Acentric factor

The acentric factor for Pitzer , even Azentrizitätsfaktor called, is a dimensionless fabric size . In thermodynamics it serves as a measure of the deviation of a molecule from the ideal spherical shape and is mainly used in thermal equations of state for real gases , e.g. B. in the Soave-Redlich-Kwong equation of state or in the Peng-Robinson equation of state . ${\displaystyle \omega }$

definition

The acentric factor is defined as:

${\displaystyle \omega =-\log _{10}\left({\frac {p_{\mathrm {s} }}{p_{\mathrm {c} }}}\right)_{T_{\mathrm {r} }=0{,}7}-1}$

• T _r = T / T _c - reduced temperature
• p _s - saturation vapor pressure at T _r = 0.7
• p _c - critical pressure

So is

• ${\displaystyle \omega =0}$if is ${\displaystyle \left({\frac {p_{\mathrm {s} }}{p_{\mathrm {c} }}}\right)_{T_{\mathrm {r} }=0{,}7}\;=0{,}1}$
• ${\displaystyle \omega >0}$if is ${\displaystyle \left({\frac {p_{\mathrm {s} }}{p_{\mathrm {c} }}}\right)_{T_{\mathrm {r} }=0{,}7}\;<0{,}1}$
• ${\displaystyle \omega <0}$if is. ${\displaystyle \left({\frac {p_{\mathrm {s} }}{p_{\mathrm {c} }}}\right)_{T_{\mathrm {r} }=0{,}7}\;>0{,}1}$

If the critical temperature , the critical pressure and the boiling temperature at normal pressure are known for a substance , the acentric factor can be calculated approximately according to: ${\displaystyle T_{\mathrm {c} }}$ ${\displaystyle p_{\mathrm {c} }}$ ${\displaystyle T_{\mathrm {s} }}$ ${\displaystyle p_{0}=1{,}01325\,{\rm {bar}}}$

${\displaystyle \omega ={\frac {3}{7}}\;{\frac {T_{\mathrm {s} }}{T_{\mathrm {c} }-T_{\mathrm {s} }}}\log _{10}\left({\frac {p_{\mathrm {c} }}{p_{0}}}\right)-1}$

The temperatures are absolute temperatures .

The following applies to substances whose molecules differ only slightly from the spherical shape (e.g. methane ) . ${\displaystyle \omega \approx 0}$

The acentricity factor was originally used by Pitzer as an expression in the equation for the compressibility factor . By adapting to the experimentally determined vapor pressures of hydrocarbons , the equation is quite exact for these.

Examples

material	T c	p c	${\displaystyle \omega }$
Helium-3 (He3)	3.3 K	1.1 bar	−0.473
Helium (He)	5.2 K	2.3 bar	−0.365
Argon (Ar)	150.8 K	48.7 bar	0.0001
Xenon (Xe)	289.7 K	58.4 bar	0.008
Hydrogen (H 2 )	33.0 K	12.9 bar	−0.216
Nitrogen (N 2 )	126.2 K	33.9 bar	0.039
Oxygen (O 2 )	154.6 K	50.4 bar	0.025
Fluorine (F 2 )	144.3 K	52.2 bar	0.054
Chlorine (Cl 2 )	416.9 K	79.8 bar	0.090
Bromine (Br 2 )	588.0 K	103.0 bar	0.108
Hydrogen fluoride (HF)	461.0 K	64.8 bar	0.329
Water (H 2 O)	647.3 K	221.2 bar	0.344
Heavy water (D 2 O)	644.0 K	216.6 bar	0.351
Ammonia (NH 3 )	405.5 K	113.5 bar	0.250
Methane (CH 4 )	190.4 K	46.0 bar	0.011
Ethylene (C 2 H 4 )	282.4 K	50.4 bar	0.089
Propane (C 3 H 8 )	369.8 K	42.5 bar	0.153
n -butane (C 4 H 10 )	425.2 K	38.0 bar	0.199
Isobutane (C 4 H 10 )	408.2 K	36.5 bar	0.183
Carbon monoxide (CO)	132.9 K	35.0 bar	0.066
Carbon dioxide (CO 2 )	304.1K	73.8 bar	0.239
Tetrafluoromethane (CF 4 )	227.6 K	37.4 bar	0.177
Carbon tetrachloride (CCl 4 )	556.4 K	45.6 bar	0.193
Benzene (C 6 H 6 )	562.2 K	48.9 bar	0.212
Toluene (C 7 H 8 )	591.8 K	41.0 bar	0.263
Methanol (CH 4 O)	512.6 K	80.9 bar	0.556
Ethanol (C 2 H 6 O)	513.9 K	61.4 bar	0.644
Acetone (C 3 H 6 O)	508.1K	47.0 bar	0.304
Acetic acid (C 2 H 4 O 2 )	592.7 K	57.9 bar	0.447
Sulfur dioxide (SO 2 )	430.8 K	78.8 bar	0.256
Sulfur trioxide (SO 3 )	491.0 K	82.1 bar	0.481
Mercury (Hg)	1765.0 K	1510 bar	−0.167

Individual evidence

1. ^ KS Pitzer: Corresponding States for Perfect Liquids . J. Chem. Phys., 7, 583-590, 1939.

literature

• B. Poling, J. Prausnitz, J. O'Connell: The properties of gases and liquids , 5th edition, McGraw Hill, New York 2007.

Web links

• Directory of reference works with acentric factors