Real Gases Deviation from ideal gas Law Gas
![Real Gases Deviation from ideal gas Law: -Gas particles have volume - Attraction exists Real Gases Deviation from ideal gas Law: -Gas particles have volume - Attraction exists](https://slidetodoc.com/presentation_image_h2/5d73ae32e98c364cae718a9109146c6e/image-1.jpg)
![isotherm isotherm](https://slidetodoc.com/presentation_image_h2/5d73ae32e98c364cae718a9109146c6e/image-2.jpg)
![Van der Waal’s Equation Ideal gas law needs modification: - Let’s consider the molecular Van der Waal’s Equation Ideal gas law needs modification: - Let’s consider the molecular](https://slidetodoc.com/presentation_image_h2/5d73ae32e98c364cae718a9109146c6e/image-3.jpg)
![- Let’s consider the attraction forces between molecules: - Due to attraction: - velocity - Let’s consider the attraction forces between molecules: - Due to attraction: - velocity](https://slidetodoc.com/presentation_image_h2/5d73ae32e98c364cae718a9109146c6e/image-4.jpg)
![- How big is this drop in pressure? attraction force 1 f 2 f - How big is this drop in pressure? attraction force 1 f 2 f](https://slidetodoc.com/presentation_image_h2/5d73ae32e98c364cae718a9109146c6e/image-5.jpg)
![- How big is this drop in pressure? - How big is this drop in pressure?](https://slidetodoc.com/presentation_image_h2/5d73ae32e98c364cae718a9109146c6e/image-6.jpg)
![- How big is this drop in pressure? drop in pressure proportional to attraction - How big is this drop in pressure? drop in pressure proportional to attraction](https://slidetodoc.com/presentation_image_h2/5d73ae32e98c364cae718a9109146c6e/image-7.jpg)
![Vd. W Equation of state Vd. W Equation of state](https://slidetodoc.com/presentation_image_h2/5d73ae32e98c364cae718a9109146c6e/image-8.jpg)
![b: volume of 1 mole of gas molecules. a: represents strength of attraction. b: volume of 1 mole of gas molecules. a: represents strength of attraction.](https://slidetodoc.com/presentation_image_h2/5d73ae32e98c364cae718a9109146c6e/image-9.jpg)
![](https://slidetodoc.com/presentation_image_h2/5d73ae32e98c364cae718a9109146c6e/image-10.jpg)
![Maxwell construction a 1 = a 2 Maxwell construction a 1 = a 2](https://slidetodoc.com/presentation_image_h2/5d73ae32e98c364cae718a9109146c6e/image-11.jpg)
![Many other equations of state Mostly empirical Virial Equation to correct, develop in a Many other equations of state Mostly empirical Virial Equation to correct, develop in a](https://slidetodoc.com/presentation_image_h2/5d73ae32e98c364cae718a9109146c6e/image-12.jpg)
![Compression factor z describes deviation from ideal gas behavior. For ideal gas, z=1 Compression factor z describes deviation from ideal gas behavior. For ideal gas, z=1](https://slidetodoc.com/presentation_image_h2/5d73ae32e98c364cae718a9109146c6e/image-13.jpg)
![At a given temperature, z depends on the nature of gas Why? At a given temperature, z depends on the nature of gas Why?](https://slidetodoc.com/presentation_image_h2/5d73ae32e98c364cae718a9109146c6e/image-14.jpg)
![Let’s find for a Vd. W gas at p → 0 The slope of Let’s find for a Vd. W gas at p → 0 The slope of](https://slidetodoc.com/presentation_image_h2/5d73ae32e98c364cae718a9109146c6e/image-15.jpg)
![](https://slidetodoc.com/presentation_image_h2/5d73ae32e98c364cae718a9109146c6e/image-16.jpg)
![slope at p → 0 slope at p → 0](https://slidetodoc.com/presentation_image_h2/5d73ae32e98c364cae718a9109146c6e/image-17.jpg)
![>0 =0 <0 >0 =0 <0](https://slidetodoc.com/presentation_image_h2/5d73ae32e98c364cae718a9109146c6e/image-18.jpg)
![Size effect > attraction Size effect = attraction Size effect < attraction b: volume Size effect > attraction Size effect = attraction Size effect < attraction b: volume](https://slidetodoc.com/presentation_image_h2/5d73ae32e98c364cae718a9109146c6e/image-19.jpg)
![Explain the trend! Explain the trend!](https://slidetodoc.com/presentation_image_h2/5d73ae32e98c364cae718a9109146c6e/image-20.jpg)
![Critical Point Vm range in which L and G phases coexist shrink to a Critical Point Vm range in which L and G phases coexist shrink to a](https://slidetodoc.com/presentation_image_h2/5d73ae32e98c364cae718a9109146c6e/image-21.jpg)
![](https://slidetodoc.com/presentation_image_h2/5d73ae32e98c364cae718a9109146c6e/image-22.jpg)
![Experimental measurements of pc and Tc are more accurate than that of Vc, a Experimental measurements of pc and Tc are more accurate than that of Vc, a](https://slidetodoc.com/presentation_image_h2/5d73ae32e98c364cae718a9109146c6e/image-23.jpg)
![The law of corresponding states Is it possible to find an equation of state The law of corresponding states Is it possible to find an equation of state](https://slidetodoc.com/presentation_image_h2/5d73ae32e98c364cae718a9109146c6e/image-24.jpg)
![• Two gases at the same Tr and pr have the same Vr. • Two gases at the same Tr and pr have the same Vr.](https://slidetodoc.com/presentation_image_h2/5d73ae32e98c364cae718a9109146c6e/image-25.jpg)
![](https://slidetodoc.com/presentation_image_h2/5d73ae32e98c364cae718a9109146c6e/image-26.jpg)
![](https://slidetodoc.com/presentation_image_h2/5d73ae32e98c364cae718a9109146c6e/image-27.jpg)
- Slides: 27
![Real Gases Deviation from ideal gas Law Gas particles have volume Attraction exists Real Gases Deviation from ideal gas Law: -Gas particles have volume - Attraction exists](https://slidetodoc.com/presentation_image_h2/5d73ae32e98c364cae718a9109146c6e/image-1.jpg)
Real Gases Deviation from ideal gas Law: -Gas particles have volume - Attraction exists between gas particles (liquefication) Ideal gas law applies only at low gas density: high T, low p
![isotherm isotherm](https://slidetodoc.com/presentation_image_h2/5d73ae32e98c364cae718a9109146c6e/image-2.jpg)
isotherm
![Van der Waals Equation Ideal gas law needs modification Lets consider the molecular Van der Waal’s Equation Ideal gas law needs modification: - Let’s consider the molecular](https://slidetodoc.com/presentation_image_h2/5d73ae32e98c364cae718a9109146c6e/image-3.jpg)
Van der Waal’s Equation Ideal gas law needs modification: - Let’s consider the molecular volume: b: size of 1 mole of gas molecules For 1 mole of gas: Vm, total = Vm, space + b
![Lets consider the attraction forces between molecules Due to attraction velocity - Let’s consider the attraction forces between molecules: - Due to attraction: - velocity](https://slidetodoc.com/presentation_image_h2/5d73ae32e98c364cae718a9109146c6e/image-4.jpg)
- Let’s consider the attraction forces between molecules: - Due to attraction: - velocity decreased, - colliding less with wall, - pressure drops
![How big is this drop in pressure attraction force 1 f 2 f - How big is this drop in pressure? attraction force 1 f 2 f](https://slidetodoc.com/presentation_image_h2/5d73ae32e98c364cae718a9109146c6e/image-5.jpg)
- How big is this drop in pressure? attraction force 1 f 2 f 3 f
![How big is this drop in pressure - How big is this drop in pressure?](https://slidetodoc.com/presentation_image_h2/5d73ae32e98c364cae718a9109146c6e/image-6.jpg)
- How big is this drop in pressure?
![How big is this drop in pressure drop in pressure proportional to attraction - How big is this drop in pressure? drop in pressure proportional to attraction](https://slidetodoc.com/presentation_image_h2/5d73ae32e98c364cae718a9109146c6e/image-7.jpg)
- How big is this drop in pressure? drop in pressure proportional to attraction force drop in pressure indirectly proportional to square of Vm
![Vd W Equation of state Vd. W Equation of state](https://slidetodoc.com/presentation_image_h2/5d73ae32e98c364cae718a9109146c6e/image-8.jpg)
Vd. W Equation of state
![b volume of 1 mole of gas molecules a represents strength of attraction b: volume of 1 mole of gas molecules. a: represents strength of attraction.](https://slidetodoc.com/presentation_image_h2/5d73ae32e98c364cae718a9109146c6e/image-9.jpg)
b: volume of 1 mole of gas molecules. a: represents strength of attraction.
![](https://slidetodoc.com/presentation_image_h2/5d73ae32e98c364cae718a9109146c6e/image-10.jpg)
![Maxwell construction a 1 a 2 Maxwell construction a 1 = a 2](https://slidetodoc.com/presentation_image_h2/5d73ae32e98c364cae718a9109146c6e/image-11.jpg)
Maxwell construction a 1 = a 2
![Many other equations of state Mostly empirical Virial Equation to correct develop in a Many other equations of state Mostly empirical Virial Equation to correct, develop in a](https://slidetodoc.com/presentation_image_h2/5d73ae32e98c364cae718a9109146c6e/image-12.jpg)
Many other equations of state Mostly empirical Virial Equation to correct, develop in a series (additional correction terms: B, C, …: second, third, … virial coefficients: exp. determined
![Compression factor z describes deviation from ideal gas behavior For ideal gas z1 Compression factor z describes deviation from ideal gas behavior. For ideal gas, z=1](https://slidetodoc.com/presentation_image_h2/5d73ae32e98c364cae718a9109146c6e/image-13.jpg)
Compression factor z describes deviation from ideal gas behavior. For ideal gas, z=1
![At a given temperature z depends on the nature of gas Why At a given temperature, z depends on the nature of gas Why?](https://slidetodoc.com/presentation_image_h2/5d73ae32e98c364cae718a9109146c6e/image-14.jpg)
At a given temperature, z depends on the nature of gas Why?
![Lets find for a Vd W gas at p 0 The slope of Let’s find for a Vd. W gas at p → 0 The slope of](https://slidetodoc.com/presentation_image_h2/5d73ae32e98c364cae718a9109146c6e/image-15.jpg)
Let’s find for a Vd. W gas at p → 0 The slope of the curve z=f(p) in the previous diagram.
![](https://slidetodoc.com/presentation_image_h2/5d73ae32e98c364cae718a9109146c6e/image-16.jpg)
![slope at p 0 slope at p → 0](https://slidetodoc.com/presentation_image_h2/5d73ae32e98c364cae718a9109146c6e/image-17.jpg)
slope at p → 0
![0 0 0 >0 =0 <0](https://slidetodoc.com/presentation_image_h2/5d73ae32e98c364cae718a9109146c6e/image-18.jpg)
>0 =0 <0
![Size effect attraction Size effect attraction Size effect attraction b volume Size effect > attraction Size effect = attraction Size effect < attraction b: volume](https://slidetodoc.com/presentation_image_h2/5d73ae32e98c364cae718a9109146c6e/image-19.jpg)
Size effect > attraction Size effect = attraction Size effect < attraction b: volume of 1 mole of gas molecules. represents repulsive forces a: represents strength of attraction
![Explain the trend Explain the trend!](https://slidetodoc.com/presentation_image_h2/5d73ae32e98c364cae718a9109146c6e/image-20.jpg)
Explain the trend!
![Critical Point Vm range in which L and G phases coexist shrink to a Critical Point Vm range in which L and G phases coexist shrink to a](https://slidetodoc.com/presentation_image_h2/5d73ae32e98c364cae718a9109146c6e/image-21.jpg)
Critical Point Vm range in which L and G phases coexist shrink to a single point Above Tc, L and G phases can not be distinguished from each other: Density (L) = Density (G) No Interface
![](https://slidetodoc.com/presentation_image_h2/5d73ae32e98c364cae718a9109146c6e/image-22.jpg)
![Experimental measurements of pc and Tc are more accurate than that of Vc a Experimental measurements of pc and Tc are more accurate than that of Vc, a](https://slidetodoc.com/presentation_image_h2/5d73ae32e98c364cae718a9109146c6e/image-23.jpg)
Experimental measurements of pc and Tc are more accurate than that of Vc, a and b are calculated from the experimental values of pc and Tc.
![The law of corresponding states Is it possible to find an equation of state The law of corresponding states Is it possible to find an equation of state](https://slidetodoc.com/presentation_image_h2/5d73ae32e98c364cae718a9109146c6e/image-24.jpg)
The law of corresponding states Is it possible to find an equation of state that doesn’t contain material specific constants? Reduced properties:
![Two gases at the same Tr and pr have the same Vr • Two gases at the same Tr and pr have the same Vr.](https://slidetodoc.com/presentation_image_h2/5d73ae32e98c364cae718a9109146c6e/image-25.jpg)
• Two gases at the same Tr and pr have the same Vr. • These two gases are in “corresponding states’’. • Ar (302 K and 16 atm) ↔ ethylene (381 K and 18 atm)
![](https://slidetodoc.com/presentation_image_h2/5d73ae32e98c364cae718a9109146c6e/image-26.jpg)
![](https://slidetodoc.com/presentation_image_h2/5d73ae32e98c364cae718a9109146c6e/image-27.jpg)
Deviations from ideal gas law
Gas law
Difference between ideal gas and real gas
Derive ideal gas equation
An ideal gas is an imaginary gas
Sutherland's law
Ideal gas law with mass
Gas laws formulas
Ideal gas law
Which equation agrees with the ideal gas law?
Ideal gas law examples
Deviations from the ideal gas law
Pvn=rt
Ideal gas law with density
Conditions for ideal gas
Pv nrt units
Volume of a gas formula
Ideal gas law formula
How to find density in ideal gas law
Ideal gas law to find density
Pzmore
A student collects oxygen gas by water displacement
Gas laws
Ideal gas law derivation
Ideal gases characteristics
Avogadro's law
N in ideal gas law
Charles' law worksheet with answers