How many atoms are present in 6.0g of magnesium? [Mg = 24, N.A = 6.02 x 10 $^{23}$mol]

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 those moles into the actual number of atoms.

Concept

1. Calculate Moles ($n$): The number of moles is calculated by dividing the given mass ($m$) by the molar mass ($M$) of the element. $$n = \frac{m}{M}$$
2. Calculate Atoms ($N$): The number of atoms is the number of moles multiplied by 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 this to three significant figures, we get $1.51 \times 10^{23}$.

Conclusion

Comparing our result to the given options, we can see that it matches option C.

Exam Tip

When dealing with mole calculations, always remember the "Mole Bridge": Mass $\leftrightarrow$ Moles $\leftrightarrow$ Number of Particles. If you are moving from mass to particles, you must pass through the "Mole" station first. Also, $0.25$ is the same as $1/4$; multiplying by $1/4$ is often much faster than using decimals during a timed exam!