Final answer:
To determine the grams of gold that can be extracted from 257 grams of gold (III) fluoride, the mass of the compound is divided by its molar mass and then multiplied by the molar mass of gold to get the extractable gold mass.
Step-by-step explanation:
To calculate how many grams of gold can be extracted from 257 grams of gold (III) fluoride, we first need the formula and molar mass of gold (III) fluoride, which is AuF3. The molar mass of AuF3 is the sum of the molar mass of gold (Au, 196.97 g/mol) and three times the molar mass of fluorine (F, 19.00 g/mol), resulting in 253.97 g/mol. To find out how many moles of AuF3 the 257 grams represents, we divide the mass by the molar mass (257 g ÷ 253.97 g/mol).
Once we have the number of moles of AuF3, we can then calculate the mass of gold that can be extracted. Since each mole of AuF3 contains one mole of gold, the number of moles of gold will be the same as the number of moles of AuF3. Multiplying the number of moles of gold by the molar mass of gold provides the mass of gold that can be extracted.
Therefore, the mass of extractable gold is equal to the mass of AuF3 divided by the molar mass of AuF3 times the molar mass of gold. The exact calculation would give the precise amount of gold that can be extracted from 257 grams of gold (III) fluoride.