Final answer:
The mass of a gold sample containing 1.12 x 10^24 atoms of gold is approximately 366.57 grams, calculated using Avogadro's number and the molar mass of gold.
Step-by-step explanation:
Calculating the Mass of Gold Sample
To find the mass of a gold (Au) sample containing 1.12 x 10^24 atoms, we use Avogadro's number and the molar mass of gold. Avogadro's number (6.022 x 10^23) is the number of atoms in one mole of any substance. The molar mass of gold, derived from the periodic table, is 196.97 g/mol. This means every mole of gold has a mass of 196.97 grams.
First, calculate the number of moles of gold by dividing the number of atoms in the sample by Avogadro's number:
Number of moles = 1.12 x 10^24 atoms / 6.022 x 10^23 atoms/mol
This yields approximately 1.86 moles of gold.
Next, to find the mass of these moles, multiply by the molar mass of gold:
Mass of gold = Number of moles x Molar mass of gold
Mass of gold = 1.86 moles x 196.97 g/mol
The mass of the gold sample is therefore approximately 366.57 grams.