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Important constants in the kinetic theory are: N = the number of molecules per cm3 at S.T.P.; N0 = 22415 x N = the number of molecules in a gram-molecule. The number N0, which is the same for all gases, is called Avogadro's Constant. The value of N0, and hence the absolute mass of a single molecule, have been determined by a variety of methods with an accuracy of about 1 per cent.
The most direct method is due to Rutherford and Geiger. The element radium emits atoms of helium, called α-rays, with speeds of about 2 x 109 cm. per sec. (i.e., about 100,000 times faster than gas molecules), and extremely large kinetic energy. When α-rays from a particle of radium, A, impinge on a screen of zinc-blende, B, in the spinthariscope of Crookes,
 | Fig: Spinthariscope |
each α-particle causes a flash of light visible under a lens, C. It was therefore possible to count the α-rays emitted in a given time, and by collecting the helium from a large amount of radium over a long period, the volume of helium produced from 1 gm. of radium was found to be 0.46 mm3 per 24 hours. By comparing this with the counted number of a-particles (helium atoms) emitted from a known weight of radium in a given time, it was easy to calculate the number of molecules (atoms) per c.c. of helium. This is N; its value is 2.7 x 1019. Thence N0 = 6.05 x 1023.
A second method used by Rutherford and Geiger (1908) depends on the capacity of the α-particles of rendering a gas through which they pass a conductor of electricity. A long glass "firing tube" A A' (450 cm. long and 2-5 cm. wide),
 | Fig: Rutherford and Geigers apparatus |
was exhausted, and at the end A was placed a preparation of radium on a lead plate, a, which expelled α-particles. Some of these were shot along the tube and passed through the narrow tube, B, into the brass ionisation chamber C, where the gas at low pressure was rendered conducting, or ionised. A mica window at F shut off the gas from the evacuated tube, A A'. Running axially through C, and insulated from it by the ebonite ends, was a metal wire, w which was connected through a battery and electrometer to the outer surface of the brass vessel. As each α-particle entered the ionisation chamber (at the rate of about one every second), it made the gas conducting, and the electrometer gave a deflection In this way the individual α-rays were counted, and the method of calculation was similar to that in the first method. The value N0 = 6.14 x 1023 was found.
The determinations of N0 have been made by counting, as above, and from other radioactive experiments, from experiments on colloidal solutions, the spectrum, the radiation of heat, the formation of clouds, and the blue colour of the sky. The numbers obtained from the recent experiments are in excellent agreement, and leave no doubt that the latter cannot possibly be the result of chance. Everything points to the real existence of molecules.
Table of Values of Avogadro's Constant, N0.
| Method | N0 | | Classical kinetic theory | 10 x 1023 (approximately) | | Cloud formation | 8.3 x 1023 | | Brownian movement | 6.30 x 1023 | | Radiant heat | 6.19 x 1023 | | Counting α-particles | 6.14 x 1023 | | Electronic charge (Millikan) | 6.06 x 1023 |
Table of Molecular Magnitudes.
| Number of molecules per c.c. of gas at S.T.P. | N | 2.70 x 1019 | | Number of molecules per gram-molecule (22.415 litres in ideal state at S.T.P.) | N0 | 6.06 x 1023 | | Mass of hydrogen atom | | 1.67 x 10-24 gm. | | Mean speed of hydrogen molecule at 0° | ΩH2 | 16.94 x 104 cm./sec. | | Translational kinetic energy of a molecule at 0° | | 5.61 x 10-14 erg. | | Rate of change of translational kinetic energy per 1° | | 2.056 x 10-16 erg/degree. |
A few special magnitudes, not known with the accuracy of the above, may be given for comparative purposes:
| Diameter of hydrogen molecule | 2.40 x 10-8 cm. | | Mean free path of hydrogen molecules at S.T.P. | 1.22 x 10-5 cm. | | Average distance apart of gas molecules at S.T.P. | 3 x 10-7 cm. | | Number of collisions per second of oxygen molecules at S.T.P. | 4.25 x 109. | | Time of describing free path of oxygen molecules at S.T.P. | 2.3 x 10-10 sec. |
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