viscosity variations with molecular structure

Charlotte Chaze η

The phenomenon that applied shearing force that produces flow in a fluid is resisted by a force that is proportional to the gradient of flow velocity in that fluid1

In other words: viscosity is resistance to flow

Olive oil shows greater resistance to flow than water does:It has a higher viscosity

Determine viscosities of homologous series of compounds Ethanol 1-propanol 1-butanol 1-hexanol 1-octanol

Show a useful correlation between viscosity and physical properties Molecular weight Density Boiling point Enthalpy of vaporization Entropy of vaporization

The cause of differential viscosity between compounds

Remember freshman year?

Attraction felt between polar molecules due to opposite charges In 1° alcohols: hydrogen bonds▪ H on electronegative atom + lone e- pair on

another electronegative atom

Hydrogen is a small atom, allowing a small bond length between it and oxygen▪ strong dipole-dipole interaction

H

H

H

H H

H

HO

HO

H

HH

H

δ+

δ+

δ-

δ-

H

H

H

H

H

H

H

H

H

H

H

H

H

H

H

H

H

H

H

H

H

H

H

O

OH

H

H

H

H

H

H

H

H

H

H

H

H

δ+

δ+

δ-

δ-

ethanol 1-octanol

H-bonding = Resistance to flow

Homologous compounds = similar H bonding

Images from http://www.uic.edu/classes/bios/bios100/lectures/chemistry.htm

• In ice, water molecules form a crystal lattice• In water, no crystal lattice forms• Ice is less dense than water• Which has a higher viscosity?

Ice, ice baby

The net E of interaction of permanent dipoles is given by:

Note: net E is inversely proportional to r6

Energy of interaction falls off rapidly with distance between dipoles

When electrons are distributed unsymmetrically, molecules develop temporary (instantaneous) dipoles

Image from http://www.chem.purdue.edu/gchelp/liquids/disperse.html

A second molecule can then be distorted by the dipole in the first molecule, leading to an electrostatic attraction between the two molecules

Momentary uneven electron distribution causes partial charges

Electron density of a nearby molecule is attracted to the positive charge

Image from http://www.chem.purdue.edu/gchelp/liquids/disperse.html

Larger, heavier molecules exhibit stronger dispersion forces In larger molecules, the valence electrons are

farther from the nuclei▪ They are less tightly held and can more easily form

temporary dipoles The ease with which the electron

distribution around a molecule can be distorted is called polarizability

Larger molecules are more polarizable and thus more viscous

H

H

OH

HH

H

Size of molecule defines size of electron cloud

Longer chain = larger electron cloud = more polarizability & more London dispersion forces

When molecules are more polarizable, the δ+ and δ- of different molecules is stronger, and tightly packs the molecules into a more viscous solution

1-octanol should be most viscous, ethanol should be least viscous

Measuring a homologous series of compounds

Warning: measuring viscosity requires long periods of waiting

Ostwald viscometer Calibrated by water (known viscosity)▪ Thermostat used to control temperature

Measure efflux time of compound Meniscus flowing from upper mark to

lower mark using only force of gravity

Image from http://www.tpub.com/fluid/ch1k.htm

Determines rate of flow through viscometer:

and p1-p2 is proportional to density (ρ), so:

Use this equation to solve for viscosity!

r, radiusL, length of tubep1-p2, pressure difference between two ends of tube

A, calibration constantt, time for meniscus to fall

Viscosity and Error Estimates using Water

Viscosity…It’s as easy as η = Aρt

A is the calibration constant used for all other viscosity calculations

A= 0.003499 mPa cm3 g-1

t= 411.5 sρ= 789300 g m-3

η= Aρtη=(0.003499 mPa cm3 g-1) (789300 g

m-3)(411.5 s)

η= 1.136 g m-1 s-1

Δ%A = (ΔA /A) x 100Δ%A = (1.3996 x 10-6 mPa cm3 g-1 / 3.499 x 10-3 mPa cm3

g-1) x100Δ%A= 0.04%

Δ%t = (Δt /t) x 100Δ%t = (0.1 s / 255.1 s) x100Δ%t = 0.04%

Δ%η= √[(0.04%)2 + (0.04%)2]Δ%η= 0.05657%

Experimental vs. literature viscosity values and factors contributing to viscosity values

Name Molecular Weight (g mol-1)

Efflux Time (s)

Experimental Viscosity (g m-1 s-1)

Literature Value Viscosity2 (g m-1 s-1)

Percent Error

ethanol 46.07 411.5 ± 0.3

1.136 ± 0.001

1.074 5.7

1-propanol 60.10 706.2 ± 0.4

1.976 ± 0.001

1.945 1.6

1-butanol 74.12 911.3 ± 0.3

2.581 ± 0.001

2.544 1.5

1-hexanol 102.17 1551.2 ± 1.7

4.416 ± 0.005

4.578 3.5

1-octanol 130.23 2711.9 ± 0.4

7.840 ± 0.003

7.288 7.6

• High MW = larger compound, more polarizable• Higher

viscosity

• R2

• Increases with increasing MW

• More polarizable molecules are more difficult to send into gas phase due to higher intermolecular forces

• R2

• Higher increase in entropy of vap for larger molecules

• They are more difficult to vaporize due to intermolecular forces

• R2

• High density: high viscosity

• Lowest R2 • Density least

accurate model

1-octanol:•Highest boiling point bc:• Most

polarizable• Binding forces

are the strongest

•More energy is needed to separate the molecules and send them into gas phase•R2

Name Molecular Weight (g mol-

1)

Enthalpy of Vap. at 25 C (kJ mol-1)

Entropy of Vap. at 25 C (kJ mol-1 K-

1)

Density (g cm-1)

Boiling Point (K)

Exp.Viscosity (g m-1 s-1)

ethanol 46.07 42.32 0.120 0.7893 351.351.136 ± 0.001

1-propan

ol60.10 47.45 0.128 0.7997 370.35

1.976 ± 0.001

1-butanol

74.12 52.35 0.134 0.8095 390.852.581 ± 0.001

1-hexanol

102.17 61.61 0.143 0.8136 430.754.416 ± 0.005

1-octanol

130.23 70.98 0.152 0.8262 468.257.840 ± 0.003

Dipole-dipole interactions London dispersion forces Hydrogen bonding It’s more polar

Unsymmetrical distribution

Symmetrical Distribution

Longer chain = larger electron cloud = more polarizability = more London dispersion forces!

Intermolecular forces and viscosity

Strength of dispersion forces increase with increasing molecular weight Causes increasing boiling point, enthalpy of

vaporization, and entropy of vaporization The greater the intermolecular force,

the greater the viscosity Main difference in viscosity for each

compound is London dispersion forces

Viscosity increases with increasing: Molecular weight Enthalpy of vaporization Entropy of vaporization Density Boiling point

Mostly due to London dispersion forces

1. Garland, C.; Nibler, J.; Shoemaker, D. Spectroscopy. Experiments in Physical Chemistry; McGraw-Hill Higher Education: New York, NY, 2009; pp. 129-130, 320-326.

2. Physical Constants of Organic Compounds. Handbook of Chemistry and Physics, Lide, D., Ed.; CRC Press: Boca Raton FL, 2008; 89th edition, pp. 3-4 to 3-522.