Determine the mass of copper that has the same number of atoms as there are in 15.46 mg of gold.
Answer in units of mg.
15.46 mg Au = 0.01546 g Au.
mols Au = grams/molar mass = ? = mols Cu
Then g Cu = mols Cu x atomic mass Cu.
To determine the mass of copper that has the same number of atoms as there are in 15.46 mg of gold, we need to use the concept of molar mass and Avogadro's number.
1. Convert the given mass of gold into moles:
The molar mass of gold (Au) is 197.0 g/mol.
Using the formula:
Moles = Mass / Molar Mass
Moles of gold = 15.46 mg / (197.0 g/mol * 1000 mg/g)
= 0.0785 mol
2. Determine the number of atoms in 0.0785 moles of gold:
Avogadro's number states that one mole of any substance contains 6.022 x 10^23 atoms.
Number of gold atoms = Moles of gold * Avogadro's number
= 0.0785 mol * 6.022 x 10^23 atoms/mol
= 4.722 x 10^22 atoms
3. Determine the molar mass of copper (Cu):
The molar mass of copper (Cu) is 63.55 g/mol.
4. Convert the number of copper atoms to the mass of copper:
Moles of copper = Number of copper atoms / Avogadro's number
= 4.722 x 10^22 atoms / 6.022 x 10^23 atoms/mol
= 0.07842 mol
Mass of copper = Moles of copper * Molar mass of copper
= 0.07842 mol * 63.55 g/mol
= 4.98 grams
5. Convert the mass of copper from grams to milligrams:
Mass of copper in mg = Mass of copper * 1000 mg/g
= 4.98 g * 1000 mg/g
= 4980 mg
Hence, the mass of copper that has the same number of atoms as there are in 15.46 mg of gold is 4980 mg.
To determine the mass of copper that has the same number of atoms as there are in 15.46 mg of gold, we need to use the concept of molar mass and Avogadro's number.
1. Start by finding the molar mass of gold (Au). The molar mass of gold is 196.97 g/mol or 196.97 mg/mol.
2. Use the molar mass of gold to calculate the number of moles present in 15.46 mg. Divide the mass (15.46 mg) by the molar mass of gold (196.97 mg/mol):
Number of moles of gold = Mass of gold / Molar mass of gold
Number of moles of gold = 15.46 mg / 196.97 mg/mol
3. Now, we need to use Avogadro's number to convert the number of moles of gold into the number of atoms. Avogadro's number is approximately 6.022 x 10^23 atoms/mol.
Number of atoms of gold = Number of moles of gold x Avogadro's number
4. Next, we equate the number of atoms of gold to the number of atoms of copper. Since atoms are indivisible, the number of atoms remains the same. Therefore:
Number of atoms of gold = Number of atoms of copper
5. Finally, we need to calculate the mass of copper. We know that the molar mass of copper (Cu) is 63.55 g/mol or 63.55 mg/mol. We can use this information to find the mass of copper by rearranging the equation from step 3:
Mass of copper = Number of atoms of copper x Molar mass of copper
Mass of copper = Number of atoms of gold x Molar mass of copper
Mass of copper = Number of moles of gold x Avogadro's number x Molar mass of copper
Now you can substitute the values you obtained earlier into this equation to find the mass of copper that has the same number of atoms as the given mass of gold.