States of Matter (JEE ADV.) Notes PDF

STATES OF MATTERts (JEE ADV. ) Introduction Mater exists in hree physital states 13Solid C3)Ghas 10 The phy sicql state oF substances depend on: stote CJ Interparicle...

STATES OF MATTERts (JEE ADV. ) Introduction Mater exists in hree physital states 13Solid C3)Ghas 10 The phy sicql state oF substances depend on: stote CJ Interparicle torces of attraction increases’ Solid 2J hermal energy inCreases’ G9seous state When inter-parile forces of attraction increases and thermal decreaseS andsUbstance 15 energy decreases, intereparticlel distance will exist inSolid state. When inter-paricle torces of attrachon decreases and thermal energy íncreases, interiparticle distance increases and substan ce will exist in qaseoUs state. Hgh temperature ond lou pressurer are favourable conditions for qaseOUS State. Intermoleculqr forces of Attraction ethootit eg These are weak forces ot atraction withaut any strong bond They are electrOstatic in nature and are called as yan der waal's forces' TYPES OF VANDER DER WAAL'S FoRCES nob n03 Dipole -Dipole interaction 2J Dipole -induced dipole ioterachion t ty 6J Tnstontaneous dipale interachon (London Forees IDispersion öre)  Date LIJDipole - pipole in teraction T8 hese forceseist in pol ar molecujes Qnd are alsó CQlled as kusom forces 5 Example3 æ) HCL H- CL H- (L >dipole - dipole interachon bioL n Stah on ary polar molewles (Solid): 10 SPbloDipole-Dipole Inter actión o t sroan9ta L1 C23 rotating polar moleules (Iiquid) : e Dipole-Dipole tnteraction Dipole - Induced Dipole Interaction 2o These interactions exist behueen polar and non polar moleules Example: Ci) ---Neoo 4 0 29)X oo9Bom7 dipole- induced dipole interachon Dipo le -Induced Dipole Interacion p9 C33 London forces or Disperston forces 302321I These exist In non -polar. moleculesht it Distribotion of electrons is not Symmetricalati all times in moleules,  Dute: 0r some insBant. more electrons are gatheredon one side oF the moleule and produce instantaneous polarits. uniform dist1bution binstantaneous interaction of elechrons Examples tiD Caraphite layers (iv) T2 40 nstan taneous (nteraction i JDENTIEYIN G THE INtERA CTLONS TMU 15 a p 3 0 2 3 1 0 Ti dO3 NacCand NaCc Ng cLT Nat c lon - lon jonion interachon Interacion 2] Na CU and H20 Ng lon - Dipoleio l Interacion F r O-H8+ HSt C3] NOz andT2 will have' ion - induced dipole interacthion H-cu'----H dipole -dipole interaction  Dote : Q.Exercise 6. A[6J ()iton cion> ibn +dipole > dipole - dipole tJC2)-Londoh disp ersion and dipole -dpoe 5 Pressure ressure is the amount of force applied to Qcertain aY ea 10 Unit - NÍm Pressure =, Force yo Area k /msO Pasca (Pa) SI UNIT OF PRESSURE= katms Pa 15 CoS ONT DF PRESSURE = qn /Um s 1Dynelm CD Barytte (Ba) =0.1 Pa bar9.8692 x 0 atm = 5x\0 20 torr (onvert the following units NOTE -5 () 4 bar = 10 Pa & torr = mm of Ha () 1 atm =iI325 Pa A atm = 60 mm of ta (w) 4 atm 1.0|325 bari! 25 (ív) 4 Qtm = 60 torr IMEASURIN GPRESS URE : 760 Mm =16 cm qtn ato fisofopic) 30 BAROMETER Neruny(hg)  Date: We know that P=F P=Ax hx Px9 P=h9 where h= height, R= density9grauty MANOMETER Pgas > Patm G,AS Pgas Hg Cmerury) Yqas GaseouS Laws L Bole'sLawrelatión be hoeenPand V, at constant n and T [23 Charle's Law ’relaion bekween yand I, at constant n and P Lus sac's Lauo ’relahon behween Tand P at constant n and V [u] Avogadro's Law>relaion behween N.and n, at tonstant v and n Boyle's Charlels Gay- Lussao's Avogadro's Law Law V n.  Dote Boyle's Law The volume of a qiven mass of a qas is inyersely proportional to pressure pr at constant temperature P 10 It means that. gases are compressible. On incre asing pressure, their volume decreases and qases occupy less volume Than eorlier As interparticle distance decreases , density inrease PV = K P 151 Initial state i Final Stqte : from eaations ()and (e Pv =k->) Pi: Pt V+dt Vi K constan t As 9Va k, app lying og 0 2s 9yo) ChRAPHS of BoYLE'S LAW : P Vs V 30 P P V  Date CuJ log P vs 0g V (oJ PV vs P Jog Px (0gv t k 1 py log P P log V Charle's Law. The yolome of a given mass of gas is directly proportiona 10| its absolute temperature at constant pressure,? a V=k,T 15 Inítia State i Final sate: from eaahons (0 and (2) V, k - ’ ) T2 V2 T2 T 20 log v - loq T 3 k ’\09 v= loq T t k ) yv! Experimentally, it is observed that for each deqree change ot temperature, the yolume of qas changes by a fraction ot 273 of its vol Ume at 0'C. 273 > V Vot No XT 273 L+T 273 VT |T 273 t Tet Vo 273 273  Dato: GRAPHS OF CHARLE'S LAW CJ Vvs T (kelvin) 2] v ys T (celciuS) T (K)-+ T() 13), log V vS Log TG Cu]VT VS T 4veslope log V3lxlog T + k logv T 15 log T Giay- Lussac's Law The law States that at constant volomethe pressUre ot 20 a Fixed mass of a gas is directiy proporhiongl to the kelvin tempera t o r e Ypi PT| 25 P T lnitiql Statei Fingt State Lfrom eajuations ) iand ) T Ly (2) P2 a As P k applying log Jog P- Jog T = k >hog P 10g T tk  Date : (uRAPHS OF CAY LUSSAc's LAW: P vs T aI C2] leg P ys log T. Jog P logTtk og: P yzmntc) lo9 T Cu) P vs (T T o [4J Avog adro's Lawot 25 TE We add more amoun oF qas at constant temperature and pressore in aoballoon (ontaining 'qcertain MasS of gas, then volume of qas wíll incra Se. V=n k ’  Date: Initial state : Einal Stqte: From eauahons (0 and (2) =k n2 n2 V2 n2 ts Tuis Is the base of Avogad ro's tauw which states that i Eyual volumes of all qases at same temp erature und pressore Contain eayual humber of molewles ldeal Gioas Eqjuation. 10 On combining Boyle's lauw, Charle's law and Avogadro's_ law, we 9et an eauation Known as the ldeal gas, eayuation. we get: Boyie's Law v I ’V nT P nRT where Charie's Law’ vdT R is the úniversal Avogadro's Law ’ V«n 94s constant NOTe THE FOLLOWINGG:1 hT 20 at STPPF1 atm T60mm ot H 760 torr =.0|33 bar UNI TSoF R atm X litre EL:atm. k mol moi x k when P=latm, V= 22, 4L, n =lmolT=0c = 243K 28 then R= 0.o821 L. atm. k mo fP li0133ban,M0 thenR=0.0331L bar. mol =8.3)4 JkI' molo siN -3 kJ. kmol 30 8.314X 0 erqi k mol 2 Cal. k mol NOTE : 1 L bar = 10|.32 3|  oTHER FORMS OF IDEAL CAS EQUATION : PV nRT is the ideal gas eauation,. as 9tven mass molar mass Pv= w RT PM = WRT M P= dRT ’ PM E JRT O’d= PM M TIRT 10 (s) Combined Gas Law This law is a com bination of Boyle's law and Charle's Lau. Boyle's LQw > V L P Charle's Law Va T PV K= Constant Inihal state : Final State : Fom payvahons (D and C2) 20 T. GhßAPHS C23 P 25 P P P t -273°c oc R>P Pg>Py.T) T2) T; >Ty >V2>Vg P, < P2 P2 >P3 - T (pnstqnt M T STEP 2 + Q s o S M A. PVRT F1o PV w RT M PM =dRT Cons tont (2) Dalton's Law of Partial Pressure Ihe totapressore exerted by a mixture of non -reàcting 20 qases is eqyual to the sum Dt parhial pressure of each 99s present in the mixture non -reating qacesAB and C at constant t and v According to ideal gas eQuation : PV nRT For Ghas A: For has Bi For nasC: Substitutng these values in eqyuation C0 :  > P r ART V V PrCna t notne) RT (2) Dividing Pa by eyuahion () : DA Pr na tne tnc (V) Pe = g. PT PA 10 Pressure of dry gas = Pmoist g4s -Pwaervopovr = Pmoist qas Aayveous tension no water invol vement Exercise 5:| PL E V2)’ 2 0 0 ’ Pe 5 2. 5 atm P2 Vi P2 (3) =2.5 atm9 91 [23 Na pour density E Moleolar weignt ozmolewlar weight 2 2 L4o moleular werqnt (3) =5 [3J No. of moles of Co uy.0:lmoles hiven volumeoe 0be iven vol ume o.X22.4 22.4 2.2y C2) 2.24L ’ 5.3 X= P2 ’ P2 5.3 XtO |0YhooFS3 atm  Date : (3)= 53 atm Ha no9 2 --Co2 >n9E22=0.S m s He >n 9 = 2 m 32 m 4 )He T L8)) =A is alse but R is true 10 Kínehc Theoryi o£ Ghases POSTULATES & he q9seous moleules are conSidered to bepointm9sses L The volume oF a molecule is neqliible as compared to totel volume of the qaS C3] The mslecules neither attract nor repel each other 4JThe collisions qYe perfectty elastic,i.e there ís no loss of enerqy duing the mole cular collísions 15 The average kinetic energy oE molecules is directly proporiong to the absolute temperature of the qas.lla B] The effect of qravity on molecular motjon is heqigqible. KineticGhas Eajva thon 25 Py = mnurms where m’ mass of lmolewle of gas n’ nUmber ofmolecules of Urms> root mean sauare speed of molewev R 30 Urms =/u2 +u tu +un n E n Avogadro's number =6.022 x?5  Dale m XNe molar mass (M) mx NA X Drms (l mole) 3 PV=2 X X m x Ng XUrms 3 2 k.e. =3 PV but PV n 2 T ’ PV = T x Na 2 K.E. = 3 XRTY I 2 Ne Molecular Speed in Ghases CU R00T Me AN SOUARE SPEED IE there are n particles having'speed u ne particles'having Speed U2 and so. othen Urms= n tn2tn3t Urms 3PN 3P M M (23 AvERAGE SPEED: ’Uay n t h t n3 + M. RATIO Ump:V av:Urms C3 MoST PROBAGLE SPEED! Ump = 22T 22T M M M M = 1:. (28 224. Urms > Uqvg > Ump  Date Maxwell Boltzman Dístribution Corve df Fracton molecules Uavg. Urms On increasing temperature pealk becames broad and shifts towards the 10 Molecular Speed ’ Fbr mati o Motelutes ctzt1g) qt 300k N2(sg) 2920r C2 mass Ne mass 15 Molecular Speed’ Grahamn's Law ot Difusion: Acording to Ghraham'si law,At tonstant pressure Qnd temperature, the rate of difPusion or effusion of gas a is inversely proportional to the saju are root of its vapour or molecular mass density 25 and r2 I 30 r Vix t2 m2 ti V2 V m PvnTv  Dgie : n mi Eyerise 5.2 2103l2 tit ACA 0 3 Is proportional to temperature |3RTH2 UH2 MH2 Also, H2 =VtUN2 3RTN2. UN MN2 (2) = TH2 > Tu2iov yiotnt rv Behav iour of Real Ghases Agas that obeys the ideal qas eqyuahon at all t mperature and presure is called as ideal gas. But prachcalty deal. So, the non-ideai qases or real qases are actualls qases which Obey theiaeal qas eayuation at loo pre sSure and hgh. 20 temperature According to ideal q9s eajuation Pv =nRT0 tot) PV=2’ (ompressibil1ty nRT factor A plot of z VS P at tonstant tmperature shows 'deviahion 2s fYor ideaV behaviour. at constant CO2 temperature 2= PV Te qas be haves idealty, ideat as PV nRT  Date : CAUSES of DEVIATION: Actually. g95 Moleules do oCUpy some volume and it_cannot be neglected. OTheir must be either attractive or repulsive fores beween 5 gaseous molecules C3) So byCorrecting these too postulates oF kinetic theory of qises We can qet a new eayua 1on Pv e nRT ’ideal gas eqyuation PV 2 t n= 1 Mole 2= Pv 10 nRT 2 Vm (real) where Vm molar volume < T E Vm Cideal) CiE changes due to attraction between molecules) Prssure Correction attraction 15 rep 3204a ldeai Ghas Real Gas Pi =Pt P! where, y22910 al O 20 p>observed pressue of he qas Pi> ideal pressUre of the q9s altd P> pressure correction (loss in P dye to intermolecular form of qtrachon) where a is vander-waat's 25 uConstant9bi Pi= p+ Units of a =atm.L mol Volume Corretíon 3 ldeal qas assumes molecoles to be point masses. but at high pressure, yolume of qas mole coles cannot be neglected If ViS the volume of Container  Date :. then nb ’volume whch is incompressi ble Qs molewles are penerable spheresgAu So, (orrected yolume wilL be as foliows3ot |Veorrec ted =Vnb where 'ois yander-waal's constant and. sLnis the nom ber of moles. (orrected ideal qas eajuation which is called as yander -waal's 20Vqnder- waal'sP t an (Vnb)=nRT. Eyuation vicinity hel Nolume of A molecule =Volume of sphere =4TY 3 4n2r) Cinduding impenetrable sphere) 7 for only moleculeilat_ iatPLL 2 Exercise 5.2 A.C03) m Since No is injected with a NO 2 o0 9redter press ure than O,it 24tm +latn wil cover more distance in the e tube. Pressure 2:1 Oxygen will over One - third of the -o.33.. (2) = 0., 33 m. 2920rd0 noitetiopi! Compressibility Factor (2) :293T344909 34FS)  Date [CASE 4J2=1’ ldeal Q9s eyvstion is folt owed for all temperature and pressure. LCASE 23|2~| ’At At low pressure, real gas behaves Idealy due to very few intermoleular at ractive forces Cse 2 At hiqher pressure particles of qaseS will Come Lcleser Qnd there will be strong tnterpartkle attractive forses (tue deviahon) Gnd repuls1ve forc eg will become acthve we wit! qet volume more than ex pected. CRSE 9J2 ) T4 Vt foAt Tideal 25 below,Te -ve deviaion (2 esily gas OSurfa ce area + 27Rb wil be liquihedo molar mass Nander-waal's forces ‘ C2J Cniticat Pressure IH is he minimu mpressUre thatis 5 resyured to liqyuifya gas at crctical tenm perature Pe = 27b2 C33Criticqt yolunme - Volume occupied by gs at le ane 10 VE3b COMPRE SSIB1LTY FACToR AT (RITICAL CONDITION neT a b 27 Rb 27b Andrew's Iso thfrm curve uidLi 48°c 35.5° C 2°c10 9 tsotherm eurve Ghas rU229 0f Co2 M 21.5¬ shouing cratiareqsn )'00Nolume Liajvid State EVAPORATIÛN Itis a protess ot change o liauid into Vopoyr state at any given temperature.  Date: evap oraton, cooling occors ds qverage Kineh energy ok remaining malerules decrease. The rafe of evaporton depends on intermolecolarforces Slower will: be the rate of evaporathon. 5 Rate ofe Evaporation d Surface Area Te mperature Vapour Pressure 1E is the pressure exerted by vapour on its surface at eauilibrium. Rate of Condens ation Rate of Evaporation dynamic eqyuitibr iurm 15 (zlis0gH5 CMs0H H20 4otm 3416C 8.5°c 20 Boiling Pont The temperature at whiCh vapour pressure becomes equaL to 25 atmas pheric pressure. for H0 Standard boiling point at 4 bar = 99.6'C Normai boiling point at 4 atm = lo0°c Clausius (lopeyron log P2= AH Pi 2.3032  line any qradíent to Date anqles decreQses. cosíty viscosity nn right ’vis tlow of at area dy (oeficientt ce S=f Nm Surface the unit poise ln) surfa where, resist sion, neta the ’ to neta of on ten liauid F-n Nm Surface Tension Adv reciprocql Tne tore achng ok unit lenqth Surface o. Viscosityof Property = Fluidity Poise to is Due It 4 15 20 2