1Help me solve pic problem steps by steps As much as possibl


1.Help me solve pic problem steps by steps. As much as possible.
2.Also add a questions or conjecture after it ( for example, could we have finite order elements in an infinite group?)
1. Find an isomorphism from R2 to R2 addn

Solution

find the isomersim for R2 to R2

You don\'t need many trial and error but you need a few

You know that the ester group is

COO

The general formula for the ester is

R1COOR2

You also know that you have C4H10 to play with

So if R1 = H

R2 = C4H7

There are 4 structural isomers of C4 H7

They are n-butyl CH3CH2CH2CH2-

isobutyl or 3methylpropyl

(CH3)2CHCH2

sec-butyl or 2methylpropyl

CH3CH(CH3)CH2-

(by the way, this one is chiral so it really is 2 isomers)

t-butyl or 1,1-methylethyl

(CH3)3C-



If R1 = CH3 Then R2 = C3H7

There are 2 isomers of C3H7

n-propyl CH3CH2CH2

iso-propyl or 1methylethyl (CH3)2CH-

If R1 = CH3CH2 then R2 = CH3CH2- there is only one isomer

If R1 = C3H7 then R2 = CH3 As mentioned above, there are 2 isomers of C3H7

If R1 = C4H9 then R2 = H. That\'s not an ester. If R2 = H, it\'s a carboxylic acid.

So of the formate ester, 4 structural isomers one of which is chiral and has two stereoisomers for a total of 5 isomers

of the acetate ester, 2 structural isomers

of the propionate ester, 1 structural isomer

of the butrate ester, 2 structural isomers

no pentanoate esters

A total of 9 structural isomers one of which is chiral for a total of 10 isomers.

 1.Help me solve pic problem steps by steps. As much as possible. 2.Also add a questions or conjecture after it ( for example, could we have finite order elemen
 1.Help me solve pic problem steps by steps. As much as possible. 2.Also add a questions or conjecture after it ( for example, could we have finite order elemen

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