To calculate the molar mass of [tex]\( NH_4NO_3 \)[/tex], we need to determine the molar masses of the individual atoms present in the compound and then sum them according to the formula of the compound.
1. Identify the composition of [tex]\( NH_4NO_3 \)[/tex]:
- The chemical formula [tex]\( NH_4NO_3 \)[/tex] consists of:
- 2 Nitrogen (N) atoms
- 4 Hydrogen (H) atoms
- 3 Oxygen (O) atoms
2. List the atomic masses:
- The atomic mass of Nitrogen (N) is 14.01 g/mol.
- The atomic mass of Hydrogen (H) is 1.01 g/mol.
- The atomic mass of Oxygen (O) is 16.00 g/mol.
3. Calculate the total molar mass for each type of atom in [tex]\( NH_4NO_3 \)[/tex]:
- For 2 Nitrogen (N) atoms: [tex]\( 2 \times 14.01 \text{ g/mol} = 28.02 \text{ g/mol} \)[/tex]
- For 4 Hydrogen (H) atoms: [tex]\( 4 \times 1.01 \text{ g/mol} = 4.04 \text{ g/mol} \)[/tex]
- For 3 Oxygen (O) atoms: [tex]\( 3 \times 16.00 \text{ g/mol} = 48.00 \text{ g/mol} \)[/tex]
4. Sum the molar masses to find the total molar mass of [tex]\( NH_4NO_3 \)[/tex]:
[tex]\[
28.02 \text{ g/mol} + 4.04 \text{ g/mol} + 48.00 \text{ g/mol} = 80.06 \text{ g/mol}
\][/tex]
Therefore, the molar mass of [tex]\( NH_4NO_3 \)[/tex] is:
[tex]\[
\boxed{80.06 \text{ g/mol}}
\][/tex]
