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 calculate the sum of the molar masses of all the atoms present in the compound. Here's a detailed, step-by-step calculation:
1. Identify the number of atoms of each element in the compound:
- Zinc (Zn): There is 1 atom of Zn.
- Carbon (C): The acetate group [tex]\( \left( \text{C}_2\text{H}_3\text{O}_2 \right) \)[/tex] contains 2 carbon atoms, and since there are 2 acetate groups, the total number of carbon atoms is [tex]\( 2 \times 2 = 4 \)[/tex].
- Hydrogen (H): The acetate group [tex]\( \left( \text{C}_2\text{H}_3\text{O}_2 \right) \)[/tex] contains 3 hydrogen atoms, so with 2 acetate groups, the total number of hydrogen atoms is [tex]\( 2 \times 3 = 6 \)[/tex].
- Oxygen (O): The acetate group [tex]\( \left( \text{C}_2\text{H}_3\text{O}_2 \right) \)[/tex] contains 2 oxygen atoms, so with 2 acetate groups, the total number of oxygen atoms is [tex]\( 2 \times 2 = 4 \)[/tex].
2. Determine the atomic masses of each element:
- Molar mass of Zinc (Zn): [tex]\( 65.38 \, \text{g/mol} \)[/tex]
- Molar mass of Carbon (C): [tex]\( 12.01 \, \text{g/mol} \)[/tex]
- Molar mass of Hydrogen (H): [tex]\( 1.01 \, \text{g/mol} \)[/tex]
- Molar mass of Oxygen (O): [tex]\( 16.00 \, \text{g/mol} \)[/tex]
3. Calculate the contribution of each element to the total molar mass:
- Contribution of Zn: [tex]\( 1 \times 65.38 \, \text{g/mol} = 65.38 \, \text{g/mol} \)[/tex]
- Contribution of C: [tex]\( 4 \times 12.01 \, \text{g/mol} = 48.04 \, \text{g/mol} \)[/tex]
- Contribution of H: [tex]\( 6 \times 1.01 \, \text{g/mol} = 6.06 \, \text{g/mol} \)[/tex]
- Contribution of O: [tex]\( 4 \times 16.00 \, \text{g/mol} = 64.00 \, \text{g/mol} \)[/tex]
4. Add the contributions to obtain the total molar mass:
[tex]\[
65.38 \, \text{g/mol} + 48.04 \, \text{g/mol} + 6.06 \, \text{g/mol} + 64.00 \, \text{g/mol} = 183.48 \, \text{g/mol}
\][/tex]
5. Round the total molar mass to the hundredths place (which is already precise in this calculation):
- The molar mass of [tex]\( \text{Zn}\left( \text{C}_2\text{H}_3\text{O}_2 \right)_2 \)[/tex] is [tex]\( 183.48 \, \text{g/mol} \)[/tex].
Therefore, the correct answer is:
C. [tex]\( 183.48 \, \text{g/mol} \)[/tex]
