EXP. If a bulb containing a few drops of bromine is broken at the bottom of a tall cylinder, the bromine vapor is seen to diffuse rather slowly into the upper part of the cylinder, the bromine molecules, in their passage upward, rebounding from the air molecules, with which the cylinder is filled. If a second cylinder is first evacuated, and the bromine bulb is broken ‹in vacuo›, the vapor is seen to fill the cylinder instantly, the high velocity of the bromine molecules being thus revealed. But a third question, of fundamental importance in the comparison of the condition of a substance existing as a gas and its condition in a solution of the same concentration and temperature, results from a consideration of the ‹frequency of the impacts› of the solute molecules against the solvent, growing out of the reduction of the lengths of the mean free paths of the solute molecules.[41] In order to be able to take this fact properly into account, it will be necessary to consider somewhat more precisely the manner in which, according to the kinetic theory, gas pressure is produced. We may consider that we have in a cube of unit volume (1 c.c.) ‹n› molecules of a gas, each of mass ‹m› and average velocity ‹u› cm. per second. We may assume that one-third of the total number [p030] of molecules moves in each of the three dimensional directions.[42] A single molecule of mass ‹m›, striking the surface with a velocity ‹u› and rebounding with the same velocity in the opposite direction, will exert on the surface a force of 2 ‹m› ‹u› units. But, with a velocity of ‹u› cm. per second, it will reach the opposite wall and return to the surface we are considering, ‹u› / 2 times in one second. A single molecule will consequently exert a force 2 ‹m› ‹u› × ‹u› / 2 or ‹m› ‹u›^2 on the surface, and the ‹n› / 3 molecules moving in the same direction will exert a force ‹n› / 3 × ‹m› ‹u›^2 on the unit surface. This represents, therefore, the pressure of such a gas, as calculated on the basis of the assumptions of the kinetic theory. Now, when a gas is so strongly compressed, that the bulk of the molecules is not negligible in comparison with the total volume of the gas, the number of impacts on unit surface in unit time becomes sensibly greater than ‹n› / 3 × ‹u› / 2, since the distance to be covered between successive blows on the surface will be sensibly less than 2 cm., in a cube of unit volume. If we imagine, for the sake of a rough illustration, that one-third of the molecules in 1 c.c. are united into one spherical mass (indicated by A in Fig. 7), moving upwards and downwards, it is obvious that the distance covered between two successive blows on a surface is not 2 cm., but that distance diminished by twice the diameter of the sphere. For strongly compressed gases, the total number of impacts on unit surface is therefore sensibly greater than ‹n› / 3 × ‹u› / 2, and the pressure is proportionately greater. According to van der Waal's correction