Question

How many grams of magnesium (Mg, 24.30 g/mol) are in 7.43x10^22 atoms of Mg?

Answer 1

To find the grams of magnesium in 7.43x10²² atoms, divide the atoms by Avogadro's number to get moles, then multiply by magnesium's molar mass to obtain 3.00 grams of Mg.

Step-by-step explanation:

To calculate the grams of magnesium (Mg) in 7.43x10²² atoms of Mg, we can use Avogadro's number (6.02x10²³ atoms/mol) and the molar mass of Mg (24.305 g/mol). We'll first determine the number of moles of Mg represented by the given atoms and then convert those moles to grams.

Steps to calculate:

1. Find the number of moles of Mg by dividing the number of Mg atoms by Avogadro's number: (7.43x10²² atoms) / (6.02x10²³ atoms/mol).
2. Convert the moles of Mg to grams by multiplying the moles of Mg by the molar mass of Mg: Moles of Mg x (24.305 g/mol).

Now, let's perform the calculation:

1. The number of moles of Mg = (7.43x10²² atoms) / (6.02x10²³ atoms/mol) = 0.1235 moles.
2. The grams of Mg = 0.1235 moles x (24.305 g/mol) = 3.00 grams of Mg.

Answer 2

Given the number of Mg atoms is
`7.43 * 10^(22) atoms`

We know that 1 mol of any substance has Avogadro number
`(6.022 * 10^(23))` of formula units.

Converting number of atoms to mol:

`7.43 * 10^(22) atoms * (1 mol)/(6.022*10^(23) atoms) = 0.123 mol Mg`

Converting mol to mass of Mg:

`0.123 mol * (24.30 g)/(1 mol) = 2.99 g Mg`

Therefore mass of Mg is 2.99 g