Calculating the Molar Mass of Carbon Dioxide

Easy

Problem

Using standard atomic weights (C = 12.011 u, O = 15.999 u), calculate the molar mass of carbon dioxide, CO2.

Given

Atomic weight of carbon: 12.011 u
Atomic weight of oxygen: 15.999 u
Formula of carbon dioxide: CO2 (1 C atom, 2 O atoms per molecule)

Find

The molar mass of CO2 in g/mol.

Principle

Molar mass is additive: the mass of one mole of a compound equals the sum of the masses of one mole of each atom in its formula, multiplied by the subscripts. Because the unified atomic mass unit (u) and the gram per mole scale are numerically identical, atomic weights in u can be added directly to give g/mol.

Formula

M(\mathrm{CO_2}) = M(\mathrm{C}) + 2\,M(\mathrm{O})

M(CO2) = M(C) + 2 x M(O)

Solution

Identify the atoms in one CO2 molecule: 1 carbon atom and 2 oxygen atoms.
Contribution of carbon: 1 x 12.011 u = 12.011 u.
Contribution of oxygen: 2 x 15.999 u = 31.998 u.
Total: 12.011 + 31.998 = 44.009 u per molecule.
Convert units: 44.009 u = 44.009 g/mol for one mole of CO2.

M(CO2) = 44.009 g/mol.

Unit check

Atomic weights are added in the same unit (u), and the u-to-g/mol equivalence applies uniformly, so the sum carries g/mol directly — a mass per mole, exactly what molar mass requires.

What this means physically

One mole of carbon dioxide (44.009 g, about the mass of two golf balls) contains 6.022 x 10^23 CO2 molecules. This number is the key bridge used in nearly every stoichiometry calculation involving CO2.

Common mistake

Students frequently forget to multiply oxygen's atomic weight by its subscript of 2 and get 28.010 g/mol instead. Always multiply each element's weight by the number of atoms of that element in the formula.