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BY A. BOURGOUGNON. Brodie (Phil. Trans., 1850, 2, 779) investigated the action of hydrogen dioxide upon potassium permanganate in the presence of sulphuric acid, and found that this reaction required three molecules of H, 0,, whilst other chemists assert t h a t the reaction takes place with five molecules of H,O,. In either case, correct equations are obtainid. 2 K h l n 0 4 + 3 H , S 0 , + 3 H , 0 , = K 2 S0,+2Jln S 0 , + 6 H 2 0 $ 6 0 2 K Mn 0 , + 3 H 2 SO,+5 I-T,O,=K, SO,+? Mn SO,+8 H,Of 10 0. This anomalycan be explained in the following way : Let us write again the preceding equation without giving any determinate coefficient to the substances employed and obtained in the reaction, in fact, writing this equation in the most indeterminate way. aKMn0, bH,SO, + c H 2 0 , , giving x K , SO, y3In SO, z H, O + t 0. The products employed for the reaction will give : For b I€, SO,. For c H,0,. For a KMn 0,. K=a. II=L'b. 11 =2c. Mn =a. S=b. o= 2c. O=4a. O=-ib. And the products o€ the reaction For x K, SO,. For y Mn SO,. For z H,0. For t 0. K=~x. 3111=y. H=2 f. o= t. s =x. s=y. O=z. 0=4x. 0=4y.

+

+

+

T H E REACTION O F HYDROQEN PEROXIDE,

ETC.

95

Giving the following equations : a = 2x. b = X+Y. 4a 4b+ 2c=4x 4y t + z - - _ - ---(3) a=y 2b+2~=2~, from which a 3a x = v y=a, b=x+y=-, 2 s=b+c.

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+ +

+

Substituting the values of b, x, y, z in equation (3), gives 12a 4a+~+2~=2af4a+t+b+c, or

8a 3a 7+6a+2c =6a+~+t+c.

and

8a 3a

2 --2=t+c-2

c=t-c.

We have also 3a 5a 2 + t---t-a.2 Finally we obtain the following values: a 3a 5a xE~,y=a,b=--’c=t2, z=t-aa. 2 As these results represent whole numbers, i t is evident that the smallest value which can be given to a is 2, because Ya 5a -and 2 2 represent whole numbers. Taking a = 2, the other values become a = 2 , x = l , y-2, b=3, c-t-5, z=t-2. But c and z are whole and positive numbers, then necessarily t is greater than 5, otherwise t - 5 and t -2 would be negative. As we must have t > 5 , t must be thenequal toall the whole numbers, beginning with 6. z=b+c=-

Then \=l.

y=2. h = 3. rL

= ?.

c= 1, 2 , ;, 1,

t=

(J,

7,

s. '1,