#### Rates of reactions, Chemistry tutorial

Introduction:

The chemical reaction rates are the rates of change in amounts or concentrations of either reactants or products. For changes in amounts, the units can be one of mol/s, g/s, lb/s, kg/day and so on. For changes in concentrations, the units can be one of mol/(L s), g/(L s), %/s and so on.

There are numerous reasons for studying the rate of a reaction. To start with, there is intrinsic curiosity regarding why reactions encompass such very different rates. A few processes, like the primary steps in vision and photosynthesis and nuclear chain reactions, occur on a time scale as short as 10-12 s to 10-6 s. Others, such as the curing of cement and the conversion of graphite to diamond, take years or millions of years to complete. On a practical level, knowledge of reaction rates is helpful in drug design, in pollution control and in food processing. Industrial chemists frequently place more emphasis on speeding up the rate of a reaction instead of on maximizing its yield.

Reactants → Products

This equation states us that throughout the course of a reaction, reactants are consumed whereas products are formed. As an outcome, we can follow the progress of a reaction via monitoring either the reduction in concentration of the reactants or the increase in concentration of the products.

Take a simple reaction in which 'A' molecules are converted or transformed to 'B' molecules:

A → B

There is a decrease in the number of 'A' molecules and the rise in the number of 'B' molecules with time. In common, it is more suitable to express the reaction rate in terms of the change in concentration with time. Therefore, for the reaction A → B we can deduce the rate as:

rate = - Δ[A]/Δt or rate = Δ[B]/Δt

Here Δ[A] and Δ[B] are the changes in concentration (that is, molarity) over a period of time Δt. As the concentration of 'A' decreases throughout the time interval, Δ[A] is a negative quantity. The rate of reaction is a positive quantity; therefore a minus sign is required in the rate expression to make the rate positive. On other hand, the rate of product formation doesn't need a minus sign as Δ[B] is a positive quantity (that is, the concentration of B rises with time). Such rates are average rates as they are averaged over a certain period of time Δt.

The subsequent step is to see how the rate of a reaction is obtained experimentally. By definition, we are familiar that to find out the rate of a reaction we have to monitor the concentration of the reactant (or product) as the function of time. For reactions in solution, the concentration of a species can frequently be measured via spectroscopic means. Whenever ions are involved, the change in concentration can as well be detected via an electrical conductance measurement. Reactions comprising gases are most easily followed via pressure measurements. We will take two specific reactions for which various methods are employed to assess the reaction rates.

Reaction of Molecular Bromine and Formic Acid:

In aqueous solutions, the molecular bromine reacts by formic acid (HCOOH) as:

Br2 (aq) + HCOOH (aq) → 2Br- (aq) + 2H+ (aq) + CO2 (g)

The molecular bromine is reddish-brown in color. The other species in the reaction are colorless. Since the reaction progresses, the concentration of Br2 steadily reduces and its color fades. This loss of color and therefore concentration can be monitored simply by a spectrometer that is, registers the amount of visible light absorbed via bromine.

Measuring the change (or decrease) in bromine concentration at some initial time and then at some final time enables us to find out the average rate of the reaction throughout that interval:

Average rate = - Δ[Br2]/Δt

= - {[Br2]final - [Br2]initial}/(tfinal - tinitial)

By employing the data given in table shown below, we can compute the average rate over the first 50-s time interval as:

Table: Rates of Reaction between the Molecular Bromine and Formic Acid at 25oC

Time (s)    [Br2](M)     Rate (M/s)     k = rate/[Br2] (s-1)

0.0             0.0120       4.20 x 10-5      3.50 x 10-3

50.0           0.0101     3.52 x 10-5        3.49 x 10-3

100.0         0.00846    2.96 x 10-5       3.50 x 10-3

150.0         0.00710    2.49 x 10-5       3.51 x 10-3

200.0         0.00596    2.09 x 10-5       3.51 x 10-3

250.0         0.00500    1.75 x 10-5       3.50 x 10-3

300.0         0.00420    1.48 x 10-5       3.52 x 10-3

350.0        0.00353    1.23 x 10-5        3.48 x 10-3

400.0        0.00296    1.04 x 10-5        3.51 x 10-3

Average rate = - (0.0101 - 0.0120) M/50.0s = 3.80 x 10-5 M/s

If we had selected the first 100 s as our time interval, the average rate would then be represented by:

Average rate = - (0.00846 - 0.0120)M/100.0 s = 3.54 x 10-5 M/s

These computations illustrate that the average rate of the reaction based on the time interval we select.

By computing the average reaction rate over shorter and shorter intervals, we can get the rate for a given instant in time that provides us the instantaneous rate of the reaction at that time.

Decomposition of Hydrogen Peroxide:

If one of the products or reactants is a gas, we can utilize a manometer to determine the reaction rate. Take the decomposition of hydrogen peroxide at 20oC:

2H2O2 (aq) → 2H2O (l) + O2 (g)

In this condition, the rate of decomposition can be found out by monitoring the rate of oxygen evolution by a manometer. The oxygen pressure can be readily transformed to concentration by employing the ideal gas equation:

PV = nRT

P = (n/V) RT = [O2] RT

Here, n/V provides the molarity of oxygen gas. Rearranging the equation, we obtain:

[O2] = (1/RT) P

The reaction rate that is provided by the rate of oxygen production can now be represented as:

Rate = Δ[O2]/Δt = (1/RT)(ΔP/Δt)

Reaction Rates and Stoichiometry:

We have observe that for stoichiometrically simple reactions of the type A → B, the rate can be either deduced in terms of the decrease in the reactant concentration with time, -Δ[A]/Δt, or the increase in product concentration by time, Δ[B]/Δt. For more complex reactions, we should be cautious in writing the rate expressions. Take, for illustration, the reaction:

2A → B

Two moles of 'A' disappear for each and every mole of 'B' that forms; that is, the rate at which 'B' forms is one-half the rate at which 'A' disappears. Therefore, the rate can be deduced as:

Rate = - (1/2)(Δ[A]/Δt) or rate = (Δ[B]/Δt)

In common, for the reaction:

aA + bB → cC + dD

The rate is represented by:

rate = -(1/a)(Δ[A]/Δt) = - (1/b)(Δ[B]/Δt) = (1/c)(Δ[C]/Δt) = (1/d)(Δ[D]/Δt)

The Rate Law:

We are familiar that the rate of a reaction is proportional to the concentration of reactants and products that the proportionality constant 'k' is termed as the rate constant. The rate law deduces the relationship of the rate of a reaction to the rate constant and the concentrations of the reactants rose to some powers. For the general reaction:

aA + bB → cC + dD

The rate law takes the form:

rate = k[A]x[B]y

Here, x and y are the numbers which should be found out experimentally. Note that, in common, x and y are not equivalent to the stoichiometric coefficients a and b. Whenever we know the values of x, y and k, we can make use of equation (above equation) to compute the rate of the reaction, provided the concentrations of A and B.

The exponents x and y state the relationships between the concentrations of reactants A and B and the reaction rate. Added altogether, they provide us the overall reaction order, stated as the sum of the powers to which all the reactant concentrations appearing in the rate law are increased. For equation (above equation) the overall reaction order is x + y. On the other hand, we can state that the reaction is xth order in A, yth order in B, and (x + y)th order overall.

To observe how to find out the rate law of a reaction, let us taken the reaction between fluorine and chlorine dioxide:

F2 (g) + 2ClO2 (g) → 2FClO2 (g)

One method to study the effect of reactant concentration on reaction rate is to find out how the initial rate based on the beginning concentrations. This is preferable to compute the initial rates since as the reaction proceeds, the concentrations of the reactants decrease and it might become difficult to measure the changes precisely. As well, there might be a reverse reaction of the kind

Products → reactants

that would introduce error to the rate measurement. Both of such complications are virtually absent throughout the early phases of the reaction.

Measuring reaction rates:

The rates of reaction are measured via monitoring the rate of change of an observable property.

A) Calorimetry assesses the intensity of a color in a reaction mixture with time, like in the oxidation of iodide ions to provide brown iodine. In clock reactions, the reaction is timed till a sudden color change occurs whenever a certain quantity of product is made up.

B) Mass change is employed whenever a gas is produced. For illustration, if calcium carbonate reacts with acids to discharge carbon-dioxide the mass of the flask reduces.

C) The volume change is an alternative to mass changes for gases. For illustration, magnesium reacts by acids to discharge hydrogen that can be collected in the syringe.

D) Titrimetric analysis employs titrations to compute changing concentrations of the reactant or product - for illustration, the fall in acid concentration throughout esterification.

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