What mass of rhodium contains as many
atoms as there are zirconium atoms in 51 g of
zirconium?
Answer in units of grams.
mols Zr = 51/91.2 = ? = mols Rh
g Rh = mols Rh x atomic mass Rh = ?
10
To determine the mass of rhodium that contains the same number of atoms as there are zirconium atoms in 51 g of zirconium, we need to use the concept of molar mass and Avogadro's number.
1. Find the number of zirconium atoms:
The periodic table tells us that the molar mass of zirconium (Zr) is approximately 91.22 g/mol. Using this information, we can determine the number of moles of zirconium in 51 g by dividing the mass by the molar mass:
Number of moles of zirconium = mass of zirconium / molar mass of zirconium
Number of moles of zirconium = 51 g / 91.22 g/mol
2. Convert moles to atoms:
One mole of any element contains Avogadro's number of atoms, which is approximately 6.022 × 10^23 atoms/mol. So, to find the number of zirconium atoms in 51 g of zirconium, multiply the number of moles obtained in step 1 by Avogadro's number:
Number of zirconium atoms = Number of moles of zirconium * Avogadro's number
Number of zirconium atoms = (51 g / 91.22 g/mol) * (6.022 × 10^23 atoms/mol)
3. Establish an atomic equivalence:
Rhodium (Rh) has a different molar mass than zirconium, so we need to find the molar mass of rhodium in order to establish an equivalence. The molar mass of rhodium is approximately 102.91 g/mol.
4. Determine the mass of rhodium:
To find the mass of rhodium that contains the same number of atoms as there are zirconium atoms in 51 g of zirconium, we can use the atomic equivalence established in step 3, and solve for the mass of rhodium:
Mass of rhodium = Number of zirconium atoms * (molar mass of rhodium / Avogadro's number)
Mass of rhodium = [(51 g / 91.22 g/mol) * (6.022 × 10^23 atoms/mol)] * (102.91 g/mol / 6.022 × 10^23 atoms/mol)
By performing the calculations, you will find that the answer is approximately 86.83 grams (rounded to two decimal places).