JEE Main & Advanced

(1) The closest distance between the centres of two molecules taking part in a collision is called molecular or collision diameter (s). The molecular diameter of all the gases is nearly same lying in the order of \[{{10}^{-8}}\,cm\].                        (2) The number of collisions taking place in unit time per unit volume, called collision frequency (z). (i) The number of collision made by a single molecule with other molecules per unit time are given by, \[{{Z}_{A}}=\sqrt{2}\pi {{\sigma }^{2}}{{u}_{\text{av}\text{.}}}n\] where n is the number of molecules per unit molar volume, \[n=\frac{\text{Avogadro number(}{{N}_{0}}\text{)}}{{{V}_{m}}}=\frac{6.02\times {{10}^{23}}}{0.0224}{{m}^{-3}}\] (ii) The total number of bimolecular collision per unit time are given by, \[{{Z}_{AA}}=\frac{1}{\sqrt{2}}\pi {{\sigma }^{2}}{{u}_{\text{av}.}}{{n}^{2}}\] (iii) If the collisions involve two unlike molecules, the number of bimolecular collision are given by, \[{{Z}_{AB}}=\sigma _{AB}^{2}{{\left[ 8\pi RT\frac{({{M}_{A}}+{{M}_{B}})}{{{M}_{A}}{{M}_{B}}} \right]}^{1/2}}\] where, \[{{\sigma }_{AB}}=\frac{{{\sigma more...

(1) Kinetic theory was developed by Bernoulli, Joule, Clausius, Maxwell and Boltzmann etc. and represents dynamic particle or microscopic model for different gases since it throws light on the behaviour of the particles (atoms and molecules) which constitute the gases and cannot be seen. Properties of gases which we studied earlier are part of macroscopic model. (2) Postulates (i) Every gas consists of a large number of small particles called molecules moving with very high velocities in all possible directions. (ii) The volume of the individual molecule is negligible as compared to the total volume of the gas. (iii) Gaseous molecules are perfectly elastic so that there is no net loss of kinetic energy due to their collisions. (iv) The effect of gravity on the motion of the molecules is negligible. (v) Gaseous molecules are considered as point masses because they do not posses potential energy. So the attractive and repulsive more...

(1) Diffusion is the process of spontaneous spreading and intermixing of gases to form homogenous mixture irrespective of force of gravity. While Effusion is the escape of gas molecules through a tiny hole such as pinhole in a balloon.

• All gases spontaneously diffuse into one another when they are brought into contact.
• Diffusion into a vacuum will take place much more rapidly than diffusion into another place.
• Both the rate of diffusion of a gas and its rate of effusion depend on its molar mass. Lighter gases diffuses faster than heavier gases. The gas with highest rate of diffusion is hydrogen.

(2) According to this law, “At constant pressure and temperature, the rate of diffusion or effusion of a gas is inversely proportional to the square root of its vapour density.” Thus, rate of diffusion \[(r)\propto \frac{1}{\sqrt{d}}\]         (T and P constant) For two or more gases more...

(1) According to this law, “When two or more gases, which do not react chemically are kept in a closed vessel, the total pressure exerted by the mixture is equal to the sum of the partial pressures of individual gases.” Thus, \[{{P}_{\text{total}}}={{P}_{1}}+{{P}_{2}}+{{P}_{3}}+.........\] Where \[{{P}_{1}},\,{{P}_{2}},\,{{P}_{3}},......\] are partial pressures of gas number 1, 2, 3 ......... (2) Partial pressure is the pressure exerted by a gas when it is present alone in the same container and at the same temperature. Partial pressure of a gas \[({{P}_{1}})=\frac{\text{Number of moles of the gas (}{{n}_{1}}\text{)}\times {{P}_{\text{Total}}}}{\text{Total number of moles (}n\text{) in the mixture}}=\text{Mole fraction (}{{X}_{1}}\text{)}\times {{P}_{\text{Total}}}\] (3) If a number of gases having volume \[{{V}_{1}},\,{{V}_{2}},\,{{V}_{3}}......\] at pressure \[{{P}_{1}},\,{{P}_{2}},\,{{P}_{3}}........\] are mixed together in container of volume V, then, \[{{P}_{\text{Total}}}=\frac{{{P}_{1}}{{V}_{1}}+{{P}_{2}}{{V}_{2}}+{{P}_{3}}{{V}_{3}}.....}{V}\] or  \[=({{n}_{1}}+{{n}_{2}}+{{n}_{3}}.....)\frac{RT}{V}\]           \[(\because PV=nRT)\]  or  \[=n\frac{RT}{V}\]    \[(\because n={{n}_{1}}+{{n}_{2}}+{{n}_{3}}.....)\] (4) Applications : This law is used in the calculation of following relationships, (i) Mole fraction of a gas more...

(1) The simple gas laws relating gas volume to pressure, temperature and amount of gas, respectively, are stated below: Boyle's law :        \[P\propto \frac{1}{V}\] or \[V\propto \frac{1}{P}\] (n and T constant) Charle's law :      \[V\propto \text{T}\]                      (n and P constant) Avogadro's law : \[V\propto n\]                (T and P constant) If all the above law's combines, then \[V\propto \frac{nT}{P}\] or                   \[V=\frac{nRT}{P}\] (\[R=\] Ideal gas constant) or                \[PV=nRT\] This is called ideal gas equation. R is called ideal gas constant. This equation is obeyed by isothermal and adiabatic processes. (2) Nature and values of R : From the ideal gas equation, \[R=\frac{PV}{nT}=\frac{\text{Pressure}\times \text{Volume}}{\text{mole}\times \text{Temperature}}\] \[=\frac{\frac{\text{Force}}{\text{Area}}\times \text{Volume}}{\text{mole}\times \text{Temperature}}=\frac{\text{Force}\times \text{Length}}{\text{mole}\times \text{Temperature}}\] \[=\frac{\text{Work or energy}}{\text{mole}\times \text{Temperature}}\]. R is expressed in the unit of work or energy \[mo{{l}^{-1}}\,{{K}^{-1}}\]. Since different values of R are summarised below : \[R=0.0821\,L\,atm\,mo{{l}^{-1}}\,{{K}^{-1}}\] \[=8.3143\,joule\,mo{{l}^{-1}}\,{{K}^{-1}}\]  (S.I. unit) \[=8.3143\,Nm\,mo{{l}^{-1}}\,{{K}^{-1}}\]  \[=8.3143\,KPa\,d{{m}^{3}}\,mo{{l}^{-1}}\,{{K}^{-1}}\] \[=8.3143\,MPa\,c{{m}^{3}}\,mo{{l}^{-1}}\,{{K}^{-1}}\] \[=5.189\times {{10}^{19}}\,eV\,mo{{l}^{-1}}\,{{K}^{-1}}\] \[=1.99\,cal\,mo{{l}^{-1}}\,{{K}^{-1}}\] (3) Gas constant, R for a single more...

(1) According to this law, “Equal volumes of any two gases at the same temperature and pressure contain the same number of molecules.” Thus, \[V\propto n\]   (at constant T and P) or \[V=Kn\] (where K is constant) or \[\frac{{{V}_{1}}}{{{n}_{1}}}=\frac{{{V}_{2}}}{{{n}_{2}}}=.......=K\] Example, \[\underset{1n\,litre}{\mathop{\underset{1\,litre}{\mathop{\underset{2\,litres}{\mathop{\underset{2\,volumes}{\mathop{\underset{2\,moles}{\mathop{2{{H}_{2}}(g)}}\,}}\,}}\,}}\,}}\,+\underset{1/2n\,litre}{\mathop{\underset{1/2\,litre}{\mathop{\underset{1\,litre}{\mathop{\underset{1\,volume}{\mathop{\underset{1\,mole}{\mathop{{{O}_{2}}(g)}}\,}}\,}}\,}}\,}}\,\xrightarrow{{}}\underset{1n\,litre}{\mathop{\underset{1\,litre}{\mathop{\underset{2\,litres}{\mathop{\underset{2\,volumes}{\mathop{\underset{2\,moles}{\mathop{2{{H}_{2}}O(g)}}\,}}\,}}\,}}\,}}\,\]  (2) One mole of any gas contains the same number of molecules (Avogadro's number \[=6.02\times {{10}^{23}}\]) and by this law must occupy the same volume at a given temperature and pressure. The volume of one mole of a gas is called molar volume, Vm which is 22.4 L \[mo{{l}^{-1}}\] at S.T.P. or N.T.P.  (3) This law can also express as, “The molar gas volume at a given temperature and pressure is a specific constant independent of the nature of the gas”.   Thus, \[{{V}_{m}}=\] specific constant \[=22.4\,L\,mo{{l}^{-1}}\] at S.T.P. or N.T.P.

(1) In 1802, French chemist Joseph Gay-Lussac studied the variation of pressure with temperature and extende the Charle’s law so, this law is also called Charle’s-Gay Lussac’s law. (2) It states that, “The pressure of a given mass of a gas is directly proportional to the absolute temperature \[(={{\,}^{o}}C+273)\] at constant volume.” Thus, \[P\propto T\] at constant volume and mass or \[P=KT=K(t{{(}^{o}}C)+273.15)\]          (where K is constant) \[K=\frac{P}{T}\] or \[\frac{{{P}_{1}}}{{{T}_{1}}}=\frac{{{P}_{2}}}{{{T}_{2}}}=K\] (For two or more gases) (3) If \[t={{0}^{o}}C\], then \[P={{P}_{0}}\] Hence, \[{{P}_{0}}=K\times 273.15\] \[\therefore \]   \[K=\frac{{{P}_{0}}}{273.15}\]   \[P=\frac{{{P}_{0}}}{273.15}[t+273.15]={{P}_{0}}\left[ 1+\frac{t}{273.15} \right]={{P}_{0}}[1+\alpha t]\] where \[{{\alpha }_{P}}\] is the pressure coefficient, \[{{\alpha }_{P}}=\frac{P-{{P}_{0}}}{t{{P}_{0}}}=\frac{1}{273.15}=3.661\times {{10}^{-3}}{{\,}^{o}}{{C}^{-1}}\] Thus, for every \[{{1}^{o}}\] change in temperature, the pressure of a gas changes by \[\frac{1}{273.15}\left( \approx \frac{1}{273} \right)\] of the pressure at \[{{0}^{o}}C\]. (4) This law fails at low temperatures, because the volume of the gas molecules be come significant. (5) Graphical representation of Gay-Lussac's law : A graph between P more...

(1) French chemist, Jacques Charles first studied variation of volume with temperature, in 1787. (2) It states that, “The volume of a given mass of a gas is directly proportional to the absolute temperature \[(={{\,}^{o}}C+273)\] at constant pressure”. Thus, \[V\propto T\] at constant pressure and mass or \[V=KT=K(t({{\,}^{o}}C)+273.15)\] ,   (where k is constant),               \[K=\frac{V}{T}\] or \[\frac{{{V}_{1}}}{{{T}_{1}}}=\frac{{{V}_{2}}}{{{T}_{2}}}=K\] (For two or more gases) (3) If \[t={{0}^{o}}C\], then \[V={{V}_{0}}\] hence,    \[{{V}_{0}}=K\times 273.15\] \ \[K=\frac{{{V}_{0}}}{273.15}\]                   \[V=\frac{{{V}_{0}}}{273.15}[t+273.15]={{V}_{0}}\left[ 1+\frac{t}{273.15} \right]={{V}_{0}}[1+{{\alpha }_{v}}t]\] where \[{{\alpha }_{v}}\] is the volume coefficient, \[{{\alpha }_{v}}=\frac{V-{{V}_{0}}}{t{{V}_{0}}}=\frac{1}{273.15}=3.661\times {{10}^{-3}}{{\,}^{o}}{{C}^{-1}}\] Thus, for every \[{{1}^{o}}\] change in temperature, the volume of a gas changes by \[\frac{1}{273.15}\left( \approx \frac{1}{273} \right)\] of the volume at \[{{0}^{o}}C\]. (4) Graphical representation of Charle's law : Graph between V and T at constant pressure is called isobar or isoplestics and is always a straight line. A plot of V versus \[t({{\,}^{o}}C)\] at constant pressure is a straight line cutting the temperature more...

(1) In 1662, Robert Boyle discovered the first of several relationships among gas variables (P, T, V).            (2) It states that, "For a fixed amount of a gas at constant temperature, the gas volume is inversely proportional to the gas pressure."                 Thus, \[P\propto 1/V\] at constant temperature and mass                 or \[P=K/V\] (where K is constant)                 or\[PV=K\] or \[{{P}_{1}}{{V}_{1}}={{P}_{2}}{{V}_{2}}=K\] (For two or more gases)            (3) Graphical representation of Boyle's law : Graph between P and V at constant temperature is called isotherm and is an equilateral (or rectangular) hyperbola. By plotting P versus \[1/V\], this hyperbola can be converted to a straight line. Other types of isotherms are also shown below,         more...

(1) The characteristics of gases are described fully in terms of four parameters or measurable properties : (i) The volume, V, of the gas. (ii) Its pressure, P (iii) Its temperature, T (iv) The amount of the gas (i.e., mass or number of moles). (2) Volume : (i) Since gases occupy the entire space available to them, the measurement of volume of a gas only requires a measurement of the container confining the gas. (ii) Volume is expressed in litres (L), millilitres (mL) or cubic centimetres \[(c{{m}^{3}})\] or cubic metres \[({{m}^{3}})\]. (iii) \[1L=1000\,mL\]; \[1\,mL={{10}^{-3}}L\];  \[1\,L=1\,d{{m}^{3}}={{10}^{-3}}{{m}^{3}}\] \[1\,{{m}^{3}}={{10}^{3}}\,d{{m}^{3}}={{10}^{6}}c{{m}^{3}}={{10}^{6}}\,mL={{10}^{3}}\,L\] (3) Mass : (i) The mass of a gas can be determined by weighing the container in which the gas is enclosed and again weighing the container after removing the gas. The difference between the two weights gives the mass of the gas. (ii) The mass of the gas is related to the number more...