Please help I have no idea how to do this.

There are three different dichloroethylenes (molecular formulaC2H2Cl2), which we can designate X, Y, and Z.
Compound X has no dipole moment, but compound Z does.
Compounds X and Z each combine with hydrogen to give the same product:

C2H2Cl2 (X or Z) + H2 → ClCH2single bondCH2Cl.

What are the structures of X, Y, and Z? (Draw complete Lewis structures. Assign lone pairs, radical electrons, and atomic charges where appropriate.)

We can't draw diagrams on this forum. You have three isomers of C2H2Cl2. They are given below and you can (should) draw the structures from this.

1,1-dichloroethylene
1,2-dichloroethylene (the cis form)
1,2-dichloroethylene (the trans form)

Draw all of th structures so you can see what they look like. The trans form is the one with no dipole moment. The 1,1 is the one with a dipole moment. The third one is the one that's left. Hope this helps.

To determine the structures of compounds X, Y, and Z, we need to first understand the information given about each compound.

1. Compound X has no dipole moment: This suggests that compound X is symmetrical and nonpolar.

2. Compound Z has a dipole moment: This suggests that compound Z is asymmetrical and polar.

3. Compounds X and Z each combine with hydrogen to give the same product: This indicates that X and Z have the same molecular formula and, consequently, the same number of atoms of each element.

Based on this information, let's approach the problem step by step:

Step 1: Start with compound X which is nonpolar. When drawing the Lewis structure for X, we can assume that the carbon atoms in X are connected by a double bond, and then add the chlorine atoms to complete the structure. Remember that carbon needs to form four bonds and chlorine requires only one.

The Lewis structure for compound X will look like this:

Cl Cl
| |
C = C

Step 2: Next, determine compound Z, which is polar. The presence of a dipole moment indicates an asymmetrical distribution of charge. Since compounds X and Z have the same molecular formula and H2 combines with both to give the same product, compound Z must be a structural isomer of X.

One possible isomer for X would be if both chlorine atoms were on the same carbon atom:

Cl Cl
\ /
C = C

However, this structure would not result in a dipole moment as the chlorine atoms would cancel each other's dipole. Therefore, compound Z must have the chlorine atoms on different carbon atoms:

Cl Cl
| |
C = C

Step 3: Finally, compound Y can be determined by the process of elimination. Since compounds X and Z have been assigned structures, Y must be the remaining isomer of C2H2Cl2. In this case, both chlorine atoms are on the same carbon atom:

Cl-Cl
|
C = C

This completes the Lewis structure for compound Y.

To summarize, the structures of X, Y, and Z are as follows:

X: Cl Cl
\ /
C = C

Y: Cl - Cl
|
C = C

Z: Cl Cl
| |
C = C

Remember that this is one possible set of isomeric structures for compounds X, Y, and Z. There may be other valid structures as well.