Ideal Gas and Real Gases

Transcription

1 Ideal Gas and Real Gases Lectures in Physical Chemistry 1 Tamás Turányi Institute of Chemistry, ELTE State roerties state roerty: determines the macroscoic state of a hysical system state roerties of single comonent gases: amount of matter, ressure, volume, temerature n,,, T amount of matter ressure denoted by n name of the unit: mole (denoted by mol ) 1 mol matter contains N A = 6, articles, Avogadro constant definition = F/A, (force F acting erendicularly on area A) SI unit ascal (denoted by: Pa): 1 Pa = 1 N m - 1 bar= 10 5 Pa; 1 atm=760 Hgmm=760 torr=10135 Pa 1

2 State roerties state roerties of single comonent gases: n,,, T volume denoted by, SI unit: m 3 volume of one mole matter m molar volume temerature characterizes the thermal state of a body many features of a matter deend on their thermal state: e.g. volume of a liquid, colour of a metal 3 Temerature scales 1: Fahrenheit Fahrenheit scale (1709): 0 F (-17,77 C) the coldest temerature measured in the winter of F (37,77 C) temerature measured in the rectum of Fahrenheit s cow between these temeratures the scale is linear (measured by an alcohol thermometer) Daniel Gabriel Fahrenheit ( ) hysicists, instrument maker Problem: Fahrenheit ersonally had to make coies from his original thermometer lower and uer reference temerature arbitrary lower and uer reference temerature not reroducible an original thermometer was needed for making further coies 4

3 Temerature scales : Celsius centigrade scale or Celsius scale (174; 1750): 0 C temerature of melting ice in 1 atm air 100 C temerature of boiling water in 1 atm air between these temeratures the scale is linear (measured by an alcohol thermometer) Anders Celsius ( ) Swedish astronomer Problem: if other liquids are used (e.g. Hg), then different middle temeratures are measured lower and uer reference temerature arbitrary lower and uer reference temerature reroducible anyone can make a new centigrade scale thermometer 5 Temerature scales 3: Kelvin Kelvin scale or absolut temerature scale (1848): Lord Kelvin born as William Thomson ( ) Scottish hysicist 0 K (-73,15 C) extraolated zero volume of an ideal gas 73,16 K (0,01 C) temerature of the trile oint of water between these temeratures the scale is linear (measured by a gas thermometer) Problem: ideal gas does not exist lower and uer reference temeratures hysically well based lower and uer reference temeratures reroducible this is the real ( thermodynamic ) temerature scale 6 3

4 Zeroth Law of Thermodynamics If substance A is in thermal equilibrium with substance B and substance B is in thermal equilibrium with substance C then substance A is in thermal equilibrium with substance C. Note: the condition is thermal equilibrium, not thermodynamic equilibrium! What does it mean: Using thermometer B, the temerature of body A, then the temerature of body C is measured. If the thermometer shows the same reading, then the temerature of bodies A and C are equal. 7 Equation of state of the ideal gas: ideal gas law = n R T or m = R T ressure (Pa) volume (m 3 ) n amount of matter (mol) T temerature (K) R gas constant R= J K -1 mol -1 Regnault constant Henri ictor Regnault ( ) at high temerature and not very high ressure French chemist the equation of state of the ideal gas is a good aroximation. DEF: ideal gas or erfect gas: imagined gas that obeys exactly the erfect gas equation of state. 8 4

5 7 names on the Eiffel tower htt://en.wikiedia.org/wiki/list_of_the_7_names_on_the_eiffel_tower 9 Dalton s Law DEF For mixtures of gases, artial ressure of a comonent gas is the ressure exerted by this gas occuying the same volume alone. Dalton s Law: the ressure of a mixture of erfect gasses is equal to the sum of the artial ressures. = ( n + n + K+ n )RT 1 K n RT n RT n RT 1 K = + + K+ = K+ K n j x = n + n + j / RT = / RT j = 1 KnK j mole fraction n j of comonent j is the ratio of the corresonding artial ressure and of the total ressure. John Dalton ( ) 10 English chemist 5

6 Real gases DEF Imerfection of real gases can be characterized by the comression factor Z Z = m / RT 1,30 Z = m/rt 1,5 1,0 1,15 1,10 1,05 1,00 0,95 e d c b a 0, /bar comression factor vs. ressure diagram of nitrogen gas the significant effects are above 10 bar! f a: 33K (-40 C) b: 55 K (-18 C) c: 73 K ( 0 C) d: 37, K (54,05 C) e: 478 K (05 C) 11 Comression diagram DEF Comression diagram: Z curve 1,30 1,5 1,15 lease note: 1,10 - at (almost) zero ressure Z = 1 1,05 1,00 - for an ideal gas Z = 1 always 0,95 - real gas, high ressure: high Z 0,90 - at the Boyle temerature: Z starts horizontally - below the Boyle temerature: Z starts below 1 - above the Boyle temerature: Z is always above 1 Z = m/rt 1,0 e d c b a /bar f DEF: Boyle temerature: Z() starts horizontally at this temerature significance: at the Boyle temerature the real gases behave (almost) like the ideal gases if the ressure is not very high (e.g. < 30 bar) Boyle temerature for N : 54,05 C ( air behaves like an ideal gas at 98K) shae of the Z() curve: curvature downwards: attracting forces between the molecules going u: reelling forces / own volume of the molecules 1 6

7 Equations of state of real gases T virial equation of state Z = m / RT = 1+ B + C + K lease note: using the virial equation of state, the Z() curve is aroximated with a olynomial the constant term is 1, because if =0 then Z=1 olynomial of any order can be used any accuracy can be achieved B, C... temerature deendent emirical constants the favourite of chemical engineers due to its high accuracy Robert Boyle ( ) English chemist 13 Equations of state of real gases van der Waals equation of state n a + = ( nb) nrt the idea of van der Waals: let us take the equation of state of ideal gases: = n R T Johannes Diderik van der Waals ( ) Dutch hysicist ressure is corrected with a term that takes into account the attractive forces between the molecules. This term includes emirical constant a. (the volume of the box) is corrected by the own volume of the molecules. This volume is b for 1 mole, nb for n moles of molecules a and b are emirical constants and do not deend on temerature This equation of state is simle, but not very accurate (say, error is below 1%). 7

8 Isotherms of ideal gases DEF isotherms of gases: () curve at constant temerature (axis x: volume, axis y: ressure) lower temerature: the isotherm is getting closer to the axes, but keeing the hyerbolic shae 15 (since = constant always) Isotherms of real gases c C T T c T 1 c T 3 T 4 high temerature: nearly hyerbolic (nearly ideal gas) lower temerature: distorted hyerbolic function critical isotherm: a oint having horizontal tangent aears (critical oint) critical temerature: temerature of the critical isotherm critical ressure: ressure belonging to the critical oint critical molar volume: molar volume belonging to of the critical oint significance of the critical temerature: if the temerature is higher, the gas cannot be liquefied by comression 16 8

9 Isotherms of real gases measured isotherms of CO critical temerature: K (31,1 C) critical ressure: 7.38 MPa (73,8 bar) above the critical temerature: below the critical temerature: gas vaour (liquefaction via comression) grey area: vaour and liquid are in equilibrium at the vaour ressure left of the gray area and below critical temerature: liquid 17 THE END of toic ideal gas and real gases 18 9