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I dont know whether there is any such formula but the best and safest way is to draw and then calculate.
And for ur question, I dont think any gud level exam will give u a molecule with 15-20 C atoms. Only bullsh*t exams can do this thing. Gud exams(like JEE, AIEEE, BITSAT) want to u to draw and then calculate and hence make mistakes(remember that competitive exams, dont select the students, they reject them).
So practice a lot of such questions by drawing all the possible isomers.
Start from the C at one end and with the longest possible chain. And keep shortening the chain as u draw more compounds. Go step by step, u will never miss any isomer and will always get ur answer right.
Hope it helps.
yeah 15-20 c prob. is unlikely to be asked....but do consider the prob.
Me-CH=C=C=CH-CH(Cl)-CH=CH-Cl TO calculate stereo isomers...
G.I. = 4
O.I.=2
S.I. = 8 U CAN FIND OUT IN NO TIME.(which is what matters)....and in probs where simple alkane is given draw and see....this just helps in stereo isomers....
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there is no specific formula for structural isomers.,...the've to be drawn and seen....
though you can always check the D.B.E. (double bond equivalent = C + 1 - ( H + X - N)/ 2
C= NO OF CARBONS
H = HYDROGENS
X= HALOGENS
N= NITROGEN
THIS NO. IS THE AMOUNT OF 'UNSATURATION' e.g. if DBE= 2 either there are 2 pi bonds (i.e. 2 double bonds or one triple bond ) or one ring and one pi or 2 rings.......THIS MAKES IT SOMEWHAT EASY AS U KNOW WHICH TYPE OF COMPD. U CAN TRY THINKING OF....(though in most problems compd. given is an alkane so u'll have to draw and see)
IF ONLY STEREOISOMERS ARE CONCERNED...
no. of G.I. = 2N IF END GROUPS OF THE DOUBLE BOND ARE DIFFERENT
no of G.I. = 2(N-1) + 2(P-1) IF THEY ARE IDENTICAL
N = CONTRIBUTING DOUBLE BONDS
P= N/2 IF N IS EVEN
OR (N+1)/2 IF N IS ODD
SAME IS APPLICABLE FOR OPTICAL ISOMERS WHERE U KEEP N = NO. OF CHIRAL CARBONS.....
O.I. = 2N IF SYMMETRY IS NOT PRESENT IN ANY FORM OF THE MOLECULE
O.I. = 2(N-1) + 2(P-1) IF SYMMETRY IS PRESENT IN SOME FORM OF THE MOLECULE
p.s : total stereo isomers = no. of G.I. * no. of O.I. (coz i used to make the mistake of adding them!!)