals the sum of the enthalpies of formation of the products, minus the sum of the enthalpies of formation of the reactants. Note that when doing these calculations, stoichiometry must be taken into account. Also, any element in its standard state will have an enthalpy of formation of 0. A common example of this is when oxygen gas appears in a reaction. It is not included in the calculation.

Lecture 2 Entropy Entropy There are several definitions of entropy (S). One of the more accurate definitions is that it is a measure of the number of possible arrangements of particles in a system. Effectively, it measures disorder or randomness. For example, take two molecules held in a flask (a). The barrier between the first and second flask is then removed so that the molecules can move between flasks (b).

The result with the highest entropy is the one that has 1 molecule in each flask, as there are more possible arrangements of the molecules. An “ordered” system, where there are two molecules in the left flask, is unlikely (a 1 in 4 chance here). Think of this on a larger scale, like if there were 1 mol of molecules. In this case, there would be less than a 1 in 10100 chance that all the molecules would be “ordered” and stay in the left flask. What we gather from this is that there is a very small chance of an ordered system, and system spontaneously becomes more disordered (undergoes an increase in entropy).

Second Law Of Thermodynamics The second law of thermodynamics says that whenever a spontaneous event takes place our universe, the total entropy of the universe increases. In thermodynamics, the universe consists of the system of interest, plus the surroundings. Because of this, the entropy of a system can decrease during a spontaneous process, as long as the entropy of the surroundings increases by a larger amount. The enthalpy of the universe is constant, but the entropy is increasing. The available energy is

constantly being dispersed throughout the universe.

Measuring Entropy Unlike enthalpy, it is possible to measure the absolute values of entropy for a substance. This is because, the third law of thermodynamics states that at absolute zero, the entropy of a perfectly ordered pure crystalline substance is zero (there is no disorder). A value measured at 1 bar pressure (approximately atmospheric pressure) is called a standard entropy value (S°). The units are joules per mole per kelvin (J mol-1 K-1). Solids have the lowest entropies, followed by liquids, and then gases, which have the highest: - S° (H2O(s)) = 41 J mol-1 K-1 - S° (H2O(l)) = 70 J mol-1 K-1 - S° (H2O(g)) = 189 J mol-1 K-1 In contrast to enthalpy of formation, standard enthalpy for an element in its standard state is not zero, because the reference point for entropy is the pure crystalline solid at 0 K (absolute zero).

Standard Entropy Of Reaction We can write the standard entropy of reaction in the same way as we did for standard enthalpy of reaction: ∘ Δr S ∘ = Σ[ΔSproducts ] − Σ[ΔS ∘reactants ]

We can often qualitatively predict the change in entropy for a chemical reaction from the states of the substances involved: - A reaction which results in the formation of a gas from a solid or liquid will very likely have a positive entropy change. - A reaction having fewer moles of products than reactants (all in the same case) will very likely have a negative entropy change.

Lecture 3 Gibbs Energy Gibbs Energy Gibbs energy is defined as:

G = H − TS H is the enthalpy of the system, S is the entropy of the system, and T is the temperature (in Kelvin, 0°C = 273K). We can’t measure absolute values of G, so we always talk about the change in G for a process (ΔG). When referring to chemical reactions, we use the terminology:

Δr G = Δr H − TΔr S The sign of ΔG tells us whether or not a particular process is spontaneous: - If ΔG is negative, the process is spontaneous. - If ΔG is zero, the system is at equilibrium. - If ΔG is positive, the process is non-spontaneous If a process is non-spontaneous, its reverse will be spontaneous. The magnitude of ΔG is important in telling us how far a spontaneous process will proceed towards completion. Examples of the use of this concept include the melting and freezing of water:

H2O(s) → H2O(l ) ΔH is positive and ΔS is negative. We would therefore expect this reaction to be spontaneous only at high temperatures (above 0°C).

H2O(l) → H2O(s) ΔH is negative and ΔS is negative. We would therefore expect this reaction to be spontaneous only at low temperatures (below 0°C). We can also find ΔrG° in a similar way to how we found ΔrH° with several ΔfH° values: ∘ ∘ Δr G ∘ = Σ[Δf Gproducts ] − Σ[Δf Greactants ]

Entropy Of Dissolution Take the dissolution of potassium chloride: + KCl(s) → K(aq) + Cl(−aq)

The entropy chance for dissolution of any ionic salt (77 J mol-1 K-1 in this case) is favourable, as it always involves the formation of a less ordered system. The enthalpy change for this reaction is slightly positive (17 kJ mol-1). Putting this into the Gibbs energy equation, we find:

ΔG ∘ = ΔH ∘ − TΔS ∘ = 17 × 103 − (298 × 77) = − 5900 Because the value is negative, the process is spontaneous. Note that we had to convert the enthalpy change into joules per mole before doing the calculation.

Coupled Reactions We can use a spontaneous reaction (negative ΔG) to drive a non-spontaneous reaction (positive ΔG) by coupling the two reactions together. In biological systems, the hydrolysis of adenosine triphosphate (ATP) is often involved.

Due to coupling the glucose reaction with the ATP reaction, the glucose reaction is able to happen spontaneously.

Equilibrium & Gibbs Energy When ΔG is neither positive or negative (is zero), there is no driving force for chemical or physical change. Therefore, the system is at equilibrium. In an equilibrium mixture, the forward and reverse reactions are both occurring at the same rate, so there is no net change in composition. Neither the forward or reverse reactions proceed to completing, because equilibrium is

the point where G is minimised. The reaction mixture will reach equilibrium when it reaches the composition corresponding to the minimum G value. ΔrG is the criteria of spontaneity of a process. It is related to ΔrG° which can be obtained from tables, by the equation:

Δr G = Δr G ∘ + RT lnQ We have already seen that is ΔrG is zero, the system is at equilibrium. Also, we know that Q equals K at equilibrium. Therefore:

Δr G ∘ = − RT ln K The “R” is the gas constant (8.314 J mol-1 K-1).

Lecture 4 Rates Of Reaction Chemical Kinetics There are two important things about a chemical reaction: - How far it goes (thermodynamics). - How fast it goes (kinetics). These two are not related. Chemical kinetics is concerned with how quickly a reaction occurs. There are two parts to chemical kinetics: - Experimental - measuring reaction rates, studying factors influencing rates. - Theoretical - understanding rates in molecular terms, using experimental data to probe reaction mechanisms.

Rate & Measurement Rate is the same as the speed of a reaction. Lets examine how the following reaction undergoes changes in concentration over time:

N2O4(g) ⇌ 2NO2(g) At the start, only N2O4 is present. Then the concentration of N2O4 falls rapidly, and the concentration of NO2 rises rapidly. The change in concentration of both substances then slows, and eventually they stop changing. The speed is found from the gradient of plot of either [N2O4] or [NO2] with time. Such a gradient is called a rate. We know from the stoichiometry of the equation that the rate of loss of N2O4 is half the rate of formation of NO2. Using methods of calculus:

d [N2O4] dt 1 d [NO2] = 2 dt

ra te = −

We cannot have a negative rate, so we must put a negative sign in front of the term for reactants, where the concentration decreases with time. For a general reaction:

a A + bB → cC + d D

1 d [A] ra te = − a

d [B] 1 =−b

d [C ] 1 = c

d [D] 1 = d dt

The units for rate is always mol L-1 s-1.

Rate Law There are various factors which affect the rate of reaction, including: - Chemical nature of the reaction. - Physical states of reactants and products. - Concentration of reactants. - Temperature. - Substances not involved in the stoichiometric equation (catalysts or inhibitors). Concentration does not affect all reactions in the same way. For some reactions, increasing the concentration increases the rate. For other reactions, increasing the concentration has no effect on the rate. The rate law describes how rate depends on concentration. For the reaction:

a A + bB → cC + d D ra te = k[A]x[B]y Where x is the order with respect to A, y is the order with respect to B, and k is the rate constant. The rate law must be determined experimentally, we cannot know it from the chemical equation. In the case of the rate law, we can ignore the stoichiometry. The orders with respect to each substance are added up to get the overall order of the reaction. The exponents in the rate law equation indicate how the rate is affected by the concentration of each reactant. If the order with respect to A is 1, then when the concentration of A doubles, the rate will double. If the order with respect to A is 2, then when the concentration of A doubles, the rate will quadruple. It is when the order with respect to A is 0 that changing the concentration does not affect the rate.

The rate constant (k) is independant of concentration, and increases with temperature. The units for k depend on the overall order of the reaction. First Order Reactions With first order reactions, only the concentration of 1 of the reactants affects the rate. This will occur when: - There is only 1 reactant. - There is more than 1 reactant but the order with respect to one of the reactants is 1 and all the others are 0.

Initial Rates We can experimentally measure the reaction rate. A common way to do this is the isolation method. This is because on the initial rates of reaction. The concentration of one reactant is varies, while all others are held constant.

i nit i al r ate = k[A]0x[B]y0 [A]0 and [B]0 are the initial concentrations (when time is 0s). These are set by the experimenter, and are therefore known. The orders (x and y) are unknown. To find x, we measure the initial rates for different values of [A]0, while holding [B]0 constant. To find y, we measure the initial rates for different values of [B]0, while holding [A]0 constant. We measure initial rates because as the reaction proceeds, [A] and [B] decrease, therefore the rate will decrease. We examine the reaction rate over a short time scale, so that [A] and [B] remain close to [A]0 and [B]0. If we study initial rates, the change

in [A] and [B] with time is essentially linear. We can also calculate the rate constant (k) from initial rates:

i nit i al r ate [A]x0[B]y0

k=

For a first order reaction:

ln [A]t = ln [A]0 − k t This is another method to calculate k. However, we can also calculate the concentration of A after some time, if we already know k and [A]t. This equation comes from a straight line plot, shown on the right.

Lecture 5 Half Life & Mechanisms Half Life Half life is an easy way to describe how fast a reaction occurs. It is common in nuclear physics and medicine. The half life is the time taken for the concentration of a reactant to reach half its initial value. For reactant A, half life occurs when:

[A ]t 1 = 2

[A ]0 2

For a first order reaction, the half life can be calculated by:

t1 = 2

0.693 k

For first order kinetics, the half life is independant of the initial concentration of A. For other order reactions, the half life depends on initial concentration and the half life concept is rarely used.

Reaction Mechanisms The reason we cannot predict the rate law from the overall chemical equation is that almost all reactions take place in a series of steps called elementary reactions (steps). For example:

2ICl + H2 → 2HCl + I2 This reaction consists of two steps:

ICl + H2 → HI + HCl HI + ICl → HCl + I2 Elementary steps are usually unimolecular or bimolecular. They may involve reaction intermediates (species which play a role in the reaction but do not appear in the overall equation). In this example, HI is a reaction intermediate. Because intermediates are neither a reactant or product, they do not appear in the overall rate law. A series of elementary reactions describing an overall reaction is called a reaction mechanism. In a reaction mechanism, the sum of the elementary steps must equal the overall equation. We can write rate laws from chemical equations, using stoichiometric coefficients, with elementary steps only:

ste p 1 ra te = k[ICl ][H2] ste p 2 ra te = k[HI ][ICl ] These individual rate laws can be collected into an overall rate law, which should agree with the experimentally determined rate law. But although the predicted rate law may agree with the experimental rate law, the proposed mechanism may be incorrect (a different mechanism may lead to the same rate law). So experimental rate law can only support the proposed mechanism, it can never fully prove it.

Rate Determining Step To derive a predicted rate law, we need to propose a rate determining step. The rate determining step: - Is the elementary step in a reaction mechanism that is considered slower than any other step. - Controls the overall rate of reaction. - Is essentially a “bottleneck” of the reaction. For example, derive a mechanism for:

NO2(g) + CO( g) → NO( g) + CO2(g) The experimental rate law is:

ra te = k[NO2]2 One of the proposed mechanisms for the reaction is:

2NO2

k1

NO3 + NO

NO3 + CO

k2

NO2 + CO2

Step 2 is much faster than step 1, so step 1 must be rate determining (note that you will always be given the elementary steps and which one is slow). The predicted rate law can therefore be written direction from the stoichiometry of step 1:

ra te = k1[NO2]2 This predicted rate law is the same as the experimental rate law. So the proposed mechanism could possibly be correct, but further confirmation is needed (for example, detection of the NO3 intermediate). Take this example where the second step is rate determining (and therefore the reaction intermediate is in the rate law):

2NO(g) + O2(g) → 2NO2(g) The experimental rate law is

ra te = k[NO ]2[O2] A possible mechanism for this reaction is a fast pre-equilibrium, follows by a slow step:

NO + O2 ⇌ NO3 NO3 + NO

k2

2NO2

Since step 2 is rate determining:

ra te = k 2[NO3][NO] Because NO3 is an intermediate, it is hard to determine the concentration. We need to involve reactants of known concentration. We can do this by using the equilibrium constant expression for step 1:

[NO ] K1 = [NO ][3O2] [NO3] = K1[NO ][O2] We can then substitute this into the rate equation:

ra te = k 2[NO ]K1[NO ][O2] = k[NO2]2[O2] Where k is another constant (K1 x k2). This is the same as the experimental law.

Reaction Energy Profile A reaction energy profile is a plot of energy changes during a reaction. For a proposed mechanism, the two peaks correspond to two elementary reactions. Whichever step is slower will have a higher activation energy (Ea).

Lecture 6 Collision Model & Activation Energy The Collision Model Experiments show that an increase in temperature speeds up all reactions. k is the only term in the rate law that depends on the temperature, therefore, k is given for a certain temperature. Why does increasing the temperature speed up the reaction? Kinetic theory of gases indicates all molecules are in constant motion. Molecules constantly collide, so energy is transferred from one molecule to ano...