Draw the possible chair forms of cis and trans 1-isopropyl-3-methylcyclohexane. Are the two forms identical, enantiomeric, or diastereomeric? In each case, indicate which chair term will be more stable and explain why. Is either of these molecules chiral?
The most important thing to understand when trying to draw cis and trans cyclohexanes is knowing the "up" and "down" positions. For instance when we say this cyclohexane has 2 cis groups it means that both groups are either "up" or both are "down". Up and down will change to "axial or equatorial" depending on the carbon they are situated on. According to the figure above if we start counting from the carbon containing the isopropul group (1st structure). I can tell you that carbons 1,3, and 5 have the "up" as an axial position and the down as equatorial. As for carbons 2,4,6 will have the "up" as equatorial and the down as axial.
You can see from the attached ...
In both situations I've shown a chair flip that shows you how one configuration can change to another. Make sure you understand that the ones where it shows chair flips are exactly the same structure with the same stereo chemistry. However one configuration is more stable than the other (the one with more equatorial positions occupied... or with the bulky groups in equatorial position).
A molecule could be chiral if it has one or more carbons that contain 4 different groups (this is by far the simplest definition of the term).