To determine the molar mass of copper(II) nitrate, [tex]\( \text{Cu(NO}_3\text{)}_2 \)[/tex], we need to add the molar masses of all the atoms in the compound. Here are the steps:
1. Identify the atomic masses:
- Copper (Cu): [tex]\( 63.55 \, \text{g/mol} \)[/tex]
- Nitrogen (N): [tex]\( 14.01 \, \text{g/mol} \)[/tex]
- Oxygen (O): [tex]\( 16.00 \, \text{g/mol} \)[/tex]
2. Break down the formula and count the atoms:
- 1 atom of Copper (Cu)
- 2 atoms of Nitrogen (N), since we have two nitrate groups [tex]\( (NO_3) \)[/tex] and each contains one nitrogen atom
- 6 atoms of Oxygen (O), since each nitrate group [tex]\( (NO_3) \)[/tex] has 3 oxygen atoms and we have two nitrate groups
3. Calculate the contributions of each element:
- The mass contributed by Copper:
[tex]\[
1 \times 63.55 \, \text{g/mol} = 63.55 \, \text{g/mol}
\][/tex]
- The mass contributed by Nitrogen:
[tex]\[
2 \times 14.01 \, \text{g/mol} = 28.02 \, \text{g/mol}
\][/tex]
- The mass contributed by Oxygen:
[tex]\[
6 \times 16.00 \, \text{g/mol} = 96.00 \, \text{g/mol}
\][/tex]
4. Sum the total molar mass:
[tex]\[
63.55 \, \text{g/mol} + 28.02 \, \text{g/mol} + 96.00 \, \text{g/mol} = 187.57 \, \text{g/mol}
\][/tex]
Therefore, the molar mass of copper(II) nitrate, [tex]\( \text{Cu(NO}_3\text{)}_2 \)[/tex], is [tex]\( \boxed{187.57 \, \text{g/mol}} \)[/tex].
