CHKOMIUM, MOLYBDENUM, TUNGSTEN, UKANIUM, ETC. 315 



C 2 H 2 4 , which in oxidising gives carbonic anhydride, whilst, with 

 an excess of sulphuric acid, the potassiym permanganate is converted 

 into manganous sulphate, MnS0 4 , so that the ultimate oxidation 

 will be expressed by the equation: 5C 2 H 2 4 -f2MnK0 4 + 3H 2 S0 4 

 = 10C0 2 + K 2 S0 4 + 2MnS0 4 + 6H 2 O. The influence of the relative 

 amount of sulphuric acid is seen from the annexed table, which gives 

 the measure of reaction p per 100 parts of potassium permanganate, 

 taken four minutes after mixing, using n molecules of sulphuric acid, 

 H 2 S0 4 , per 2KMnO 4 + 5C 2 H 2 4 



n = 2 4 6 8 12 16 22 



p =22 36 51 63 77 86 92. 



showing that in a given time (4 minutes) the oxidation is the more 

 perfect the greater the amount of sulphuric acid taken for given amounts 

 of KMnO 4 and C 2 H 2 O 4 . It is obvious also that the temperature and 

 relative amount of every one of the acting and resulting substances 

 should show its influence on the relative velocity of reaction ; thus; for 

 instance, direct experiment showed the influence of the admixture 

 of manganous sulphate. When a large proportion of oxalic acid (108 

 molecules) was taken to a large mass of water and to 2 molecules of 

 permanganate 14 molecules of manganous sulphate were added, the 

 quantity x of the potassium permanganate acted on (in percentages 

 of the potassium permanganate taken) in t minutes (at 16)- was as 

 follows : 



*=2 5 8 11 14 44 47 53 61 68 

 JB= 5-2 12-1 18-7 25-1 31-3 68-4 717 75-8 79-8 83-0 



These figures show that the rate of reaction that is, the quantity of 

 permanganate changed in one minute decreases proportionally to the 

 decrease in the amount of unchanged potassium permanganate. At the 



different meaning in chemistry from what it has in mechanics. Their only common factor 

 is time. If dt be the increment of time and dx the quantity of a substance changed in 

 this space of time, then the fraction (or quotient) dx.'dt will express the rate of the 

 reaction. The natural conclusion, come to both byHarcourt andEsson, and previously to 

 them (1850) by Wilhelmj (who investigated the rate of conversion, or inversion, of sugar 

 in its passage into glucose), consists in establishing that this velocity is proportional to 

 the quantity of substances still unchanged i.e. that dx'dt = C(A.-x), where C is a 

 constant coefficient of proportionality, and where A is the quantity of a substance taken 

 for reaction at the moment when t = and a? = that is, at the beginning of the 

 experiment, from which the time t and quantity x of substance changed is counted. 

 On integrating the preceding equation we obtain \og(A./A-x)--=kt, where A; is a new 

 constant, if we take ordinary (and not natural) logarithms. Hence, knowing A, x, and t, 

 for each reaction, we find k, and it proves to be a constant quantity. Thus from the 

 figures cited in the text for the reaction 2KMnO 4 + 108C2H 2 O4+14MnSO 4 , it may be 

 calculated that /t = 0'0114; for example, < = 44, a; = 68'4 (A = 100), whence A;i = 0'5004 and 

 # = 0-0114, (see also Chapter XIV., Note 3, and Chapter XXVII., Note 25 bis). 



