Suppose you inherit 3.00 mol of gold from your uncle (an eccentric chemist) at a time when this metal is selling for $14.75 per gram. Consult the periodic table in Appendix D and Table 12.1. (a) To the nearest dollar, what is this gold worth? (b) If you have your gold formed into a spherical nugget, what is its diameter?
Solution 23E Introduction We will first calculate the molar mass of gold. From the molar mass we can find the mass of the inherited gold and the the price of the gold. And from the mass and density of the gold, we can calculate the volume and from volume we can calculate the diameter of the gold nugget. Step 1 The atomic mass number of gold is 197. And since gold is monatomic solid, we the molar mass of the gold is M = 197 g/mol . I have inherited 3.00 mol of gold, hence the mass of inherited gold is m = Mn = (197 g/mol)(3.00 mol) = 591 g Now the price of gold is $14.75 per gram. Hence the price of the inherited gold is ($14.75/g)(591 g) = $8717.2 So the price of the gold rounded to the nearest dollar is $8717.