Looks easy but soon gets surprisingly hard and the coefficients become pretty high, which makes you wonder if you have not made some mistake (see some balancing hints at the bottom of that page). This first example doesn't look convincing - why do we have to solve set of equations when the reaction equation can be easily balanced by other means? Good point - but what if the reaction can be not easily balanced? To find them we can assume one of the coefficients to be 1: In algebra it usually means that the set of equations doesn't have a unique solution, but in the case of chemical equations we have one additional information - all coefficients must be integer and they must be the smallest ones. In this case we have very simple equation a = 6×b that we can use to substitute 6×b for a in the second and third equation to get:īoth equations are identical. Such equation sets is not a thing that you may want to solve manually, although when balancing chemical equations in most cases it can be done relatively easy, as most equations don't contain all unknowns. Quite often you will end with many more equations and many more unknows. We have three equations, and three unknowns - nothing particularly difficult to solve. We can write similar equations for the remining elements - hydrogen:Īs there are no free terms in this set of equations, it has a trivial solution (a = b = c = 0) which we are not interested in. Using coefficients a, b and c we can tell that we have 1×a atoms of boron on the left (one atom per each H 3BO 3 molecule), and 6×b + 0×c on the right (6 atoms of boron per each H 4B 6O 11 molecule and no boron in water). Our reaction has three coefficients a, b and c: What does 'balanced' mean? It means that for every element, there is the same number of atoms on both sides of the reaction equation. It can be rather easily balanced by inspection, but let's try a more systematic approach. That's the method EBAS - our chemical reaction equation balancer - uses. General algebraic method of balancing chemical reaction equationsĪpart from the three already described methods, there is also a general method, often less user friendly - but thanks to its systematic approach perfect for use in computer programs.
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