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?

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Tooth enamel is composed of hydroxyapatite, whose simplest formula is $\mathrm{Ca}_{5}\left(\mathrm{PO}_{4}\right)_{3} \mathrm{OH}$ , and whose corresponding $K_{\mathrm{sp}}=6.8 \times 10^{-27}$ . As discussed in the Chemistry and Life box on page $746,$ fluoride in fluorinated water or in toothpaste reacts with hydroxyapatite to form fluoroapatite, $\mathrm{Ca}_{5}\left(\mathrm{PO}_{4}\right)_{3} \mathrm{F},$ whose $K_{s p}=1.0 \times 10^{-60}$ (a) Write the expression for the solubility-constant for hydroxyapatite and for fluoroapatite. (b) Calculate the molar solubility of each of these compounds.

Consider the following unbalanced equation:

$$

\mathrm{Ca}_{3}\left(\mathrm{PO}_{4}\right)_{2}(s)+\mathrm{H}_{2} \mathrm{SO}_{4}(a q) \longrightarrow \mathrm{CaSO}_{4}(s)+\mathrm{H}_{3} \mathrm{PO}_{4}(a q)

$$

What masses of calcium sulfate and phosphoric acid can be produced from the reaction of 1.0 $\mathrm{kg}$ calcium phosphate with 1.0 $\mathrm{kg}$ concentrated sulfuric acid $\left(98 \% \mathrm{H}_{2} \mathrm{SO}_{4} \text { by mass)? }\right.$