To determine the molar mass of the compound [tex]\( \text{Zn}\left(\text{C}_2\text{H}_3\text{O}_2\right)_2 \)[/tex], we need to sum the molar masses of all the atoms present in the compound. Here is a step-by-step calculation:
1. Identify the elements and their respective quantities within the compound:
- The chemical formula [tex]\( \text{Zn}\left(\text{C}_2\text{H}_3\text{O}_2\right)_2 \)[/tex] consists of:
- 1 Zinc (Zn)
- 2 groups of [tex]\( \text{C}_2\text{H}_3\text{O}_2 \)[/tex]
2. Find the atomic mass of each element from the periodic table and round to hundredths:
- [tex]\( \text{Zn} \)[/tex] (Zinc): 65.38 g/mol
- [tex]\( \text{C} \)[/tex] (Carbon): 12.01 g/mol
- [tex]\( \text{H} \)[/tex] (Hydrogen): 1.01 g/mol
- [tex]\( \text{O} \)[/tex] (Oxygen): 16.00 g/mol
3. Calculate the molar mass of one [tex]\( \text{C}_2\text{H}_3\text{O}_2 \)[/tex] group:
- [tex]\( 2 \times \text{C} \)[/tex] = [tex]\( 2 \times 12.01 \)[/tex] g/mol = 24.02 g/mol
- [tex]\( 3 \times \text{H} \)[/tex] = [tex]\( 3 \times 1.01 \)[/tex] g/mol = 3.03 g/mol
- [tex]\( 2 \times \text{O} \)[/tex] = [tex]\( 2 \times 16.00 \)[/tex] g/mol = 32.00 g/mol
Total for [tex]\( \text{C}_2\text{H}_3\text{O}_2 \)[/tex] = 24.02 g/mol + 3.03 g/mol + 32.00 g/mol = 59.05 g/mol
4. Since there are two [tex]\( \text{C}_2\text{H}_3\text{O}_2 \)[/tex] groups in the compound, multiply the molar mass by 2:
- 2 \times 59.05 g/mol = 118.10 g/mol
5. Add the molar mass of Zinc (Zn):
- [tex]\( 118.10 \)[/tex] g/mol (from two [tex]\( \text{C}_2\text{H}_3\text{O}_2 \)[/tex] groups) + [tex]\( 65.38 \)[/tex] g/mol (for Zn)
6. Combine the molar masses to get the total molar mass of the compound:
- 118.10 g/mol + 65.38 g/mol = 183.48 g/mol
Therefore, the molar mass of [tex]\( \text{Zn}\left(\text{C}_2\text{H}_3\text{O}_2\right)_2 \)[/tex] is 183.48 g/mol. The correct answer among the options given is:
[tex]\[ \boxed{183.48 \, \text{g/mol}} \][/tex]
