Chemical Equilibrium

The Concept of Equilibrium and Equilibrium Constant

Chemical Equilibrium

            -is achieved when the rates of forward and reverse reactions are equal and the concentrations of the reactants and products remain constant

Physical Equilibrium

            -because the changes that occur are physical processes

Rate_forward=Rate_backward

 

Rules in Writing Equilibrium Constant

1.      1. [A] [B] [C] and [D] are molar concentrations in equilibrium. P_a, P_b, P_c, P_d  are equilibrium pressures in terms of atmosphere.

2.      2. The products are always in the numerator, and reactants are always in the denominator.

3.      3. The coefficients of the reactants and the products in the balanced equations correspond to their exponents for the expression.

4.      4. Compounds or molecules in a solid or liquid phase are ignored. They are not included in expression. 

5.      5. K_eq does not have a unit since it is an expression for a ration.

6.      6. Only substances in a gas phase are expressed in the K_p expression.

 

Writing Equilibrium Constants in terms of Pressure (K_p)

            K_c ≠ K_p         

            K_p

                    _-tells us that equilibrium  concentrations are expressed in terms of pressure

  

Reaction Mechanism

REACTION MECHANISM          

            - the step by step sequence of elementary reactions by which overall chemical change occurs.
            - A mechanism describes in detail exactly what takes place at each stage of a chemical transformation. It also describes each transition state, which bonds are broken (and in what order), which bonds are formed (and in what order) and what the relative rates of the steps are. A complete mechanism must also account for all reactants used, the function of a catalyst, stereochemistry, all products formed and the amount of each.
            -A reaction mechanism must also account for the order in which molecules react. Often what appears to be a single step conversion is in fact a multi-step reaction.

Consider the following reaction:

CO + NO₂ → CO₂ + NO

In this case, it has been experimentally determined that this reaction takes place according to the rate law  R = k [NO₂]². Therefore, a possible mechanism by which this reaction takes place is:

2 NO₂ → NO₃ + NO (slow)

NO₃ + CO → NO₂ + CO₂ (fast)

Each step is called an elementary step, and each has its own rate law and molecularity. All of the elementary steps must add up to the original reaction, by means of organic reactions

            2 NO₂ → NO₃ + NO   (1)
            NO₃ + CO → NO₂ + CO₂  (2)
                _{------------------------------------------------------}
                CO + NO₂ → CO₂ + NO    (3)

When determining the overall rate law for a reaction, the slowest step is the step that determines the reaction rate. Because the first step (in the above reaction) is the slowest step, it is the rate-determining step. Because it involves the collision of two NO₂ molecules, it is a bimolecular reaction with a rate law of R = k [NO₂]². If we were to cancel out all the molecules that appear on both sides of the reaction, we would be left with the original reaction (3).

In organic chemistry, one of the first reaction mechanisms proposed was that for the benzoin condensation, put forward in 1903 by A. J. Lapworth.

DEFINITION OF TERMS

Transition State- a particular configuration along the reaction coordinate. It is defined as the state corresponding to the highest energy along this reaction coordinate. At this point, assuming a perfectly irreversible reaction, colliding reactant molecules will always go on to form products

Rate law- a chemical reaction is an equation which links the reaction rate with concentrations or pressures of reactants and constant parameters (normally rate coefficients and partial reaction orders)

Molecularity- is the number of colliding molecular entities that are involved in a single reaction step. While the order of a reaction is derived experimentally, the molecularity is a theoretical concept and can only be applied to elementary reactions.

Intermediates

            -appear in the mechanism of the reaction but not in the overall balanced equation

Rate-determining step

            -the slowest step in the sequence of steps leading to product Formation

Benzoin Condensation- is a reaction between two aromatic aldehydes, particularly benzaldehyde. The reaction is catalyzed by a nucleophile such as the cyanide anion or an N-heterocyclic carbene. The reaction product is an aromatic acyloin with benzoin as the parent compound. An early version of the reaction was developed in 1832 by Justus von Liebig and Friederich Woehler during their research on bitter almond oil.

In the first step in this reaction, the cyanide anion (as sodium cyanide) reacts with the aldehyde in a nucleophilic addition. Rearrangement of the intermediate results in polarity reversal of the carbonyl group, which then adds to the second carbonyl group in a second nucleophilic addition. Proton transfer and elimination of the cyanide ion affords benzoin as the product. This is a reversible reaction.

The cyanide ion serves three different purposes in the course of this reaction. It acts as a nucleophile, facilitates proton abstraction, and is also the leaving group in the final step. The benzoin condensation is in effect a dimerization and not a condensation because a small molecule like water is not released in this reaction. For this reason the reaction is also called a benzoin addition. In this reaction, the two aldehydes serve different purposes; one aldehyde donates a proton and one aldehyde accepts a proton. 4-Dimethylaminobenzaldehyde is an efficient proton donor while benzaldehyde is both a proton acceptor and donor. In this way it is possible to synthesise mixed benzoins, i.e. products with different groups on each half of the product.

Video Lessons for Chemical Kinetics

First part

Second Part

Third Part

Fourth Part

Chemical Kinetics

Chemical kinetics deals with

• Study of rates of reactions 
• Study of mechanisms of reaction
• Factors affecting rate of reaction

1.1 Reaction Rates

      Reaction rate is a measure of how fast a reaction occurs, or how something changes during a given time period. The speed of a chemical reaction or its reaction the is expressed as the change in concentration of a reactant or product per unit time. It is usually expressed in molarity per second (M/s).

We often define the rate of a chemical reaction as: 

Δ[concentration]

Δ[time]

A graph illustrating this equation is shown below. There is an explanation included in the graph.

Therefore, if we wanted to express the rate of the following reaction:

SO₂(g) + NO₂(g) → SO₃(g) + NO(g)

We can write it as:

 rate = -Δ[SO2] = -Δ[NO2] = Δ[SO3] = Δ[NO]    

       Δt                Δt             Δt          Δt

 The rate law of this equation is:

     Rate = k[SO2]^x[NO2]^y

A Rate Law is an equation that tells us how fast the reaction proceeds and how the reaction rate depends on the concentrations of the chemical species involved.

1.2 Collision Theory

• The collision theory states that for a chemical reaction to occur the reacting particles must collide with one another.  
• The rate of the reaction depends on the frequency of collisions
• The theory also tells us that reacting particles often collide without reacting. This is called ineffective collision.
• In order for collisions to be successful or be an effective collision, reacting particles must collide
  
  • with sufficient energy, and
  • with the proper orientation
  Activation Energy Video

1.3 Factors Affecting Rates of Reactions

1. Nature of Reactants

      

      A chemical reaction involves the breaking of old bonds and the formation of new bonds. The rate of a reaction depends on the particular reactants and the number of bonds that have to be broken and formed.

      If the two reactants have the same bond or state, then they will react easily to each other. If the two reactants have different bond or state, then they will not react easily to each other.

2.  Concentration

       The collision theory explains the effect of change in concentration of reactants on the rates. An increase in concentration means an increase in the number of molecules or particles per volume, and thus a decrease in spaces between the reacting particles. With less distance to travel inside the vessel, the more frequent the collision, the faster the rate of reaction.

3. Temperature

        

       The average kinetic and hence, the number of collisions increase with absolute temperature. Hence, the rate of reaction increases with increase in temperature.

        The rate of reaction is usually doubled when the temperature is increased by 10^oC.

4. Surface Area

         
       The surface area of a solid reactant has an important effect on the rate of reaction. The smaller the size of particles, the larger the surface area exposed. A larger surface area increases the frequency of collision, hence the rate of  reaction increases.

5. Effect of Catalysts

           Another way to speed up a reaction is to use catalyst. A catalyst provides an alternate pathway of lower activation energy. It increases the rate of reaction, but is not used up in the reaction. Catalysts in the body, such as those involved in breaking down sugar or protein, are called enzymes. Enzymes increase the speed of reactions essential to life that would otherwise be very slow.

Sample Problems

1. Given the below initial rate data, determine the rate law and rate constant for the following reaction:

 

Solution:

Using the method of initial rates, we take the ratio of rates between reactions 2 and 1 to determine the order of the reaction in permanganate.

By taking the ratios of the rates of experiments 3 and 1 we can obtain the order of the reaction in chlorite.

Finally, by taking the ratios of the rates of experiments 4 and 1 we can obtain the order of the reaction in H⁺.

Now that we know the order of the reaction in permanganate is 2, chlorite is 1, and H⁺ is 1/2, we can use the rate and concentration data in experiment 1 to calculate the rate constant.

 

2.  Consider the following reaction:

N₂(g) + 3 H₂(g) → 2 NH₃(g)

If the rate of loss of hydrogen gas is 0.03 mol · L^-1· s^-1, what is the rate of production of ammonia?

Solution:
From the balanced equation we see that there are 2 moles NH₃ produced for every 3 moles H₂ used. Thus:

rate NH3 production	=	2 3	× (0.03 mol · L-1· s-1)
	= 0.02 mol · L-1· s-1

 3.  In the following decomposition reaction,

 2 N₂O₅ → 4 NO₂ + O₂

oxygen gas is produced at the average rate of 9.1 × 10^-4 mol · L^-1 · s^-1. Over the same period, what is the average rate of the following:

• the production of NO₂
• the loss of N₂O₅

Solution:

• From the equation we see that for every 1 mole of oxygen formed, four moles of nitrogen dioxide are produced. Thus, the rate of production of nitrogen dioxide is four times that of oxygen:

rate NO2 production	= 4 × (9.1 × 10-4 mol · L-1· s-1)
	= 3.6 × 10-3 mol · L-1· s-1

• N₂O₅ is consumed at twice the rate that oxygen is produced:

rate loss of N2O5	= 2× (9.1 × 10-4 mol · L-1· s-1)
	= 1.8 × 10-3 mol · L-1· s-1

4. Given the following experimental data, find the rate law and the rate constant for the reaction:

                         

NO (g)   +   NO₂  (g)   +  O₂ (g)  ž  N₂O₅ (g)

Run     [NO]_o , M        [NO₂[_o , M       [O₂]_o , M          Initial Rate, Ms^-1

   1          0.10 M          0.10 M               0.10 M             2.1 x 10^-2

   2          0.20 M          0.10 M               0.10 M             4.2 x 10^-2

   3          0.20 M          0.30 M              0.20 M             1.26 x 10^-1

   4          0.10 M          0.10 M               0.20 M             2.1 x 10^-2

 Solution: 

From the equation Rate =  k[NO] [NO₂], we can derive the equation for k:

k =     Rate

       [NO][NO₂]

Substituting,

k =        2.1 x 10^-2 M/s

         [0.10 M] [0.10 M]

k = 2.1 ¹/_M·s

Trial

First Entry.