JEE Main & Advanced

Radioisotopes find numerous applications in a variety of areas such as medicine, agriculture, biology, chemistry, archeology, engineering and industry. (1) Age determination : The age of earth has been determined by uranium dating technique as follows. Samples of uranium ores are found to contain \[P{{b}^{206}}\] as a result of long series of a- and b-decays. Now if it is assumed that the ore sample contained no lead at the moment of its formation, and if none of the lead formed from \[{{U}^{238}}\] decay has been lost then the measurement of the \[P{{b}^{206}}/{{U}^{238}}\] ratio will give the value of time t of the mineral.                 \[\frac{\text{No}\text{. of atoms of }P{{b}^{206}}}{\text{No}\text{. of atoms of }{{U}^{238}}\text{ left}}={{e}^{-\lambda t-1}}\]   where l is the decay constant of uranium-238 Alternatively, \[t=\frac{2.303}{\lambda }\log \frac{\text{Initial amount of }{{U}^{238}}}{\text{Amount of }{{U}^{238}}\text{ in the mineral present till date}}\] Similarly, the less abundant isotope of uranium, \[{{U}^{235}}\] eventually decays to \[P{{b}^{207}};\,T{{h}^{232}}\] decays more...

The increased pace of synthesis and use of radio isotopes has led to increased concern about the effect of radiations on matter, particularly in biological systems. The accident of Chernobyl occurred in 1986 in USSR is no older when radioisotopes caused a hazard there. The nuclear radiations (alpha, beta, gamma as well as X-rays) possess energies far in excess of ordinary bond energies and ionisation energies. Consequently, these radiations are able to break up and ionise the molecules present in living organisms if they are exposed to such radiations. This disrupts the normal functions of living organisms. The damage caused by the radiations, however, depends upon the radiations received. The resultant radiation damage to living system can be classified as, (1)Somatic or pathological damage : This affects the organism during its own life time. It is a permanent damage to living civilization produced in body. Larger dose of radiations cause more...

A chemical reaction is said to have taken place when the concentration of reactants decreases, and the concentration of the products increases with time. The chemical reactions are classified on the basis of the extent to which they proceed, into the following two classes; (1) Reversible reactions : Reaction in which entire amount of the reactants is not converted into products is termed as reversible reaction. (i) Characteristics of reversible reactions (a) These reactions can be started from either side,               (b) These reactions are never complete, (c) These reactions have a tendency to attain a state of equilibrium, in which Free energy change is zero (DG = 0), (d) This sign \[(\rightleftharpoons )\] represents the reversibility of the reaction, (ii) Examples of reversible reactions (a) Neutralisation between an acid and a base either of which or both are weak e.g., \[CH{}_{3}COOH+Na\,OH\]\[\rightleftharpoons \]\[C{{H}_{3}}COONa+{{H}_{2}}O\] (b) Salt hydrolysis, e.g., \[Fe\,C{{l}_{3}}+3{{H}_{2}}O\]\[ \rightleftharpoons \] \[Fe\,{{\left( OH more...

"Equilibrium is the state at which the concentration of reactants and products do not change with time. i.e. concentrations of reactants and products become constant." The important characteristics of equilibrium state are, (1) Equilibrium state can be recognised by the constancy of certain measurable properties such as pressure, density, colour, concentration etc. by changing these conditions of the system, we can control the extent to which a reaction proceeds. (2) Equilibrium state can only be achieved in close vessel. (3) Equilibrium state is reversible in nature. (4) Equilibrium state is also dynamic in nature. (5) At equilibrium state, Rate of forward reaction = Rate of backward reaction (6) At equilibrium state, DG = 0, so that DH = TDS.

On the basis of observations of many equilibrium reactions, two Norwegian chemists Goldberg and Waage suggested (1864) a quantitative relationship between the rates of reactions and the concentration of the reacting substances. This relationship is known as law of mass action. It states that “The rate of a chemical reaction is directly proportional to the product of the molar concentrations of the reactants at a constant temperature at any given time.” The molar concentration i.e. number of moles per litre is also called active mass. It is expressed by enclosing the symbols of formulae of the substance in square brackets. For example, molar concentration of A is expressed as [A]. Consider a simple reversible reaction  \[aA+bB\]? \[cC+dD\]          (At a certain temperature) According to law of mass action Rate of forward reaction \[\propto {{[A]}^{a}}{{[B]}^{b}}={{k}_{f}}{{[A]}^{a}}{{[B]}^{b}}\] Rate of backward reaction \[\propto {{[C]}^{c}}{{[D]}^{d}}={{k}_{b}}{{[C]}^{c}}{{[D]}^{d}}\] At equilibrium, Rate of forward reaction = Rate of backward more...

  The equilibrium between different chemical species present in the same or different phases is called chemical equilibrium. There are two types of chemical equilibrium. (1) Homogeneous equilibrium : The equilibrium reactions in which all the reactants and the products are in the same phase are called homogeneous equilibrium reactions. \[{{C}_{2}}{{H}_{5}}OH\,(l)+C{{H}_{3}}COOH\,(l)\]? \[C{{H}_{3}}COO{{C}_{2}}{{H}_{5}}\,(l)+{{H}_{2}}O(l)\]                            \[{{N}_{2}}\,(g)+3{{H}_{2}}\,(g)\] ? \[2N{{H}_{3}}(g)\]                \[2S{{O}_{2}}\,(g)+{{O}_{2}}\,(g)\] ? \[2S{{O}_{3}}(g)\] (2) Heterogeneous equilibrium : The equilibrium reactions in which the reactants and the products are present in different phases are called heterogeneous equilibrium reactions.           \[2NaHC{{O}_{3}}\,(s)\]? \[N{{a}_{2}}C{{O}_{3}}\,(s)+C{{O}_{2}}\,(g)+{{H}_{2}}O\,(g)\] \[Ca{{(OH)}_{2}}(s)+{{H}_{2}}O\,(l)\] ? \[C{{a}^{2+}}(aq)+2O{{H}^{-}}\,(aq)\]                  \[CaC{{O}_{3}}\,(s)\] ? \[CaO\,(s)+C{{O}_{2}}\,(g)\]                    \[{{H}_{2}}O\,(l)\] ? \[{{H}_{2}}O\,(g)\]   Homogeneous equilibria and equations for equilibrium constant (Equilibrium pressure is P atm in a V L flask)
  \[\Delta n=0\,;\,\,{{K}_{p}}={{K}_{c}}\] \[\Delta n<0\] ;  \[{{K}_{p}}<{{K}_{c}}\] more...
Factors which Change the State of Equilibrium: Le-Chatelier's Principle.   Le-Chatelier and Braun (1884), French chemists, made certain generalizations to explain the effect of changes in concentration, temperature or pressure on the state of system in equilibrium. When a system is subjected to a change in one of these factors, the equilibrium gets disturbed and the system readjusts itself until it returns to equilibrium. The generalization is known as Le-Chatelier's principle. It may stated as: “Change in any of the factors that determine the equilibrium conditions of a system will shift the equilibrium in such a manner to reduce or to counteract the effect of the change.” The principle is very helpful in predicting qualitatively the effect of change in concentration, pressure or temperature on a system in equilibrium. This is applicable to all physical and chemical equilibria.   (1) Effect of change of concentration : According to Le-Chatelier's principle, more...

The Le-Chateliers principle has a great significance for the chemical, physical systems and in every day life in a state of equilibrium. (1) Applications to the chemical equilibrium (i) Synthesis of ammonia (Haber’s process) \[\underset{1\ vol}{\mathop{{{N}_{2}}}}\,+\underset{3\ vol}{\mathop{3{{H}_{2}}}}\,\] \[\rightleftharpoons \] \[\underset{2\ vol}{\mathop{2N{{H}_{3}}}}\,+23kcal\] (exothermic) (a) High pressure \[(\Delta n<0)\] (b) Low temperature (c) Excess of \[{{N}_{2}}\] and \[{{H}_{2}}\] (d) Removal of \[N{{H}_{3}}\] favours forward reaction. (ii) Formation of sulphur trioxide \[\underset{2\ vol}{\mathop{2S{{O}_{2}}}}\,+\underset{1\ vol}{\mathop{{{O}_{2}}}}\,\] \[\rightleftharpoons \] \[\underset{2\ vol}{\mathop{2S{{O}_{3}}}}\,+45\ kcal\]  (exothermic)
  • High pressure \[(\Delta n<0)\]
(b) Low temperature (c) Excess of \[S{{O}_{2}}\] and \[{{O}_{2}}\], favours the reaction in forward direction. (iii) Synthesis of nitric oxide \[\underset{1\ vol}{\mathop{{{N}_{2}}}}\,+\underset{1\ vol}{\mathop{{{O}_{2}}}}\,\] \[\rightleftharpoons \] \[\underset{2\ vol}{\mathop{2N{{O}_{{}}}}}\,-43.2\ kcal\] (endothermic ) (a) High temperature (b) Excess of \[{{N}_{2}}\] and \[{{O}_{2}}\] (c) Since reaction takes place without change in volume   i.e., \[\Delta n=0\], pressure has no effect on equilibrium. (iv) Formation of nitrogen dioxide \[\underset{2\ vol}{\mathop{2N{{O}_{{}}}}}\,+\underset{1\ vol}{\mathop{{{O}_{2}}}}\,\] \[\rightleftharpoons \] \[\underset{2\ vol}{\mathop{2N{{O}_{2}}}}\,+27.8\ more...

In the following reversible chemical equation.                                      \[A\]  \[\rightleftharpoons \]   \[yB\] Initial mole              1              0 At equilibrium  (1–x)                   yx        x = degree of dissociation Number of moles of \[A\] and \[B\] at equilibrium \[=1-x+yx=1+x(y-1)\] If initial volume of 1 mole of A is V, then volume of equilibrium mixture of \[A\] and \[B\] is,\[=[1+x(y-1)]V\] Molar density before dissociation,  \[D=\frac{\text{molecular}\ \text{weight}}{\text{volume}}=\frac{m}{V}\] Molar density after dissociation, \[d=\frac{m}{[1+x(y-1)]V}\];\[\frac{D}{d}=[1+x(y-1)]\] ; \[x=\frac{D-d}{d(y-1)}\] \[y\] is the number of moles of products from one mole of reactant. \[\frac{D}{d}\] is also called Van’t Hoff factor. In terms of molecular mass,\[x=\frac{M-m}{(y-1)\,m}\] Where \[M=\] Initial molecular mass,    \[m=\] molecular mass at equilibrium  Thus for the equilibria (I) \[PC{{l}_{5(g)}}\] \[\rightleftharpoons \]  \[PC{{l}_{3(g)}}+C{{l}_{2(g)}},y=2\] (II) \[{{N}_{2}}{{O}_{4(g)}}\] \[\rightleftharpoons \]  \[2N{{O}_{2(g)}},\ y=2\] (III) \[2N{{O}_{2}}\] ? \[{{N}_{2}}{{O}_{4}},\ y=\frac{1}{2}\] \[\therefore \] \[x=\frac{D-d}{d}\] (for I and II)  and \[x=\frac{2(d-D)}{d}\] (for III) Also \[D\times 2=\] Molecular weight (theoretical value) \[d\times 2=\] Molecular weight (abnormal value) more...

Substances, which allow electric current to pass through them, are known as conductors or electrical conductors. Conductors can be divided into two types, (1) Conductors which conduct electricity without undergoing any chemical change are known as metallic or electronic conductors. (2) Conductors which undergo decomposition (a chemical change) when an electric current is passed through them are known as electrolytic conductors or electrolytes. Electrolytes are further divided into two types on the basis of their strengths, (i) Substances which almost completely ionize into ions in their aqueous solution are called strong electrolytes. Degree of ionization for this type of electrolyte is one i.e., \[\alpha \approx 1\]. For example : \[HCl,\ {{H}_{2}}S{{O}_{4}},\ NaCl,\ HN{{O}_{3}},\ KOH,\ \]\[NaOH,\ \] \[HN{{O}_{3}},AgN{{O}_{3}},\ CuS{{O}_{4}}\] etc. means all strong acids, bases and all types of salts. (ii) Substances which ionize to a small extent in their aqueous solution are known as weak electrolytes. Degree of ionization for more...


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