41. Sample Problem 42-6 gives the fraction of silicon atoms that must be replaced by phosphorus atoms. We
find the number the silicon atoms in 1.0 g, then the number that must be replaced, and finally the mass
of the replacement phosphorus atoms. The molar mass of silicon is 28.086 g/mol, so the mass of one
silicon atom is (28.086 g/mol)/(6.022 × 1023 mol-1) =4.66 × 10-23 g and the number of atoms in 1.0g
is (1.0g)/(4.66 × 10-23 g) = 2.14 × 1022. According to Sample Problem 42-6 one of every 5 × 106 silicon
atoms is replaced with a phosphorus atom. This means there will be (2.14×1022)/(5×106) =4.29×1015
phosphorus atoms in 1.0 g of silicon. The molar mass of phosphorus is 30.9758 g/mol so the mass of a
phosphorus atom is (30.9758 g/mol)/(6.022 × 10-23 mol-1) =5.14 × 10-23 g. The mass of phosphorus
that must be added to 1.0 g of silicon is (4.29 × 1015)(5.14 × 10-23 g) = 2.2 × 10-7 g.
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