Mumtaz Yousaf,Muhammad Mujtaba Shaikh,Abdul Wasim Shaikh,



Chemical reactions,Mathematical programming,Linear algebra, Gauss elimination,Linear programming,Applied Chemistry,Mathematical Chemistry,


The equations of chemical reactions usually describe the breakup of some desired or consequent products and the breakup of reactants used in chemical reactions. Usually, the equations in skeleton form are unbalanced, and a deeper analysis requires the balanced form which is not quite easy for complex reactions. In instances, the balancing can be done quickly with hit and trial and simple logic. In such cases, the trials are found not attractive, although they are helpful at a simple level at an advanced level they become more tough and unpredictable.  For complex cases, many mathematical techniques can be used for balancing equations of chemical reactions. In this study, some efficient mathematical techniques are suggested which can be more suitable from all perspectives to balance chemical equations and to provide a case to case recommendations for the practitioners. Particularly, we suggest and utilize the linear algebra Gauss elimination (LA-GE) and the linear programming two-phase (LP-2P) approaches to successfully for chemical equation balancing. A number of chemical equations have been taken from literature to see the performance of both approaches. The advantages and disadvantages of both approaches are discussed, mainly with the computer programming in MATLAB and TORA systems, and an exhaustive comparison based on floating point operations (FLOPS) is carried out. The recommendations will prove fruitful for the practitioners for using efficient and yet simpler mathematical programming techniques for the balancing of equations of chemical reactions in the future.


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