Avogadro's Number — Question 1

Question 1

Molecules and constituent atoms are different counting units

Use $N_A=6.02214076\times10^{23}\,\mathrm{mol^{-1}}$, exact. A 9.00 g sample of pure water has assigned molar mass 18.0 g/mol. Each molecule contains two hydrogen atoms and one oxygen atom. Treat the assigned molar mass as exact for this exercise.

1. Find amounts and counts of water molecules, hydrogen atoms and all atoms.

2. How much water would contain exactly the same number of molecules as the original sample contains hydrogen atoms?

Question 1 - Solution

Molecules and constituent atoms are different counting units

(a) Method and calculation

$$n_{\mathrm{water}}=m/M=9.00/18.0=.500\,\mathrm{mol},\quad N_{\mathrm{water}}=.500N_A=3.01107038\times10^{23}.$$$$n_H=1.00\,\mathrm{mol},\quad N_H=N_A;\qquad n_{\mathrm{atoms}}=1.50\,\mathrm{mol},\quad N_{\mathrm{atoms}}=9.03321114\times10^{23}.$$

(b) Interpretation and further calculation

$$N_{\mathrm{new}}=N_H=N_A\ \Rightarrow\ n_{\mathrm{new}}=1.00\,\mathrm{mol}.$$$$m_{\mathrm{new}}=n_{\mathrm{new}}M=18.0\,\mathrm g.$$The factor of two comes from the specified constituent count, not from a change in Avogadro's constant.

Physical check

A mole must name its entities; a mole of atoms and a mole of molecules are not interchangeable.