I had been asked by one of my chemistry teachers to find out about an equation. The equation is:

\(3S + 4O_{2} \to SO_{2} + 2SO_{3}\)

\(4S + 5O_{2} \to 2SO_{2} + 2SO_{3}\)

How is it possible than an equation can be balanced in two ways even when it is in the simplest form ?

Also this equation cannot be balanced by P.O.A.C. method.

Please anyone help me out and enlighten me on this topic.

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TopNewestSulphur is going into different oxidation states in sulphur dioxide and sulphur trioxide. So in the first equation one of the sulphur atoms is getting oxidised into sulphur dioxide and the other two into sulphur trioxide. In the second one two sulphur atoms each are going into sulphur dioxide and troxide. Any such reaction could be made with some \(x\) sulphur atoms getting oxidised into dioxide and \(y\) into trioxide. Now the question is how is this possible that different number of sulphur atoms are getting oxidised in the reactions. The answer is simple. It is because the above reaction is actually a combination of two reactions - one being \( S + O_2 \rightarrow SO_2 \) and the other being \( 2 S + 3 O_2 \rightarrow 2 SO_3 \). So if the first reaction is added two the second one you would obtain the first reaction given by your teacher. Figure out what happens when you add \(2\) times the first reaction to the second reaction.

Realize the idea?

Hope this helps. – Sudeep Salgia · 1 year, 11 months ago

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– Rishabh Tripathi · 1 year, 11 months ago

yeah.. after doing it gives another balanced equation that too in simplest form. So, this reaction as a whole cannot be possible without breaking it into two different reactions ?Log in to reply

actuallya linear combination of two reactions. The question isn't whether the reaction is possible by breaking it into two different reactions. – Sudeep Salgia · 1 year, 11 months agoLog in to reply

– Rishabh Tripathi · 1 year, 11 months ago

I see. Well Thank you.. :)Log in to reply

– Rahul Saha · 1 year, 11 months ago

Nice explanation.Log in to reply

– Sudeep Salgia · 1 year, 11 months ago

Thanks.Log in to reply

Mathematically, this can be explained as follows. Suppose that you can balance the equation as follows.

\(aS+bO_2\rightarrow cSO_2+dSO_3\)

Now, comparing the number of sulfur and oxygen atoms on both sides,

\(a=c+d\) and \(2b=2c+3d\)

Now suppose you want \(a,b,c,d\) to be integers. It is clear from the second equation that \(d\) must be even. Hence \(d=2D\). So \((a,b,c,d)=(c+2D,c+3D,c,2D)\) for any pair of positive integers \(c\) and \(D\). In your first reaction you have \((c,D)=(1,1)\) and in the second reaction, you have \((c,D)=(2,1)\). You can find other solutions for other values of \(c\) and \(d\).

I don't know if there is a chemical reason behind this. – Rahul Saha · 1 year, 11 months ago

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– Rishabh Tripathi · 1 year, 11 months ago

Your explanation doesn't make it clear why this actually happens.Log in to reply

– Rahul Saha · 1 year, 11 months ago

Well, I find Sudeep Salgia's answer to be more insightful, especially because he divides the equation into two separate equations. My answer basically shows you how to convert this into a number theoretic problem.Log in to reply

– Krishna Ar · 1 year, 11 months ago

IMO, You explained it better.Log in to reply

– Rishabh Tripathi · 1 year, 11 months ago

IMO ?? What it means here ?Log in to reply

– Ruturaj Sharbidre · 6 months, 2 weeks ago

maybe IMO mean international mathematical olympaid...anyway... i do not sure about possibilities comming with extra bonding in the sulphur atomic model or sulphur molecule.Log in to reply