# JEE Main & Advanced Chemistry Chemical Kinetics Rate of a Reaction

Rate of a Reaction

Category : JEE Main & Advanced

Rate of a Reaction

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

$A\xrightarrow{{}}$Product

When,   $t=0$   a             0

After,    $t=t$   (a–x)    x

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.

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

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 can not 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, $aA+bB+........\xrightarrow{{}}c\,C+dD$+ ……….

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 $\Delta t$ approaches the instantaneous rate as $\Delta t$ approaches zero.

(ii) Instantaneous rate of reaction : The instantaneous rate of reaction gives the tendency of the reaction at a particular instant. The term $\Delta t$ becomes smaller and eventually approaches zero, then the rate of reaction at a particular moment called the instantaneous rate $({{R}_{t}})$ is given by,

Instantaneous rate = (Average rate)$_{\Delta t\to 0}$

${{R}_{t}}={{\left( \frac{-\Delta [A]}{\Delta t} \right)}_{\Delta t\to 0}}={{\left( \frac{\Delta [B]}{\Delta t} \right)}_{\Delta t\to 0}}$ or ${{R}_{t}}=-\frac{d[A]}{dt}=\frac{d[B]}{dt}$

Where, $d[A],\ d[B]$ and $dt$ 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 = $\tan \,\theta =\frac{dx}{dt}$

(2) Unit of rate of reaction : Unit of rate of reaction = $\frac{\text{Unit of concentration}}{\text{Unit of time}}$=$mole\text{ }litr{{e}^{1}}tim{{e}^{1}}$

(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 $atm\text{ }se{{c}^{1}}$ or $atm\text{ }mi{{n}^{1}}$

(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 $(mol\,{{l}^{-1}}\,{{y}^{-1}})$

Examples based on Rate of reaction

Example : 1      For the reaction ${{N}_{2}}+3{{H}_{2}}$ ? $2N{{H}_{3}}$, if $\frac{\Delta [N{{H}_{3}}]}{\Delta t}=2\times {{10}^{-4}}mol\ {{l}^{-1}}{{s}^{-1}},$the value of $\frac{-\Delta [{{H}_{2}}]}{\Delta t}$ would be

[MP PMT 2000]

(a) $1\times {{10}^{-4}}mol{{l}^{-1}}{{s}^{-1}}$                            (b) $3\times {{10}^{-4}}mol\,{{l}^{-1}}{{s}^{-1}}$

(c) $4\times {{10}^{-4}}mol{{l}^{-1}}{{s}^{-1}}$                            (d) $6\times {{10}^{-4}}mol\,{{l}^{-1}}{{s}^{-1}}$

Solution: (b) ${{N}_{2}}+3{{H}_{2}}$? $2N{{H}_{3}}$

$\frac{-\Delta [{{N}_{2}}]}{\Delta t}=-\frac{1}{3}\frac{\Delta [{{H}_{2}}]}{\Delta t}=\frac{1}{2}\frac{\Delta [N{{H}_{3}}]}{\Delta t}$; $\therefore \,\,\frac{\Delta [{{H}_{2}}]}{\Delta t}=\frac{3}{2}\times \frac{\Delta [N{{H}_{3}}]}{\Delta t}=\frac{3}{2}\times 2\times {{10}^{-4}}$ $=3\times {{10}^{-4}}mol\,{{l}^{-1}}{{s}^{-1}}$.

Example : 2 A gaseous hypothetical chemical equation $2A$?$4B+C$ is carried out in a closed vessel. The concentration of B is found to increase by $5\times {{10}^{-3}}mol\,{{l}^{-1}}$ in 10 second. The rate of appearance of B is [AFMC 2001]

(a) $5\times {{10}^{-4}}mol\,{{l}^{-1\,}}{{\sec }^{-1}}$                               (b) $5\times {{10}^{-5}}mol\,{{l}^{-1\,}}{{\sec }^{-1}}$

(c) $6\times {{10}^{-5}}mol\,{{l}^{-1\,}}{{\sec }^{-1}}$                               (d) $4\times {{10}^{-4}}mol\,{{l}^{-1\,}}{{\sec }^{-1}}$

Solution: (a) Increase in concentration of $B=5\times {{10}^{-3}}mol\,{{l}^{-1\,}}$,  Time = 10 sec.

Rate of appearance of B$=\frac{\text{Increase of concentration of }\int_{{}}^{{}}{{}}}{{}}$$=\frac{5\times {{10}^{-3}}\,mol\,{{l}^{-1}}}{10\,\sec }=5\times {{10}^{-4}}mol\,{{l}^{-1}}{{\sec }^{-1}}$.

Example : 3      If $3A\to 2B$ then the rate of reaction of $+\frac{d(B)}{dt}$ is equal to [CBSE 2002]

(a) $+2\frac{d(A)}{dt}$ (b) $-\frac{1}{3}\frac{d(A)}{dt}$            (c) $-\frac{2}{3}\frac{d(A)}{dt}$            (d) $-\frac{3}{2}\frac{d(A)}{dt}$

Solution: (c)     $3A\to 2B$;  Rate $=-\frac{1}{3}\frac{d\,[A]}{dt}=\frac{1}{2}\frac{d\,[B]}{dt}$;  $\therefore \,\,+\frac{d\,[B]}{dt}=-\frac{2}{3}\frac{d\,[A]}{dt}$

Example: 4 A gaseous reaction, ${{A}_{2}}(g)\to B(g)+\frac{1}{2}C(g)$ ; Shows increase in pressure from 100 mm to 120 mm in 5 minutes. The rate of disappearance of ${{A}_{2}}$ is

(a) $4\,mm\,\,{{\min }^{-1}}$              (b) $8\,mm\,\,{{\min }^{-1}}$              (c) $16\,mm\,\,{{\min }^{-1}}$     (d) $2\,mm\,\,{{\min }^{-1}}$

Solution: (b)     ${{A}_{2}}(g)\to B(g)+\frac{1}{2}C(g)$

100          0         0

$100-p$      p        $\frac{1}{2}p$

$100-p+p+\frac{1}{2}p=120$ or $p=40mm$

$\therefore$$-\frac{d{{p}_{{{A}_{2}}}}}{dt}=\frac{40}{5}=8\,mm\,\,{{\min }^{-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.

Factors affecting Reaction rate.

The rate of a chemical reaction depends on the rate of encounter between the molecules of the reactants which in turn depends on the following things.

(1) Effect of temperature on reaction rate: The rate of chemical reaction generally increases on increasing the temperature.

(2) Nature of reactants: (i) Reactions involving polar and ionic substances including the proton transfer reactions are usually very fast. On the other hand, the reaction in which bonds is rearranged, or electrons transferred are slow.

(ii) Oxidation-reduction reactions, which involve transfer of electrons, are also slow as compared to the ionic substance.

(iii) Substitution reactions are relatively much slower.

(3) pH of the medium: The rate of a reaction taking place in aqueous solution often depends upon the ${{H}^{+}}$ion concentration. Some reactions become fast on increasing the H+ ion concentration while some become slow.

(4) Concentration of reactants: The rate of a chemical reaction is directly proportional to the concentration of the reactants means rate of reaction decreases with decrease in concentration.

(5) Surface area of reactant: Larger the surface area of reactant, the probability of collisions on the surface of the reactant particles by the surrounding molecules increases and thus rate of reaction increases.

(6) Presence of catalyst: The function of a catalyst is to lower down the activation energy. The greater the decrease in the activation energy caused by the catalyst, higher will be the reaction rate. In the presence of a catalyst, the reaction follows a path of lower activation energy. Under this condition, a large number of reacting molecules are able to cross over the energy barrier and thus the rate of reaction increases.  Fig. shows how the activation energy is lowered in presence of a catalyst. energy is lowered in presence of a catalyst.

(7) Effect of sunlight:  There are many chemical reactions whose rate are influenced by radiations particularly by ultraviolet and visible light. Such reactions are called photochemical reactions. For example, Photosynthesis, Photography, Blue printing, Photochemical synthesis of compounds etc.

${{H}_{2}}+C{{l}_{2}}\xrightarrow{\text{sunlight}\ \text{(}h\nu \text{) }}2HCl$: The radiant energy initiates the chemical reaction by supplying the necessary activation energy required for the reaction.

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