Draw; 1,2,3- trimethylcyclohexane using a hexagon to represent the ring. How many cis-trans stereoisomers are possible?

To draw 1,2,3-trimethylcyclohexane, we start by drawing a hexagon to represent the cyclohexane ring. Then, we add three methyl groups (CH3) to the carbon atoms numbered 1, 2, and 3. Here is the structure:

CH3
|
CH3 - C - CH3
|
CH3

Now, let's determine the number of cis-trans stereoisomers possible. In this case, we have three methyl groups attached to the cyclohexane ring. Since the cyclohexane ring is symmetrical, the cis-trans isomerism will only occur between the methyl groups.

To determine the number of cis-trans isomers, we need to consider the relative positions of the methyl groups. Since there are three methyl groups, we can have three different combinations:

1) cis-1,2,3-trimethylcyclohexane: In this isomer, all three methyl groups are on the same side of the ring.
2) cis-1,2,3-trimethylcyclohexane: In this isomer, two methyl groups are on one side of the ring, and one methyl group is on the opposite side.
3) trans-1,2,3-trimethylcyclohexane: In this isomer, all three methyl groups are on opposite sides of the ring.

Therefore, there are three cis-trans stereoisomers possible for 1,2,3-trimethylcyclohexane.