How many atoms are present in 6.0g of magnesium? [Mg = 24, NA = 6.02 x 1023 $mol^{-1}$]

Analysis

To find the number of atoms in a given mass of an element, we need to relate the mass to the number of moles, and then use Avogadro's constant ($N_A$) to convert moles into the number of atoms.

Concept

1. Calculate Moles ($n$): The number of moles is calculated by dividing the given mass ($m$) by the molar mass ($M$). $$n = \frac{m}{M}$$
2. Calculate Atoms ($N$): The number of atoms is the product of the number of moles and Avogadro's constant ($N_A$). $$N = n \times N_A$$

Step-by-Step Solution

Step 1: Identify the given values

• Mass of Magnesium ($m$) = 6.0 g
• Molar mass of Magnesium ($M$) = 24 g/mol
• Avogadro's constant ($N_A$) = $6.02 \times 10^{23} \text{ mol}^{-1}$

Step 2: Calculate the number of moles of Magnesium

Step 3: Calculate the number of atoms

Rounding to two decimal places as presented in the options, we get $1.51 \times 10^{23}$.

Conclusion

Comparing our result to the options provided, the calculated value matches option C.

Exam Tip

When dealing with mole calculations, always check your units. If you are given mass in grams and molar mass in g/mol, your result will be in moles. If you ever get stuck, remember the "Mole Map": Mass $\rightarrow$ Moles $\rightarrow$ Particles (Atoms/Molecules). Dividing by molar mass takes you to moles; multiplying by Avogadro's number takes you to particles.