To find the mass in grams of \(2.00 \times 10^{23}\) molecules of Magnesium metal (Mg), we need to use Avogadro's number and the molar mass of Magnesium (Mg).
Here are the steps we'll follow to solve the problem:
**Step 1: Understand Avogadro's Number**
Avogadro's number is a constant that represents the number of atoms or molecules in one mole of a substance. Avogadro's number is \(6.02214076 \times 10^{23}\) entities per mole.
**Step 2: Calculate the Number of Moles of Magnesium**
Since we have \(2.00 \times 10^{23}\) Magnesium molecules, we must first determine how many moles this number represents. We do this by dividing the number of molecules by Avogadro's number.
\[
\text{Number of moles} = \frac{\text{Number of molecules}}{\text{Avogadro's number}}
\]
\[
\text{Number of moles (Mg)} = \frac{2.00 \times 10^{23}}{6.02214076 \times 10^{23}} \approx 0.3321 \text{ moles}
\]
**Step 3: Find the Molar Mass of Magnesium**
The molar mass of an element is the mass of one mole of that element. The molar mass of Magnesium is \(24.305 \text{ g/mol}\).
**Step 4: Calculate the Mass of Magnesium**
To find the mass, multiply the number of moles by the molar mass of Magnesium.
\[
\text{Mass} = \text{Number of moles} \times \text{Molar mass of Magnesium}
\]
\[
\text{Mass (Mg)} = 0.3321 \text{ moles} \times 24.305 \text{ g/mol} \approx 8.0719 \text{ grams}
\]
So, the mass in grams of \(2.00 \times 10^{23}\) molecules of Magnesium is approximately \(8.0719\) grams.
