382 



NA TURE 



[August 17, 1905 



more dilute solution. This fact must be my excuse _ for 

 placing before you the results of a few simple calculations 

 as to the molecular distribution in these solutions, which 

 have certainly given me an entirely new view of what con- 

 stitutes a really dilute solution from the molecular point 

 of view. 



In estimating the number of molecules in a given volume 

 of solution the method adopted is to divide the space into 

 minute cubical cells, each of which can exactly contain a 

 sphere of the diameter of the molecule. In this way a 

 form of piling for the molecules is assumed which, though 

 not the closest possible, may quite probably represent the 

 piling of water molecules. Taking the molecular diameter 

 as 0-2XI0-' millimetres — a figure which is possibly too 

 small for the water molecules and too large for the gold 

 — it is found that a cubic millimetre of solution contains 

 125x10" molecules, or 125 quadrillions. The head of an 

 ordinary pin, if it were spherical, would have a volume 

 of about 1 cubic millimetre. 



If these water molecules could be arranged in a single 

 row, each molecule just touching its two nearest neighbours, 

 the length of the row would be 25,000,000 kilometres. A 

 thread of these fairy beads, which contained the molecules 

 of one very small drop of a volume of 6 cubic millimetres, 

 would reach from the earth to the sun, a distance of 

 about 150,000,000 kilometres. 



In a solution containing ij grains of gold per ton, or i 

 decigram per cubic metre, the ratio of gold molecules to 

 water molecules is as i : 193,000,000. Each cubic milli- 

 metre of the solution, therefore, contains 6,500,000,000 gold 

 molecules. If these are uniformly distributed throughout 

 the solution each will be about 400 micro-millimetres, or 

 1/60,000 of an inch, from its nearest neighbours. This 

 is not really very wide spacing, for the point of the finest 

 sewing-needle would cover about 1,500 gold molecules. 



If a cubic metre of solution could be spread out in a 

 sheet one molecule in thickness it would cover an area of 

 1,680 square miles, and nowhere in this area would it be 

 possible to put down the point of the needle without touch- 

 ing some hundreds of gold molecules simultaneously. 



According to Prof. Liversidge, sea-water contains on 

 the average about 1 grain of gold per ton. If this is the 

 case, then the above figures for the dilute cyanide solution 

 apply with only a slight modification to sea-water. No 

 drop, however small it may be, can be removed from the 

 ocean which will not contain many millions of gold mole- 

 cules, and no point of its surface can be touched which is 

 not thickly strewn with these. From this molecular point 

 of view we must realise that our ships literally float on a 

 gilded ocean ! 



From time to time adventurers arise who attempt to 

 launch upon this gilded ocean unseaworthy ships freighted 

 with the savings of the trusting investor. In order that 

 nothing which has been said here may tempt anyone to 

 contribute to the freighting of these sfiips, let me hasten 

 to point out that the weakest of the cyanide solutions here 

 referred to is richer in gold than sea-water is reported to 

 be. The practical conclusion from this comparison is 

 sufliciently obvious. If the cyaniding expert, whose business 

 it is to extract gold from dilute solutions, finds that it 

 does not pay to carry this extraction beyond a concentra- 

 tion of 2 or 3 grains per ton, even when the solution is 

 already in his hand, and when, therefore, the costs of 

 treatment are at their minimum, how can it possibly 

 pay to begin the work of extraction on sea-water, a 

 solution of one-half the richness, which would have to 

 be impounded and treated by methods which could not 

 fail to be more costly in labour and materials than the 

 simple process of zinc-box precipitation? It is generally 

 unsafe to prophesy, but in this case I am rash enough to 

 risk the prediction that if ever the gold mines of the 

 Transvaal are shut up it will not be owing to the com- 

 petition of the gold resources of the ocean. 



In these calculations with reference to the dilute cyanide 

 solutions it is assumed that the gold molecules are uni- 

 formly distributed, that they are practically equidistant 

 from each other. There appears to me to be considerable 

 doubt whether we have any right to make this assumption. 

 Leaving out of account for the moment the action of 

 the water molecules, it w'ould appear that as long as the 

 gold molecules are so numerous that a uniform distribution 



NO. 1868, VOL . 72] 



would bring them within the range of each other's at- 

 traction, we can imagine that all submerged molecules 

 would be in equilibrium so far as the attractions of their 

 own kind are concerned, being subjected to a uniform pull 

 in all directions. This condition would certainly make 

 for uniform distribution. But when the distance between 

 them exceeds the range of the molecular forces, it is 

 evident that an entirely new condition is introduced, and 

 it seems not improbable that the widely distributed mole- 

 cules would tend to drift into clouds in w'hich they are 

 brought back within the range of these forces. The range 

 of the cohesive forces in w'ater and aqueous liquids is 

 usually taken from 50 to 100 micro-millimetres, and I am 

 disposed to think that ten times this amount would not 

 be an excessive estimate of the range in the case of gold. 

 If the range for gold be taken as 500 micro-millimetres, 

 then the gold molecules of the dilute gold solution, which 

 are spaced at 400 micro-millimetres apart, are just within 

 the range of each other's attraction, and their distribution 

 is, therefore, likely to be uniform. But by a further dilu- 

 tion to half concentration, the equilibrium would be liable 

 to be dislurbed, and denser clouds of gold molecules would 

 be formed, with less dense intervals between them. 



In preparing the zinc boxes through which the gold solu- 

 tion is passed, very great care has to be exercised to 

 ensure that the contact surface of the zinc is used to the 

 best advantage. With this object the packing of the zinc 

 shavings is so managed that the solution is spread over 

 the zinc surface in as thin sheets as possible. The object, 

 of course, is to bring as many of the gold molecules as 

 possible into actual contact with the zinc. The gold mole- 

 cules found in the solution leaving the boxes are those 

 which have not been in contact with the zinc. Yet we 

 have seen that these molecules are still so numerous that 

 they are within 1/60,000 of an inch of each other. If 

 these molecules are in a state analogous to the gaseous 

 state, with diffusive energy of the same order as that of 

 the gas molecule, it is difficult to imagine how they can 

 escape without coming in contact with the zinc surface 

 during their tortuous passage through the boxes and being 

 deposited there. Yet they do escape, even when the velocity 

 of the solution in passing over the zinc surfaces is so slow 

 as 10 cm. per minute or i-6 mm. per second. I 



We may regard the condition of these isolated gold 

 molecules, or the more complex auricyanide of potassium 

 molecules, as typical of that of the solute molecules in a 

 dilute solution of anv non-volatile solid. They are soYxd 

 molecules sparsely distributed among a multitude of in- 

 tensely active solvent molecules, the temperature of the 

 solution being many hundred degrees below that at which 

 they could of themselves assume the greater free'dom of 

 the liquid or gaseous state. These solute molecules have 

 to a great extent been set free from the constraining effect 

 of their cohesive forces, hut it is important to remember 

 that this freedom has not been attained by the increase 

 of their on'n kinetic energy as in liquefaction by heat, 1 

 Their freedom and the e.\tra kinetic energy they have \ 

 acquired have in some way been imparted to them by 

 the more active solvent molecules ; for, if the solvent could 

 be suddenly removed, leaving the solute molecules still 

 similarly distributed in a vacuous space, thev would eventu- 

 ally condense into a solid aggregate. This must be the 

 case, for the non-volatile solute has no measurable vapour 

 pressure at the temperature of the solution. The kinetic 

 energy of the solute molecules is of itself quite insufficient 

 to endow them with the properties of the gaseous or even 

 of the liquid molecule, even when their cohesive forces 

 have been weakened or overcome by separation. 



// the energy employed in this separation is not intrinsic 

 to the solute molecule then it must in some way have been 

 imparted by the solvent molecules. It therefore becomes 

 important to compare the energy endowment of one set of 

 molecules with that of the other. 



Compared with other solids, ice at its freezing point has 

 very little hardness or tenacity : the cohesion of its 

 molecules has been much relaxed by the great absorption 

 of heat energy between the absolute zero and I he freezing 

 point. If an average specific heat of 05 over the wholf 

 range be assumed, the heat absorption of one gram amounts 

 to 1365 calories. In the transition to the liquid state at 

 0° a further absorption of 79 calories takes place, so that 



