Page:Text-book of Electrochemistry.djvu/168

 direction AB. It acts on all the molecules in the cubic centimetre between A and B, and as the solution is (taken

as a whole) normal, it acts on fKTTR gram-molecules. If the

force necessary to drive a gram-molecule of the dissolved substance with a velocity of 1 cm. per sec. is P kilograms — this force is known as the coeffiderU of friction of the substance — the velocity r, which is proportional to the force acting on a gmm-molecule, is given by —

2312 1000 ., ^ ,, ,

V =• ^,- • (i + at) cm. per second.

The factor (1 + a^, the temperature coefficient, allows the formula to be applied for other temperatures than 0°. The quantity of dissolved substance which passes B in one second is found from the number of molecules lying between the plane B and another plane v cm. distant. The .number of milligram-molecules in this volume (t? c.c.) is v x w = iV^ N is therefore given by —

.V = 2312a+il) . 1000.

and is the number of (milligram-) molecules which are driven through 1 cm. per second, when the fall of concentration is 1, i.e. when the concentration changes by 1 unit per centimetre. N is called the diffusion coefficient.

This coefficient is 1000 times greater than the osmotic pressure per sq. cm. of a normal solution at the given tem- perature divided by the friction P in kilog. of a gram-molecule of the substance.

If we have an electrolyte instead of a non-conductor in the solution, then, as this is completely dissociated in dilute solution, the osmotic pressure is double that calculated. The friction P is made up of two factors. Pi the friction of the positive ion, and P^ that of the negative ion (see below). At 18° we find the value of the numerator of the expression for iVT to be 46,240 (1 -f- ^^s) = 49,289.

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