To determine whether a molecule with an accurate mass of 60.0574 is 1,2-diaminoethane (C₂H₈N₂) or propan-1-ol (C₃H₈O), we need to calculate the molecular masses of both compounds and compare them to the given accurate mass.
### Step 1: Molecular Mass of 1,2-Diaminoethane (C₂H₈N₂)
1,2-Diaminoethane has the molecular formula C₂H₈N₂. The atomic masses of the constituent elements are:
- Carbon (C): 12.0107
- Hydrogen (H): 1.00794
- Nitrogen (N): 14.0067
Using these atomic masses, we can calculate the molecular mass of 1,2-diaminoethane as follows:
[tex]\[
M_{\text{C}_2\text{H}_8\text{N}_2} = 2 \times 12.0107 + 8 \times 1.00794 + 2 \times 14.0067
\][/tex]
Perform the multiplications:
[tex]\[
2 \times 12.0107 = 24.0214
\][/tex]
[tex]\[
8 \times 1.00794 = 8.06352
\][/tex]
[tex]\[
2 \times 14.0067 = 28.0134
\][/tex]
Add these results together to get the molecular mass:
[tex]\[
M_{\text{C}_2\text{H}_8\text{N}_2} = 24.0214 + 8.06352 + 28.0134 = 60.09832
\][/tex]
### Step 2: Molecular Mass of Propan-1-ol (C₃H₈O)
Propan-1-ol has the molecular formula C₃H₈O. The atomic masses of the constituent elements are:
- Carbon (C): 12.0107
- Hydrogen (H): 1.00794
- Oxygen (O): 15.9994
Using these atomic masses, we can calculate the molecular mass of propan-1-ol as follows:
[tex]\[
M_{\text{C}_3\text{H}_8\text{O}} = 3 \times 12.0107 + 8 \times 1.00794 + 1 \times 15.9994
\][/tex]
Perform the multiplications:
[tex]\[
3 \times 12.0107 = 36.0321
\][/tex]
[tex]\[
8 \times 1.00794 = 8.06352
\][/tex]
[tex]\[
1 \times 15.9994 = 15.9994
\][/tex]
Add these results together to get the molecular mass:
[tex]\[
M_{\text{C}_3\text{H}_8\text{O}} = 36.0321 + 8.06352 + 15.9994 = 60.09502
\][/tex]
### Step 3: Comparing the Calculated Molecular Masses with the Accurate Mass
Now we compare the calculated molecular masses with the given accurate mass of 60.0574:
- The molecular mass of 1,2-diaminoethane (C₂H₈N₂) is 60.09832.
- The molecular mass of propan-1-ol (C₃H₈O) is 60.09502.
To determine which one is closer to the accurate mass:
- Difference for 1,2-diaminoethane:
[tex]\[
|60.09832 - 60.0574| = 0.04092
\][/tex]
- Difference for propan-1-ol:
[tex]\[
|60.09502 - 60.0574| = 0.03762
\][/tex]
### Step 4: Conclusion
Since the difference between the molecular mass of propan-1-ol (C₃H₈O) and the accurate mass (0.03762) is smaller than the difference for 1,2-diaminoethane (C₂H₈N₂) (0.04092), the molecule with an accurate mass of 60.0574 is more likely to be propan-1-ol.
Therefore, the molecule is propan-1-ol (C₃H₈O).
