- Identify the composition of propane as \(C_3H_8\) (3 carbon atoms and 8 hydrogen atoms).
- Use standard atomic masses: \(12.011 \, \text{g/mol}\) for C and \(1.008 \, \text{g/mol}\) for H.
- Calculate the total molar mass: \(3 \times 12.011 + 8 \times 1.008 = 44.097 \, \text{g/mol}\).
- Round the final result to two decimal places: \(\boxed{44.10} \, \text{g/mol}\).
Explanation
- Identify Atoms and Atomic Masses
Propane is an alkane with the chemical formula \(C_3H_8\). To calculate its molar mass, we must identify the number of atoms for each element and their respective atomic masses. A molecule of propane consists of 3 carbon atoms and 8 hydrogen atoms. We use the standard atomic masses: the atomic mass of carbon (C) is approximately \(12.011 \, \text{g/mol}\), and the atomic mass of hydrogen (H) is approximately \(1.008 \, \text{g/mol}\).
- Calculate Molar Mass
The total molar mass of propane is found by summing the molar masses of all its constituent atoms. The expression for the molar mass (\(M\)) is:
\[M = 3 \times (\text{atomic mass of C}) + 8 \times (\text{atomic mass of H})\]
Substituting the values:
\[M = 3 \times 12.011 + 8 \times 1.008\]
Performing the calculations:
\[M = 36.033 + 8.064 = 44.097 \, \text{g/mol}\]
- Final Rounding and Result
To find the final result rounded to two decimal places, we look at the third decimal digit. Since the digit is 7, which is 5 or greater, we round up the second digit:
\[44.097 \approx 44.10\]
Therefore, the molar mass of propane is \(\boxed{44.10} \, \text{g/mol}\).
Examples
Calculating molar mass is fundamental in chemistry for determining stoichiometric ratios in chemical reactions. For instance, if you are burning propane as a fuel source, knowing the molar mass allows you to calculate how much oxygen is required for complete combustion and how much carbon dioxide will be produced. This is essential for industrial safety, environmental monitoring, and efficient energy production.