Chemical Kinetics : Rate of reaction

 

The branch of physical chemistry which deals with the rate at which the chemical reactions occur, the mechanism by which the chemical reactions take place and the influence of various factors such as concentration, temperature, pressure, catalyst etc., on the reaction rates is called the chemical kinetics.

 

Chemical reactions

On the basis of reaction rates, the chemical reactions have been classified into the following three groups:-

(1)     Very fast or instantaneous reactions : These reactions occur at a very fast rate generally these reactions involve ionic species and known as ionic reactions.

These reactions take about 10–14 or 10–16 seconds for completion. It’s rate can be measured by employing special methods. So, it is almost impossible to determine the rates of these reactions.

Examples :

 (i)        AgNO_{ 3 }+NaCl\rightarrow \underset { (ppt) }{ AgCl } +NaNO_{ 3 }   (Precipitation reaction)

(ii)        \underset { (acid) }{ HCl } +\underset { (base) }{ NaOH } \rightarrow \underset { Salt }{ NaCl } +H_{ 2 }O  (Neutralization reaction)

 

(2)     Moderate reaction : These  type of reactions proceed with a measurable rates at normal temperature.  In this a large number of bonds have to be broken in reactants molecules and a large number of new bonds have to be formed in product molecules. Mostly these reactions are molecular in nature.

Examples :

(i)      Decomposition of H2O2 :  2H2O2 → 2H2O + O2   

(ii)     Decomposition of N2O5 :  2N2O5 → 2N2O4 + O2

(iii)    Hydrolysis of ester : CH3COOC2H5 + NaOH→CH3COONa + C2H5OH

(iv)    Reaction of NO with chlorine :  NO + Cl2 → NOCl2

(v)     Inversion of cane sugar in aqueous solution : C_{ 12 }H_{ 22 }O_{ 11 }+H_{ 2 }O\rightarrow \underset { (Glucose) }{ C_{ 6 }H_{ 12 }O_{ 6 } } +\underset { Fructose }{ C_{ 6 }H_{ 12 }O_{ 6 } }

(vi)    2FeCl3(aq) + SnCl2 → 2FeCl2(aq) + SnCl4(aq)

(vii)   NO2 + CO → NO + CO2

(viii) Decolourisation of acidified potassium permanganate with sodium oxalate.

 

(3)     Very slow reactions : These reactions are extremely slow and take months together to show any measurable change. The rate of such type of reactions are very slow. So, it is also very difficult to determine the rate of these reactions.

Examples :

(i)      Rusting of iron : Fe_{ 2 }O_{ 3 }+xH_{ 2 }O\rightarrow \underset { (Hydrated\quad ferric\quad oxide\quad Rust) }{ Fe_{ 2 }O_{ 3 }.\quad xH_{ 2 }O }                 

(ii)     Reaction between H2 and O2 to form H2O at ordinary temperature in absence of catalyst.

(iii)    Reaction of atmospheric H2S on basic lead acetate paint.

White basic lead acetate paint  \xrightarrow [ H_{ 2 }S ]{ atmospheric }   Blackening of paint ocuurs very slowly

             

Note :       The chemical reactions can be slowed down or speed up by changing conditions under which they occur. e.g. 

CO + 2H2  \xrightarrow [ temp ]{ At\quad room }   CH3OH.  (very slow reaction)

The reaction can be speeded up by maintaining temperature around 400°C, pressure about 300 atm and using a catalyst containing ZnO and Cr2O3.

 

Rate of reaction

Where a is the initial concentration and (a-x) is concentration of reactant after time t and x will be the concentration of product after time t.

“The rate (speed or velocity) of reaction is the rate of change in  concentration of reactants or products in unit time.” 

                               A →  Product

  When,        t = 0           a               0

  After,         t = t            (a–x)         x

 

 

 

 

 

 

Rate of reaction = \frac { Total\quad change\quad in\quad concentration\quad of\quad reactants\quad or\quad products }{ Change\quad in\quad time\quad (in\quad sec.) }

If dx is the change in concentration in time interval dt then,

The reaction rate for reactants = -\frac { dx }{ dt }  

The reaction rate for products =  +\frac { dx }{ dt }

The negative sign indicates that the concentration of reactant decreases with time.

The positive sign indicates that the concentration of products increases with time.

The concentration change may be positive or negative but the rate of reaction is always positive.

The rate of chemical reaction decreases as the reaction proceeds.

The concept of mechanical speed or velocity cannot be used in measuring rate of reaction. Rate of reaction depends on molar concentration.

(1)     Types of rate of reactions : There are two types of rate of reactions.

(i)      Average rate of reaction : The average rate is defined as the change in the concentration (active mass) of reactants or products over a long time interval.

Consider the general chemical reaction,

aA + bB + …….. → cC + dD + ……

Average rate = Amount of reactant consumed (or product formed)/time interval.

            Average rate = -\frac { \Delta [A] }{ a\Delta t } =-\frac { \Delta [B] }{ b\Delta t } .....+\frac { \Delta [C] }{ c\Delta t } =\frac { \Delta [D] }{ d\Delta t } =+....

The average rate over the time interval Δt approaches the instantaneous rate as Δt approaches zero.

(ii)     Instantaneous rate of reaction : The instantaneous rate of  reaction gives the tendency of the reaction at a particular instant. The term Δt becomes smaller and eventually approaches zero, then the rate of reaction at a particular moment called the instantaneous rate (Rt) is given by,

            Instantaneous rate = (Average rate)Δt→0

             

 

Rt = \left( \frac { \Delta [A] }{ \Delta t } \right) _{ \Delta t\rightarrow 0 }=\left( \frac { \Delta [B] }{ \Delta t } \right) _{ \Delta t\rightarrow 0 }  or    Rt = – \frac { d[A] }{ dt } =\frac { d[B] }{ dt }

Where, d[A], d[B] and  being infinitesimally small changes in the concentration of A and B, that of time respectively. Instantaneous rate of reaction at any instant of time is obtained by finding the slope of the tangent to the curve (which is obtained by plotting concentration of any suitable reactant or product versus time) at the point corresponding to that instant of time. Rate of reaction = tan θ = \frac { dx }{ dt }

 

(2)     Unit of rate of reaction :

Unit of rate of reaction = \frac { Unit\quad of\quad concentration }{ Unit\quad of\quad time } = mole litre –1 time –1 

(i)      If reactants and products are in gaseous state then the pressure may be taken in place of concentration thus rate will have unit of atm sec–1 or atm min–1

(ii)       The unit of time can be second, minute, hours, days and years so the unit of rate of reaction may be expressed as follows: mol/litre sec (mol l–1 s–1)  or mol/litre min (mol l–1 min–1 or mol/litre hour (mol l–1 h–1) or mol/litre day (mol l–1 d–1) or mol/litre year (mol l–1 y–1)

 

Experimental methods of Rate studies

Many physical and chemical methods are available for studying the reaction rate :

(1)     Volume or Pressure measurement : The reaction rate can be followed by measuring the volume or pressure change provided one or more of the components are gases.

(2)     Titrimetry : The reaction course can be followed using acid-base or oxidation-reduction titration if at least one of the components in the reaction is an acid or a base or an oxidising agent or a reducing agent.

(3)     Conductometry or Potentiometry : It is a suitable method based on conductivity or potentiometric measurements if one or more of the ions are present or produced in the reaction.

(4)     Spectrophotometry : When a component of the reaction has a strong absorption band at a particular wavelength region, spectrophotometers could be used for measuring the reaction rate.

(5)     Polarimetry : The reaction rate can be studied from the measurements of optical rotation when at least one of the component of a reaction is optically active.