Hi Michelle! I'll take a stab at the EK questions for you. 😀
Q41:
When you're looking for a compound that can exist in cis or trans form, FOCUS ONLY ON THE DOUBLE BOND.
To exist as cis/trans isomers, the carbons that are double-bonded must EACH be attached to two different constituents.
Take a look at C:
The carbon on the right side of the double bond is attached to a methyl group (CH3) and a hydrogen (not drawn, but implied). So far so good.
The carbon on the left side of the double bond is attached to the top of a six membered ring and the bottom of a six membered ring. Since this ring is symmetrical, this carbon is TECHNICALLY attached to "two of the same thing". So, we can eliminate C because it doesn't fit the criterion of "both carbons being attached to TWO different constituents".
Take a look at D:
The carbon on the right side of the double bond is attached to two hydrogens (not drawn, but implied). We can therefore eliminate D.
Draw out B:
https://upload.wikimedia...methyl-2-butene.svg.png
The carbon on the left side of the double bond is attached to two methyl groups (CH3). We can eliminate B.
Therefore, A is the best answer.
Q44:
When you are looking for a compound that IS optically active, you want it to have a chiral center. When a carbon is attached to four different constituents, it's a chiral center.
When you have TWO chiral centers in a molecule, there is the possibility that you have a meso compound. A meso compound is the chemistry equivalent of the spiderman meme:
https://i.redd.it/bekphnqftcb41.jpg
One half of the molecule is a mirror image of the other one.
If that's true, then EVEN THOUGH there are two chiral centers, the molecule IS NOT OPTICALLY ACTIVE (meaning that it doesn't "rotate light").
OK... so how do we spot the meso compound?
With Fischer projections, it's relatively simple. We need to look for the Fischer projection that has a "mirror plane". Something that looks like this:
https://chem.libretexts.org/@api/deki/files/1574/Meso2_(5).bmp?revision=1
But wait... none of them look like that. 😫
Recall that SINGLE bonds can SPIN. So, we need to try spinning the top half of each of the available answers, and then see if we get a mirror plane.
https://chem.libretexts.org/@api/deki/files/1577/rotated_(1).bmp?revision=1
Trying this out, we can then see that B is the only answer.
Oh boy... what a question. 😣