Molar Mass: The Bridge between Mass and Moles
A balance measures mass, while chemical equations use amounts in moles. Molar mass connects these two descriptions of a sample.
1. Definition and unit
Molar mass, symbol (M), is the mass of one mole of a substance. It is defined by:
common unit: \(\text{g mol}^{-1}\) or g/mol
Here (m) is sample mass in grams and (n) is amount of substance in moles. The unit g/mol means grams for each mole. Molar mass is a property of the substance; sample mass changes with sample size.
2. From a chemical formula to molar mass
Calculate relative formula mass (M_r) by adding all atomic contributions. The numerical value of the molar mass in g/mol is the same as the (M_r) value, although the quantities are different: (M_r) has no unit, while (M) has unit g/mol.
| Substance | Formula calculation | Molar mass |
|---|---|---|
| H2O | (2\cdot1+16=18) | 18 g/mol |
| CO2 | (12+2\cdot16=44) | 44 g/mol |
| NaCl | (23+35.5=58.5) | 58.5 g/mol |
3. The mass–mole equations
Find mass
\(m=nM\)
Multiply moles by grams per mole.
Find moles
\(n=\dfrac{m}{M}\)
Divide grams by grams per mole.
Find molar mass
\(M=\dfrac{m}{n}\)
Divide sample mass by its amount.
4. Unit analysis as a safety check
Units reveal the correct operation. For mass, ( ext{mol}\times ext{g/mol}= ext{g}). For amount, ( ext{g}\div ext{g/mol}= ext{mol}). If unwanted units do not cancel, the setup is wrong. Always write units during substitution, not only in the final answer.
5. A reliable problem-solving path
- Write the formula and calculate (M) from atomic masses.