1.  Important Pressure Units and Quantities

1.  A.  Common pressure units


1 Torr = 1 mm Hg at 0°C, standard gravity

1 atm = 760 Torr

1 micron = 1 mm Hg = 10-3 Torr = 1mTorr

1.  B.  Mean free path

The mean free path l is the average distance traveled by a gas molecule between collisions with other molecules.

The formula for l is given by Eq. (12-11) in Sime and by Eq. (1-19) in Atkins, 5th Ed.

where N* is the number density of the gas

and d is the molecular diameter.


Calculate the mean free path of a nitrogen molecule at 1 Torr, 298 K.  (Nitrogen, which makes up 80% of the atmosphere, has a molecular diameter of 3.7Å)

Observe that mean free path is inversely proportional to pressure:

Thus, one can easily calculate l at any pressure if one knows its value at one pressure.


Calculate the mean free path of a nitrogen molecule at 1 mTorr (10-3 Torr) , 298 K.

For making quick approximations of l, physical chemists memorize one value of the free path (5 cm at 1 mTorr = 10-3 Torr) and use the fact that mean free path is inversely proportional to pressure to calculate l at any pressure.

1.  C.  Importance of mean free path

Mean free path is a key property in vacuum system design.


·        If l << vacuum system diameter, then flow is viscous (molecules are transported as bulk parcels).

·        If l > vacuum system diameter, then flow is molecular (molecules are transported individually through diffusion).

The changeover occurs at 10-2 - 10-3 Torr for typical vacuum systems.

2.  Vacuum System Components

2.  A.  Pumps

2.  A.  i.  Aspirator

Principle of operation:  Bernoulli’s Principle (moving fluid reduces pressure)


Pump operation is based on bulk flow of fluids


Ultimate vacuum is approximately 24 Torr (vapor pressure of water at 25°C)

2.  A.  ii.  Rotary oil pump

Principle of operation:
         (1)  begin expansion cycle
         (2)  seal off expanded volume
         (3) compress gas out exhaust


Pump operation is based on bulk flow of gas; hence the pump works in the viscous flow regime


Used for obtaining “rough” vacuum (10-3 Torr), which is the lower limit of the viscous flow regime


Safety considerations:

·        Pump must have a belt guard (to prevent fingers and hair from getting caught!).

·        Trap vapors entering pump (to prevent degradation of pump oil and seals).

·        Do not pump on atmosphere (the pump would overheat since it is not designed to be an air compressor!).

2.  A.  iii.  Diffusion pump

Principle of operation:  momentum transfer by vapor jet stream


Individual molecules are “pushed” toward exhaust by jet stream; hence, the pump works in the molecular flow regime


Used for obtaining “high” vacuum (10-6 Torr)


Must be connected to a "rough" pump to reduce pressure to molecular flow regime (<10-2 Torr)


Safety considerations:

·        Rotary oil pump must be on to reduce the pressure to <10-2 Torr (otherwise, pump "; also, hot oil could combust in presence of oxygen)

·        Diffusion pump must be cooled with water or air (to prevent overheating)

·        Vacuum line must be protected with a trap (to prevent migration of diffusion pump oil)

2.  A.  iv.  Other pumps

Turbomolecular pump:  ultra-fast fan blades knock molecules out of vacuum system

Cryo pump:  molecules are frozen out

Sorption pump:  molecules diffuse into absorbing material

Sputter ion pump:  molecules are ionized and buried

2.  B.  Cold trap


·        Prevents pump oil from contaminating vacuum system

·        Prevents organic solvents from reaching pump (and degrading oil and seals)

·        Acts as a pump by condensing molecules


Principle of operation:  freeze out contaminants


Safety considerations:

·        Never pump air through a liquid nitrogen trap (oxygen will condense and can explode)


Put a test tube into a dewar of liquid nitrogen; condense liquid oxygen

2.  C.  Pressure gauges

2.  C.  i.  Barometer

Uses the height of a column of mercury to measure ambient atmospheric pressure


patm = h


2.  C.  ii.  Manometer

Uses the height difference of a mercury column to measures system pressure relative to ambient atmospheric pressure


patm = psys + Dh


psys = patm - Dh


Safety considerations:

·        Always change pressure of a manometer slowly (rapid movement of mercury could result in flow out of manometer)

2.  C.  iii.  Thermocouple gauge

Principle of operation:  pressure dependence of thermal conductivity.

Only works at relatively high pressures because thermal conductivity eventually becomes too small.

2.  C.  iv.  Capacitance manometer

Principle of operation:  mechanical deflection of membrane (which is one plate of a capacitor) alters capacitance in an electronic circuit

Only works at relatively high pressures because deflection eventually becomes too small.

2.  C.  v.  Ionization gauge

Principle of operation:  ionization of gas by a high voltage results in a current of charges particles

Only works at low pressures because high voltage causes gas breakdown (lightning bolts) at higher pressures.

2.  D.  Regulators

Gas flow from a pressurized cylinder is controlled with
         1)  Main cylinder valve
         2)  Pressure regulator
         3)  Outlet valve

Valves are either open or closed; when open, the pressure is equal on both sides (assuming no or slow gas flow).  The regulator allows for an adjustable pressure difference between both sides.

The cylinder pressure pcylinder forces the valve closed and seals the regulator.  The valve is attached to a flexible diaphragm that is connected to the pressure adjusting spring, which exert opening pressures pdiaphragm and pspring on the valve, respectively.  Compressing the spring pushes against the diaphragm and valve, allowing gas from the cylinder to flow past the valve.  This gas exerts closing pressure poutlet against the diaphragm, which closes the regulator.  At equilibrium the opening and closing pressures balance each other

pcylinder + poutlet = pspring + pdiaphragm

Thus, an increase in the spring pressure causes an increase in the outlet gas pressure.

Safety considerations:

·        Make sure regulator and outlet valve are closed before opening main cylinder valve (in case they were set too high by the previous user for your application)

2.  E.  Valves and stopcocks

Solid stopcocks are satisfactory for rough and low vacuum work.

Vacuum-backed or o-ring stopcocks must be used for high vacuum work.

Safety considerations:

·        Do not force a glass stopcock; instead, turn it very slowly

·        Always use two hands when turning a glass stopcock (one on body and one on handle)