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#
