二氯取代物总数:
由对称性,联n苯(n≥2)的等效位置共有(n+1)种
以联三苯为例,等效位置共4种
从两边往中间依次数,总数=
(3+4)+
(2+3+2)+
(1+2+1)+
(0+1+2)
=21(种)
同理,联四苯的二氯取代物总数=
(4+5)+
(3+4+2)+
(2+3+1)+
(1+2+2)+
(0+1+1)
=31(种)
以此类推,若n为奇数,总数=(0+n)*(n+1)/2+[1+(n+1)]*(n+1)/2+2*(n+1)/2+1*[(n+1)/2-1]=n^2+7n/2+3/2
若n为偶数,总数=(0+n)*(n+1)/2+[1+(n+1)]*(n+1)/2+(2+1)*n/2=n^2+7n/2+1
一氯一溴取代物总数:
由于两取代基不同,因此等效位置大大减少
以联三苯为例,从两边往中间依次数,总数=
(3+4)+
(3+4+2)+
(3+4+2)+
(3+4+2+2)
=36(种)
同理,联四苯的二氯取代物总数=
(4+5)+
(4+5+2)+
(4+5+2)+
(4+5+2+2)+
(4+5+2+2)
=57(种)
以此类推,若n为奇数,总数=[n+(n+1)]*(n+1)+2{[1+(n+1)/2]*(n+1)/2-(n+1)/2}=5n^2/2+4n+3/2
若n为偶数,总数=[n+(n+1)]*(n+1)+2[(1+n/2)*n/2]=5n^2/2+4n+1