Carbon and sulfur form compounds with the formulas \(\mathrm{CS}_{2}\) and \(\mathrm{C}_{3} \mathrm{~S}_{2} .\) Draw Lewis structures and predict the shapes of these two compounds.

To begin, let's count the total number of valence electrons for each compound. For CS2: Carbon (C) has 4 valence electrons and sulfur (S) has 6 valence electrons. Therefore, the total number of valence electrons in the CS2 compound is: \[4 + 2\times6 = 16 \text{ valence electrons}\] For C3S2: There are three carbon atoms and two sulfur atoms. So, the total valence electrons in the C3S2 compound are: \[3\times4 + 2\times6 = 22 \text{ valence electrons}\]

Next, we will draw the Lewis structures for both compounds. - For CS2: Place the carbon atom in the center and connect it with two sulfur atoms using single bonds. The resulting structure shows 8 valence electrons being used. Distribute the remaining 8 valence electrons to complete the octets of sulfur atoms. We end up with the following Lewis structure: \[ \text{S} \equiv \text{C} \equiv \text{S} \] - For C3S2: Start with a linear arrangement of three carbon atoms (C-C-C) and single-bond them to two sulfur atoms (S-C-C-C-S). Initially, 12 valence electrons are used. Distribute the remaining 10 valence electrons to satisfy the octet rule. We obtain the following Lewis structure: \[ \text{S} \equiv \text{C} - \text{C} - \text{C} \equiv \text{S} \]

Finally, let's predict the shapes of these compounds using the VSEPR theory, which states that electron pairs surrounding a central atom will arrange themselves to minimize repulsion. - For CS2: There are two electron pairs around the central carbon atom. According to VSEPR theory, the shape of the molecule will be linear. - For C3S2: The shape of this molecule can be broken down into individual carbon atoms: 1. The left and right carbon atoms each have three electron pairs (one single bond with another carbon, one double bond with sulfur, and one lone pair). According to VSEPR theory, they are trigonal planar. 2. The middle carbon atom has two electron pairs (two single bonds with carbon atoms). Its shape is linear. In summary, the overall shape of C3S2 can be described as a combination of a linear arrangement of trigonal planar structures.