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Inovace bakalářského studijního oboru Aplikovaná chemie Reg. č.: CZ.1.07/2.2.00/15.0247 Lecture vocabulary: State stav Equation rovnice Pressure tlak Volume objem Temperature teplota Quantity veličina Unit jednotka Gas plyn Value hodnota Mass hmota, hmotnost Current proud (adj. současný) Amount množství Substance látka Intensity intenzita Base, basic základní Derived odvozený Extensive extenzivní combine kombinovat common běžný formulation formulace, tvar deviation odchylka finite konečný behaviour chování interactions interakce compressibility stlačitelnost correction oprava, korekce cohesion koheze, přilnavost, soudržnost dew rosa superheated liquid přehřátá kapalina impossible nemožný vapor pára critical kritický solve řešit set of equations soustava rovnic following následující expression výraz obtain získat by application aplikací, použitím Specific intenzivní specifický (tj. vztažený na jednotku hmotnosti) Composed of složený z trick trik, finta Set soubor so-called takzvané Random náhodný reduced quantities redukované veličiny Move pohybovat se dissappear zmizet Interact interagovat common společný, jednotný Point bod corresponding state korespondující stav Particle částice Obey řídit se Law zákon State stav Amenable podléhající, přístupný Increase, decrease zvýšení, snížení Bubble bublina Rise stouat Intensive Surface (opposite = bulk) povrch (vnitřek) occupy zabírat, zaujímat, okupovat proportional úměrný directly přímo inversely nepřímo (též indirectly) rate rychlost container nádoba square root odmocnina density hustota molecular weight molekulární hmotnost sum součet, suma mixture směs individual jednotlivý component složka given daný, určitý liquid kapalina equilibrium rovnováha Introduction to Physical Chemistry Lecture 1 • Quantities, units and symbols in Physical Chemistry • Ideal and real gas - gas laws • Equation of state of the ideal gas • Equations of state of real gases Quantities, units and symbols in Physical Chemistry physical quantity = numerical value x unit Seven base quantities, others are derived quantities Extensive / intensive / specific / molar quantities Ideal gas • a theoretical gas composed of a set of randomly-moving, noninteracting point particles Properties: •randomly-moving •non-interacting •point particles •may be mono- di- atomic etc. Obeys: •the ideal gas laws, •a simplified equation of state, •is amenable to analysis under statistical mechanics Ideal gas laws Increase in size of bubbles as they rise to the surface Other ideal gas laws Avogadro's law: the volume occupied by an ideal gas is proportional to the amount of moles (or molecules) present in the container. Graham's law: the rate at which gas molecules diffuse is inversely proportional to the square root of its density. Combined with Avogadro's law (i.e. since equal volumes have equal number of molecules) this is the same as being inversely proportional to the root of the molecular weight. Dalton's law of partial pressures: the pressure of a mixture of gases simply is the sum of the partial pressures of the individual components. Henry's law: at a constant temperature, the amount of a given gas dissolved in a given type and volume of liquid is directly proportional to the partial pressure of that gas in equilibrium with that liquid. Ideal gas laws combine into the: Equation of state pVm R(Tcelsius 273.15) 1834 Émile Clapeyron originally 267 For: a given amount of gas (1 mole), standard pressure (101.325 kPa) and temperature (0°C) the volume of gas is: 22.42x10-3m3 p1V1 p2V2 101.3 10 22.42 10 T1 T2 273.15 3 The common formulations are: 3 Pa m3 J 8.314 R or K mol K mol pV nRT and p RT M Real gas Deviations from ideal behaviour are caused by: •finite volume of gas molecules •interactions between molecules •can be expressed by compressibility factor Van der Waal’s equation a p 2 (Vm b) RT Vm n2a p 2 (V nb) nRT V Correction for finite volume of molecules Correction for cohesion pressure Van der Waals equation of state to the left of point F normal liquid to the right of point G normal gas Light blue curves Red curve Dark blue curves Green sections Point F Point G Point K Line FG Section FA Section F′A Section AC Section CG supercritical isotherms critical isotherm isotherms below the critical temperature metastable states boiling point dew point critical point equilibrium of liquid and gaseous phases superheated liquid stretched liquid (p<0) analytic continuation of isotherm, physically impossible supercooled vapor Critical parameters Van der Waals equation and critical parameters The critical point is an inflection on the critical isotherm. pk a2 Vm ,k (Vm ,k b) RTk p 0, V Tk 2 p 2 0 V Tk By solving the set of these three equations following expressions are obtained: pk a 27b 2 ; Vm,k 3b; Tk 8a 27 Rb By application of an interesting mathematical trick, i.e. by substitution of the so-called reduced quantities defined as: pred p pk ; Vm, red Vm Vm, k ; Tred T Tk into vW equation, its reduced form is obtained: 3 pred 2 Vred 3Vred 1 8Tred Note that the parameters a and b disappeared, the equation is common for all gasses. This is the manifestation of the Theorem of corresponding states: Equations of state of real gases Redlich–Kwong model RT p(Vm b) a 1 (Vm b) Vm (Vm b)T 2 The Virial equation derives from a perturbative treatment of statistical mechanics B T C T D T PVm RT 1 2 3 V V V m m m There are numerous other real gas state equations (Berthelot and modified Berthelot, Dieterici, Clausius, Peng–Robinson, Wohl, Beattie–Bridgeman, Benedict–Webb–Rubin)