### Question 1: Skeletal Structure You are asked to draw the skeletal ("line") structure for the molecule: ``` CH3 | CH3-N-C-CH3 || O ``` **Step-by-step for drawing the skeletal structure:** 1. **Identify the main chain and branches:** - The main chain is N─C. - The N is bonded to two CH₃ groups (methyl), and the C is double-bonded to O (carbonyl) and single-bonded to a CH₃ group. 2. **Skeletal structure conventions:** - Carbon atoms are represented by vertices. - Hydrogen atoms attached to carbons are not shown. - Heteroatoms (N, O) and their attached hydrogens are shown. 3. **Draw the structure:** - Start with the N─C chain. - Attach a methyl group (line) to each side of N. - Attach a carbonyl group (=O) to the C. - Attach a methyl group to the C. **The skeletal structure should look like this:** ``` CH3 | CH3--N--C--CH3 || O ``` But in line structure, it would look like: ``` (CH3)2N-C(=O)-CH3 ``` Or, as a skeletal line diagram: ``` N / \ CH3 C--CH3 || O ``` --- ### Question 2: Calculation of Mg Atom Radius **Given Data:** - Atoms are spherical and do not fill all the space in a cube. - Only 74.0% of the space inside the cube is filled by Mg atoms. **To Find:** The radius (r) of a Mg atom in picometers. #### Solution Steps 1. **Let the cube have side length \( a \).** - Volume of cube: \( V_{cube} = a^3 \) - Volume occupied by spheres: \( 0.74 \times a^3 \) 2. **Assume the cube contains 1 atom for simplicity (or use FCC, BCC info if given):** - Volume of one sphere: \( V_{sphere} = \frac{4}{3} \pi r^3 \) 3. **Set up the equation:** \[ \frac{4}{3} \pi r^3 = 0.74 a^3 \] - If the packing type (FCC, BCC, etc.) is not specified, this is the general equation based on percent fill. 4. **Solving for \( r \):** \[ r^3 = \frac{0.74 a^3}{\frac{4}{3} \pi} \] \[ r^3 = \frac{0.74 \times 3 a^3}{4 \pi} \] \[ r = a \left( \frac{0.74 \times 3}{4 \pi} \right)^{1/3} \] 5. **To get a numeric answer, you need the value of \( a \) (cube side length) or more info about the unit cell.** - If you are just asked for the formula in terms of \( a \), use the equation above. **If you have the cube's side length, plug it in. If not, you can only give the answer in terms of \( a \):** \[ \boxed{r = a \left( \frac{0.74 \times 3}{4 \pi} \right)^{1/3}} \] - To convert to picometers, ensure \( a \) is also in picometers. --- If you provide the value for the cube's side length, I can calculate the exact radius in picometers for you!