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Explaining why a reaction takes place is fairly uncommon, especially in teenage level chemistry because inevitably one must dive head first into thermodynamic shenanigans to answer this. Hess cycles, bond enthalpies, enthalpies of formation, etc. I suppose this level of complexity is almost at the boundry of graduate level chemistry but I would certainly not propose it to be all the way there. The Armstrong mixture reaction takes place because of the stability of the phosphorus oxide double bonds mainly. We analyse a comparison of the bond enthalpies between phosphorus atoms in red phosphorus and phosphorus oxygen bonds (both single and double). It is found that the double bonds are stronger due to the higher overlap which also makes them shorter. The electronegativity of oxygen also strenthens the bond with phosphorus relative to P-P as it gives it a more dipolar character. Are you interested in tailored private online tuition from an Oxford University graduate in order to improve your grades? I teach all levels and courses, please feel free to visit my website which you can use to contact me if you need a chemistry tutor: nerichem.com I look forward to speaking with you!