Chemical Kinetics


Introduction
       Processes by which substances are transformed to one or several products are called chemical reactions. Chemical processes that occur in the presence of light, like sunlight, are called photochemical reactions. These processes can occur naturally or under controlled conditions in the laboratory.
Reaction Rates- Rate of a Chemical Reaction
       Rates of chemical reaction depends on the inherent characteristics or nature of the reactants. That is the reason, why some reactions are fast while others are slow. For E.g., oxidation of ferrous ion by KMNO4 (potassium permanganate) in acidic medium is fast, while the oxidation of oxalate ion by the same reagent is slow. For E.g., oxidation of ferrous ion by KMNO4 (potassium permanganate) in acidic medium is fast, while the oxidation of oxalate ion by the same reagent is slow.
Concentration of Reactants
       In most cases, the rate of a reaction is accelerated with increase in concentration of a reactant. A piece of wood burns faster in oxygen than in air.
Surface Area of a Solid Reactant or Catalyst
       In heterogenous reactions where one of the phase is a solid, the surface area of the solid affects the rate of a reaction. An increase in surface area leads to an increase in the rate of a reaction. For e.g., lycopodium powder is easily ignited to produce a yellow flame since a powder has a large surface area per volume and therefore burns rapidly.
Rate of a Reaction
       Rate of reaction basically means the speed at which a chemical reaction occurs. The speed of a reaction is determined by monitoring the concentrations of the reactants or products at intervals of time. The volume of the reaction vessel is kept constant and there is no addition to or removal from the reaction vessel of any of the reactants and products. For a hypothetical reaction, A B, as the reaction proceeds the concentration of the reactant (A) decreases with time while the concentration of the product (B) increases.
Expressions of Rates of Reaction
       The amounts of reactants and products in a chemical reaction are related by stoichiometry. Therefore, the concentration of any reactant or product can be used to express the rate of a reaction. Take for e.g., in the reaction A + B C for every molecule of A consumed, a molecule of B is also consumed and thereby a molecule of C, the product, is formed.
Calculation of Average Rate of Reaction
       The average rate of reaction is calculated by determining the difference in [O2] concentration over different intervals of time and dividing the difference by Dt.
Instantaneous Rate
       The plot of concentration versus time is shown in below figure. The instantaneous rates were calculated at times 6.5 hours and 16.2 hours.
Experimental Determination of Rate of Reaction
       The rate of a reaction is determined by measuring the concentration of the reactant or product at different intervals of time. The concentration is measured, by measuring a related property such as color, pressure or volume (as in the case of gas phase reactions), pH, optical rotation, electrical conductivity and thermal conductivity.
Rate Law Expression
       Experimentally, it is found that the rate of a reaction is proportional to the concentrations of the reactants raised to some power, provided that other factors, which also affect the rate of the reaction are kept constant.
Order of a Reaction
       The order of reaction is determined with respect to each reactant in the reaction. The order of a reaction is the power to which the concentration of a reactant is raised. This is the order with respect to one reactant only.
Zero Order Reaction
       Ammonia (NH3) gas decomposes over platinum catalyst to nitrogen gas (N2) and hydrogen gas (H2).
First Order Reaction
       Cyclopropane (C3H6) at room temperature has a ring structure. When it is heated, the ring opens up and cyclopropane isomerizes to propylene.
Second Order Reaction
       Nitrogen dioxide (NO2) gas reacts with fluorine gas (F2) to give nitrosyl fluoride. The chemical reaction is given by the equation.
Fractional Order Reaction or Complex Order
       Hydrogen (H2) gas reacts with bromine (Br2) gas to give hydrogen bromide vapor.
Pseudo First Order Reaction
       For a reaction A + B C + D.
     The rate law for the reaction is expressed as rate = k [A]m [B]n
Methods to Determine Order of a Reaction
       For determination of the order of a reaction, following methods are usually employed.
     a) Graphical Method
     b) Initial Rate Method
     c) Ostwald Method of Isolation.
Graphical Method of Order Determination
       First, the data of concentrations versus time is obtained by a suitable method. Then, the data is plotted as concentration versus time. From the resulting plot, the instantaneous rates are determined by drawing tangents to curve and then calculating their slopes. The reaction rate so obtained are plotted against concentrations raised to various powers. That is rates are plotted against [C]1, [C]2 and [C]3.. [C]n, n (n need not be integral numbers). From the nature of the plots, the order of the reaction can be judged. For a zero order reaction, the rate will not vary with concentration and the plot will be a line parallel to the concentration axis.
Initial Rate Method
       This method is used for reactions where more than one reactant species are involved. Initial rates of the reaction are determined by varying the concentration of only one reactant while keeping the concentrations of other reactants constant. Initial rate of reaction corresponds to the rate at the start of the reaction. The rate is calculated over the first smallest possible time interval. This calculation is done either graphically or numerically.
Isolation Method
       For reactions where many reactants are involved, the order of the reaction is determined by the method of isolation. This was developed by Ostwald. In this method, the concentrations of all the reactants except one are taken in excess.
Half Life of a Reaction
       Half life of a reaction is defined as the time required for reducing the concentration of a reactant to half its initial value. It is denoted as t1/2.
Calculation of Order of a Reaction
       A reaction is carried out at two different initial concentrations of a reactant [A], that is [A]0,1 and [A]0,2 and the respective t1/2 values (t1/2) and (t1/2)2 are obtained.
Radioactive Dating
       All radioactive decays follow first order kinetics. Therefore, the half-life of a radioactive element is independent of the amount of sample. With the help of half-life values of a suitable radioisotope of an element, which is present in a rock, or in an artefact, the age of the rock and the artefact can be determined. This is called radioactive dating.
Relationships for Zero order, First order and Second order Reactions
       Rates of most chemical reactions increases with temperature because the rate constant 'k' increases with temperature. The temperature dependence of the rate constant is given by the Arrhenius equation.
Concept of Activation Energy
       For a reaction to occur, reactant molecules must collide with each other. Only those collisions result in product formation which have energy equal or more than a certain minimum energy. This energy is called the threshold energy. This implies that there is an energy barrier between reactants and products which must be crossed before products can be formed. The energy required for crossing the energy barrier comes from the kinetic energy of reacting molecules. Hence, the minimum extra energy over and above the average potential energy of the reactants, which must be supplied so that the reactants are able to cross over the energy barrier is called the activation energy (Ea).
Energy and Orientation Barriers to Reactions
       From Arrhenius equation, it is seen that the rate constant k of a reaction increases with temperature and therefore, the rate of reaction also increases. Why does k depend on temperature? This can be explained, to a certain extent, by collision theory.
Energy Barrier
       In this theory, the rate constant is related to three factors Z, f and p by the equation
      k = Zfp b
Orientation Barrier
       As noted earlier, the rate of reaction also depends on p, the fraction of collisions that occur with proper orientation. This factor is independent of temperature.
Transition State Theory
       According to this theory, the reactant molecules must come together to form an arrangement of atoms/molecules that facilitates the formation of products. This arrangement of the reacting species is called the transition state.
Kinetic Stability of Fuels
       At normal temperature, fuels are stable even in the presence of air. This is because, the activation energy of combustion reaction is high. When a mixture of fuel and air is burned, a flame has to be applied, that is the mixture has to be ignited. Near the flame, the contents are raised to high temperature and this provides the reactants with the necessary energy to react. Once the reaction begins, a lot of heat is liberated from the combustion, and this increases the temperature of the remaining fuel and the flame once produced is sustained.
Mechanism of Reaction
       A balanced chemical equation represents the overall result of a chemical reaction. However, at the molecular level, more than one reaction step might be involved. Most reactions can be broken down into a sequence of elementary reactions. This breaking down of a reaction into a sequence of elementary reactions means elucidating the reaction mechanism.
Molecularity
       Elementary reactions are classified according to their molecularity. The number of reacting species, which are involved in simultaneous collision to bring about a chemical reaction is called the molecularity of the reaction. In a unimolecular reaction, a single molecule shakes itself apart or its atoms into a new arrangement.
Series Reactions (First Order)
       A complex reaction involving two series reactions can be of the type,
     
Reactions Involving A Slow Step
       If k1 is very much less than k2 that is k1 << k2 then the intermediate B is transformed into the product C as soon as it is formed.
Reactions Where The Steady State Approximation Is Valid
       
Reactions where The Intermediate is in Equilibrium with the Reactant
       In the reaction given below:
     
Parallel Reactions
       A parallel reaction is of the following type in which a reactant A transforms itself to two different products B and C.
     
Catalysis
       It has been mentioned earlier that a catalyst usually increases the rate of reaction. A catalyst is not consumed in the reaction, it is used up in one step and then released in the next step.
Autocatalysis
       This occurs in reactions where the reaction rate increases as a product is formed. An example of autocatalystic reaction is the Belousov-Zhabotinskii (BZ) reaction.
Photochemical Reactions
       There are many reactions that are affected by electromagnetic radiations. Chemical reactions, which occur in the presence of visible and ultraviolet light are called photochemical reactions.
Photosensitization
       There are many reactions, where in the reactants undergo transformation not by direct absorption of photons but via the process of photosensitization. In such reactions, a photosensitive substance is added which actually absorbs the photon. The absorbed energy is then passed on to one of the reactants. The photosensitiser does not undergo any chemical transformation, it only initiates a chemical reaction.
Photosynthesis
       In photosynthesis, chlorophyll present in the chloroplasts acts as a photosensitizer. Light is absorbed by chlorophyll and then this energy is used to split the water molecule into molecular oxygen and hydrogen equivalent. In the process, nicotinamide adenine dinucelotide phosphate (NADP+) is reduced to NADPH. During the process, a part of the energy is stored as ATP.
Conclusion
       Rate of reaction usually doubles when the temperature is raised by ten degrees near the normal temperature because the rate constant is dependent on temperature. The temperature dependency of rate constant is mathematically expressed by the Arrhenius equation. Arrhenius equation is an empirical equation. The equation indicates exponential dependency on temperature of the rate constant. The effect of temperature on the rate constant can be explained by Collision Theory, especially for gas phase reactions.
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