Question

How many grams of magnesium (Mg, 24.30g/mol) are in 7.43 x 1022 atoms of Mg?7.43x 1022 atoms Mg| 1 mole Mg 24.30 g Mg16.02x 1023 atoms Mg/ 1 mole Mg[?] grams Mg

Answer 1

To calculate this, we can use fractions for equivalent amounts.

So, we have the number of atoms, using the Avogadro's Constant, we know that 1 mol of Mg is approximately 6.02 x 10^23, so:

`\frac{1\text{mol Mg}}{6.02*10^(23)\text{atoms Mg}}=1`

And since we have the number of atoms of Mg, we can convert to mol of Mg by multiplying by this fraction.

Now, from mol of Mg we can convert to mass using the molar mass of 24.30 g/mol. It says that 24.30 g og Mg is equivalent to 1 mol, so:

`\frac{24.30\text{g Mg}}{1\text{mol Mg}}=1`

So, we have:

`7.43*10^(22)\text{atom Mg}\cdot\frac{1\text{mol Mg}}{6.02*10^(23)\text{atom Mg}}\cdot\frac{24.30\text{g Mg}}{1\text{mol Mg}}`

Notice that this is presented in a table in the question, so we can now just multiply all of them:

`7.43*10^(22)\text{atom Mg}\cdot\frac{1\text{mol Mg}}{6.02*10^(23)\text{atom Mg}}\cdot\frac{24.30\text{g Mg}}{1\text{mol Mg}}=\frac{7.43*10^(22)\cdot24.30\text{g Mg}}{6.02*10^(23)}=2.999\text{g Mg}\approx3.00\text{g Mg}`

Thus, this is equivalent of approximately 3.00 g of Mg.