An atom of gold has a mass of 3.271 times 10^-22g. How many atoms of gold are in 5.00g of gold?
3.271E-22 g Au/atom x #atoms = 5.00 g.
Solve for # atoms.
To determine the number of atoms in a given mass of gold, we need to use the concept of molar mass and Avogadro's number.
1. Start by calculating the molar mass of gold (Au) by referring to the periodic table. The molar mass of gold is 196.97 g/mol.
2. Now, we can find the number of moles of gold in 5.00 g. We use the formula:
Moles = Mass / Molar Mass
Moles = 5.00 g / 196.97 g/mol = 0.0254 mol
3. Next, we need to use Avogadro's number, which states that one mole of any substance contains 6.022 x 10^23 particles (atoms, molecules, etc.). We can calculate the number of atoms in 0.0254 mol using this conversion factor:
Number of atoms = Moles x Avogadro's number
Number of atoms = 0.0254 mol x 6.022 x 10^23 atoms/mol
Number of atoms = 1.53 x 10^22 atoms
Therefore, there are approximately 1.53 x 10^22 atoms of gold in 5.00g of gold.