Let the molecular formula of Beta carotene be C_xH_y and the balanced equation of its combustion in excess oxygen is as follows.
C_xH_y+(x+y/4)O_2->xCO_2+y/2H_2O
It is given that 1g beta carotene produces 3.278g" "CO_2 and 0.9397g" "H_2O
Molar mass of BC is 536.96g"/mol"
So 1" "mol or 536.96g BC will produce 3.278xx536.96~~1760.15g" "CO_2 and 0.9397xx536.96~~504.58g" "H_2O
Molar mass of CO_2=44g"/mol"
So number of moles of CO_2 produced =(1760.15g)/(44g"/mol")~~40mol
Hence number of C-atoms in one molecule of BC is =40 as one molecule of CO_2 contains one atom of Carbon.
Again Molar mass of H_2I=18g"/mol"
So number of moles of H_2O produced =(504.58g)/(18g"/mol")~~28mol
So one mole BC produces 28mol water which contain 56 mol atom Hydrogen as one molecule of water contains two atoms of Hydrogen.Hence number of Hydrogen atom present in one molecule of BC is 56.
Now we can say that molecular formula of BC is C_40H_56
