In 1961 , scientists agreed that the atomic mass unit (amu) would be defined as $\frac{1}{12}$ the mass of an atom of $^{12} \mathrm{C}$ . Before then, it was defined as $\frac{1}{16}$ the average mass of an atom of naturally occurring oxygen (a mixture of $^{16} \mathrm{O}, 17 \mathrm{O},$ and $^{18} \mathrm{O} ) .$ The current atomic mass of oxygen is 15.9994 amu. (a) Did Avogadro's number change after the definition of an amu changed and, if so, in what direction? (b) Did the definition of the mole change? (c) Did the mass of a mole of a substance change? (d) Before 1961 , was Avogadro's number $6.02 \times 10^{23}$ (to three significant figures), as it

is today?

## Discussion

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Determine the empirical and molecular formulas of each of the following substances:

(a) Styrene, a compound used to make Styrofoam' cups and insulation, contains 92.3$\% \mathrm{C}$ and 7.7$\% \mathrm{H}$ by mass and has a molar mass of 104 $\mathrm{g} / \mathrm{mol} .$

(b) Caffeine, a stimulant found in coffee, contains 49.5$\% \mathrm{C}$ , $5.15 \% \mathrm{H}, 28.9 \% \mathrm{N},$ and 16.5$\% \mathrm{O}$ by mass and has a molar mass of 195 $\mathrm{g} / \mathrm{mol} .$

(c) Monosodium glutamate (MSG), a flavor enhancer in certain foods, contains $35.51 \% \mathrm{C}, 4.77 \% \mathrm{H}, 37.85 \% \mathrm{O}$ , $8.29 \% \mathrm{N},$ and 13.60$\% \mathrm{Na}$ , and has a molar mass of 169 $\mathrm{g} / \mathrm{mol} .$

A hydrate of copper(II) chloride has the following formula: $\mathrm{CuCl}_{2} \cdot x \mathrm{H}_{2} \mathrm{O}$ . The water in a $3.41-\mathrm{g}$ sample of the hydrate is driven off by heating. The remaining sample has a mass of 2.69 $\mathrm{g}$ .Find the number of waters of hydration $(x)$ in the hydrate.

Determine the empirical and molecular formulas of each of the following substances:

(a) Ibuprofen, a headache remedy, contains 75.69$\% \mathrm{C}$ , $8.80 \% \mathrm{H},$ and 15.51$\% \mathrm{O}$ by mass and has a molar mass of 206 $\mathrm{g} / \mathrm{mol} .$

(b) Cadaverine, a foul-smelling substance produced by the action of bacteria on meat, contains 58.55$\% \mathrm{C}$ , $13.81 \% \mathrm{H},$ and 27.40$\% \mathrm{N}$ by mass; its molar mass is 102.2 $\mathrm{g} / \mathrm{mol}$

(c) Epinephrine (adrenaline), a hormone secreted into the bloodstream in times of danger or stress, contains 59.0$\%$ C, $7.1 \% \mathrm{H}, 26.2 \% \mathrm{O},$ and 7.7$\% \mathrm{N}$ by mass; its molar mass is about 180 amu.

Calculate the relative rate of diffusion of $^{1} \mathrm{H}_{2}$ (molar mass 2.0 g/mol) compared to that of $^{2} \mathrm{H}_{2}$ (molar mass 4.0 g/mol) and the relative rate of diffusion of $\mathrm{O}_{2}$ (molar mass 32 g/mol) compared to that of $\mathrm{O}_{3}$ (molar mass 48 g/mol).

Heavy water, $\mathrm{D}_{2} \mathrm{O}$ (molar mass $=20.03 \mathrm{g} \mathrm{mol}^{-1} ),$ can be separated from ordinary water, $\mathrm{H}_{2} \mathrm{O}$ (molar mass $=$ 18.01), as a result of the difference in the relative rates of diffusion of the molecules in the gas phase. Calculate the

relative rates of diffusion of $\mathrm{H}_{2} \mathrm{O}$ and $\mathrm{D}_{2} \mathrm{O}$

Serotonin is a compound that conducts nerve impulses in the brain. It contains $68.2 \% \mathrm{C}, 6.86 \% \mathrm{H}, 15.9 \% \mathrm{N},$ and 9.08$\% \mathrm{O}$ . Its molar mass is 176 $\mathrm{g} / \mathrm{mol} .$ Determine its molecular formula.

How many grams are in each of the following samples?

a. 1.000 mol $\mathrm{NaCl}$ (molar mass of $\mathrm{NaCl}=$

58.44 $\mathrm{g} / \mathrm{mol} )$

b. 2.000 $\mathrm{mol} \mathrm{H}_{2} \mathrm{O}$ (molar mass of $\mathrm{H}_{2} \mathrm{O}=$

18.02 $\mathrm{g} / \mathrm{mol} )$

c. 3.5 $\mathrm{mol} \mathrm{Ca}(\mathrm{OH})_{2}$ (molar mass of

$\mathrm{Ca}(\mathrm{OH})_{2}=74.10 \mathrm{g} / \mathrm{mol} )$