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Avogadro’s Law

Avogadro’s Law is one of the gas laws. It states that, under the same temperature and pressure conditions, equal volumes of different gases contain an equal number of molecules.

At the beginning of the 19th century, Italian scientist Lorenzo Romano Amedeo Carlo Avogadro studied the relationship between the volume and the amount of gas present. The results of certain experiments with gases led him to formulate a well-known Avogadro’s Law. It states that, under the same conditions of temperature and pressure, equal volumes of different gases contain an equal number of molecules, or:

For a fixed mass of an ideal gas at constant pressure and temperature, the volume and amount of the gas are directly proportional.

You can express this mathematically as:

V ∝ n

or

V = constant . n

where nR/V is constant and:

  • n is the amount of substance measured in moles
  • V is the volume of the gas

the constant is equal is to RT/p, where p is the absolute pressure of the gas, T is the absolute temperature, and R  is the ideal, or universal, gas constant, equal to the product of the Boltzmann constant and the Avogadro constant.

Avogadro’s Number

In tribute to Avogadro, also the number of particles (atoms, molecules, ions, or other particles) in 1 mole of a substance, 6.022×1023, was named after Avogadro as the Avogadro constant or Avogadro number. The Avogadro constant is one of the seven SI base units and is represented by NA.

The Avogadro’s Law can be used for comparing the same substance under two different sets of conditions:

V1 / n1 = V2 / n2

Molar Volume of Gases

One of the most practical results of this law is the molar volume of a gas, Vm, which is about:

Vm = 22.4 dm3 / mol

It means, at standard temperature (273.15 K, 0°C) and standard atmospheric pressure (101.325 kPa), the molar volume is the same for all ideal gases. Note that it is under the ideal gas assumption. This value is strongly dependent on the pressure and the temperature. For example:

  • for 273.15 K (0°C) and 100.00 kPa, the molar volume of an ideal gas is 22.71 dm3.mol−1
  • for 298.15 K (25°C) and 100.00 kPa, the molar volume of an ideal gas is 24.79 dm3.mol−1
 
References:
Reactor Physics and Thermal Hydraulics:
  1. J. R. Lamarsh, Introduction to Nuclear Reactor Theory, 2nd ed., Addison-Wesley, Reading, MA (1983).
  2. J. R. Lamarsh, A. J. Baratta, Introduction to Nuclear Engineering, 3d ed., Prentice-Hall, 2001, ISBN: 0-201-82498-1.
  3. W. M. Stacey, Nuclear Reactor Physics, John Wiley & Sons, 2001, ISBN: 0- 471-39127-1.
  4. Glasstone, Sesonske. Nuclear Reactor Engineering: Reactor Systems Engineering, Springer; 4th edition, 1994, ISBN: 978-0412985317
  5. Todreas Neil E., Kazimi Mujid S. Nuclear Systems Volume I: Thermal Hydraulic Fundamentals, Second Edition. CRC Press; 2 edition, 2012, ISBN: 978-0415802871
  6. Zohuri B., McDaniel P. Thermodynamics in Nuclear Power Plant Systems. Springer; 2015, ISBN: 978-3-319-13419-2
  7. Moran Michal J., Shapiro Howard N. Fundamentals of Engineering Thermodynamics, Fifth Edition, John Wiley & Sons, 2006, ISBN: 978-0-470-03037-0
  8. Kleinstreuer C. Modern Fluid Dynamics. Springer, 2010, ISBN 978-1-4020-8670-0.
  9. U.S. Department of Energy, THERMODYNAMICS, HEAT TRANSFER, AND FLUID FLOW. DOE Fundamentals Handbook, Volume 1, 2, and 3. June 1992.

See above:

Gas Laws