Convert the following to moles. (a) \(4.00 \times 10^{3} \mathrm{~g}\) of hydrazine, a rocket propellant (b) \(12.5 \mathrm{~g}\) of tin(II) fluoride, the active ingredient in fluoride toothpaste (c) \(13 \mathrm{~g}\) of caffeine, \(\mathrm{C}_{4} \mathrm{H}_{5} \mathrm{~N}_{2} \mathrm{O}\)

To find the molar mass of a compound, we must first identify the molecular formula of that compound and then add the molar masses of all the atoms present in the compound. (a) Hydrazine: \(\mathrm{N}_{2}\mathrm{H}_{4}\) Molar mass: \(2 \cdot \mathrm{(N) +} 4 \cdot \mathrm{(H)} = 2\cdot(14.01 \mathrm{g/mol}) + 4\cdot(1.008 \mathrm{g/mol}) = 32.04 \mathrm{g/mol}\) (b) Tin(II) fluoride: \(\mathrm{SnF}_{2}\) Molar mass: \(1 \cdot \mathrm{(Sn)} + 2 \cdot \mathrm{(F)} = 1\cdot(118.71 \mathrm{g/mol}) + 2\cdot(19.00 \mathrm{g/mol}) = 156.71 \mathrm{g/mol}\) (c) Caffeine: \(\mathrm{C}_{8}\mathrm{H}_{10}\mathrm{N}_{4}\mathrm{O}_{2}\) Molar mass: \(8 \cdot \mathrm{(C)} + 10 \cdot \mathrm{(H)} + 4 \cdot \mathrm{(N)} + 2 \cdot \mathrm{(O)} = 8\cdot(12.01 \mathrm{g/mol}) + 10\cdot(1.008 \mathrm{g/mol}) + 4\cdot(14.01 \mathrm{g/mol}) + 2\cdot(16.00 \mathrm{g/mol}) = 194.19 \mathrm{g/mol}\)

To find the number of moles, divide the mass of the substance by its molar mass. (a) Moles of hydrazine: \(\dfrac{4.00 \times 10^{3} \mathrm{~g \; of \; hydrazine}}{32.04 \mathrm{g/mol}} = 124.84 \ \mathrm{moles}\) (b) Moles of tin(II) fluoride: \(\dfrac{12.5 \mathrm{~g \; of \; tin(II) \, fluoride}}{156.71 \mathrm{g/mol}} = 0.0797 \ \mathrm{moles}\) (c) Moles of caffeine: \(\dfrac{13 \mathrm{~g \; of \; caffeine}}{194.19 \mathrm{g/mol}} = 0.0669 \ \mathrm{moles}\) In conclusion: a) There are \(124.84 \, \mathrm{moles}\) of hydrazine b) There are \(0.0797 \, \mathrm{moles}\) of tin(II) fluoride c) There are \(0.0669 \, \mathrm{moles}\) of caffeine