Downloaded from www.studiestoday.com Important Formulas of Physical Chemistry THE SOLID STATE 1. Calculation of numer of particles / atoms / ions in a Unit Cell : 2. Type of Numer of Relationship Unit Cell particles per between edge Unit Cell length (a) and radius (r) of atom/ion Simple cubic 1 a = 2r 4 Body centred cubic 2 a = r 3 Face centred cubic 4 a = 2 2 r 3. Density of unit cell (d) Z ×M d= a3 × NA Where Z is rank of unit cell (no. of atoms per unit cell), m is molar mass/ atomic mass, ‘a’ is edge length of the cube, ‘a3’ is volume of cubic unit cell and NA is Avogatro number. d × NA 4 3 4. Packing efficiency = × π r × 100 M 3 Here ‘M’ is molar mass ‘r’ is radius of atom, ‘d’ is density and NA is Avogaotro’s number (6.022 1023 mol–1). Rank of unit cell can be computed by packing efficiency value Type of Packing Rank of Unit Cell efficiency Unit Cell SC 52.4% 1 BCC 68.% 2 FCC 74% 4 5 XII – Chemistry Downloaded from www.studiestoday.com 6. Raoults law for a solution of non-volatile solute and volatile solvent : pA ° – pA n WB × MA = i xB i B = i (for dilute solution) pA ° NA MB × WA pA ° – pA Where xB is mole fraction of solute. Raoult’s law for a solution of volatile solute in volatile solvent : pA = pA° xA pB = p B° x B Where pA and pB are partial vapour pressures of component ‘A’ and component ‘B’ in solution. and xB = nA + nB nA +nB xA + xB = 1 Moles of solute 2. Moality (m) = Mass of solvent in kilograms 4. Parts per million (ppm) Number of parts of the component = × 10 6 Total number of parts of all components of the solution 5. pA° and pB° are vapour pressures of pure components ‘A’ and ‘B’ respectively. i is van’t Hoff factor and is pA ° relative lowering of vapour pressure. Mole fraction (x) if the number of moles of A and B are nA and nB respectrively.com . 6 XII – Chemistry Downloaded from www.studiestoday. the mole fraction of A and B will be x nB xA = . Molarity (M) = Volume of solution in litres Moles of solute 3. Downloaded from www.studiestoday.com Solution 1. com . Elevation in boiling point (Tb) Tb = i. Van't Hoff factor (i) Observed colligative property i= Theoretically calculated colligative property Normal molar mass i= Abnormal molar mass 7 XII – Chemistry Downloaded from www. Osmotic pressure () of a solution V = inRT or = i CRT where = osmotic pressure in bar or atm V = volume in litres i = Van't Hoff factor c = molar concentration in moles per litres n = number of moles T = Temperature on Kelvin Scale R = 0.083 L bar mol–1 K–1 R = 0. 9.studiestoday. Downloaded from www.studiestoday.0821 L atm mol–1 K–1 10.Kb m where T b = T b – T b° Kb = molal boiling point elevation constant m = molality of solution.Kf m where T f = T f° – T f Kf = molal depression constant m = molality of solution.com 7. Depression in freezing point (Tf ) Tf = i. 8. studiestoday.studiestoday.p. Relationship between relative lowering in vapour prescure and elevation in b. its limiting molar conductivity is given by m = + + – °– Here ° and °– are the limiting molar conductivities of cation and anion respectively and + and – are the number of cations and anions furnished by one formula unit. Kohlrausch’s law (a) In general if an electrolyte on dissociation gives + cations and – anions then.com . l/A = cell constant (G*) and is resistivity. 8 XII – Chemistry Downloaded from www. P 2. i is van't Hoff factor. Conductivity (k) 1 1 l K= = × = G × G* P R A 1 Where R is resistance. k is conductivity and C is molar concentration. pA° is vapour pressure of pure solvent.. Downloaded from www. Relationship between k and Λ m 1000 × k Λm = c Where Λ m is molar conductance. Kb is molal elevation constant and MA is molar mass of solvent Electrochemistry 1. ∆p ∆Tb =i MA × 1000 pA ° Kb Here p is lowering in vapour pressure. Tb is elevation in boiling point.com i > 1 For dissociation of molecules i < 1 For association of molecules i = 1 For ideal solution 11. G = – 2. G = – nF Ecell Where G = standard Gibbs energy change and nF is the amount of charge passed. Nernst Equation for electrode reaction : Mn+ + ne– M.303 RT log Kc 9 XII – Chemistry Downloaded from www. 2.com .303 RT 1 E = Eθ – log nF [Mn+ ] – ne For Cell potential of electrochemical reaction aA : bB → cC + dD 2.059v Eθ cell = log KC n 5. (c) Dissociation constant (K. Downloaded from www.303RT = Eθcell – Ecell log [QC ] nF 4.com (b) Degree of dissociation () is given by : c Λ α = m° Λm Here °m is molar conductivity at the concentration C and °m is limiting molar conductivity of the electrolyte. Relationship between E° cell and equilibrium constant (Kc) 2.303RT E θ cell = log K C nF 0.studiestoday.) of weak electrolyte 2 Λ cm C Λ om Cα 2 K= = 1–α Λm 1– Λ o m 3.studiestoday. studiestoday. R is universal gas contant and T is absolute temperature.com Chemical Kinetics 1.303 R T T 2 a 2 1 (b) 1 1 2 Where k1 is rate constant at temperature T1 and k2 is rate constant at temperature T 2.com . [R]° is initial molar concentration and [R] is final concentration at time ‘t’. k E T –T log k = 2. Ea is the energy of activation. –Ea/ RT gives the fraction of collisions having energy equal to or greater than Ea. (b) Half life period ( t 12 ) for first order reaction : 0. Integrated rate law equation for first order reaction 2. Integrated rate law equation for zero order reaction [R] – [R] (a) k = t Where k is rate constant and [R]0 is initial molar concentration. 2 2. Anhenius epuation (a) k = A –Ea/RT e Where ‘A’ is frequency factor. Downloaded from www.693 t1 = 2 k 3.studiestoday.303 log [R] (a) k = t [R ] Where k is rate constant. t1 = [R] (b) 2 2k t1 is half life period of zero order reaction. 10 XII – Chemistry Downloaded from www.
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