Question

Calculate the number of atoms in 48 g of Mg.
A) $12.04 \times {10^{23}}$
B) $6.02 \times {10^{23}}$
C) $18.06 \times {10^{23}}$
D) $24.08 \times {10^{23}}$

Answer 1

Hint: In order to find the number of atoms in 48 g of Mg, use the formula which relates the number of particles/atoms with the Avogadro number and number of moles of the substance and this required formula is: number of atoms = number of moles $ \times $ Avogadro's number. You need to calculate the number of moles in 48 g of Mg to find the number of atoms.

Complete step by step solution:
Molar mass of magnesium (Mg) is 24 g/mol.
You must know that the number of particles or atoms or molecules in a given substance is the multiplication of the number of moles of the given substance and the Avogadro number. Avogadro number (denoted by ${N_A}$) is a constant value which is equal to $6.022 \times {10^{23}}$atoms/mol.
And, the formula to find the number of moles is:
Number of moles = $\dfrac{{{\text{given mass}}}}{{{\text{molar mass}}}}$
Here, we are given 48 g of Mg, therefore it is the given mass.
Thus, number of moles of Mg in 48 g = $\dfrac{{48}}{{24}} = 2mol$
Now, coming back to the formula to find the number of atoms.
Number of atoms = number of moles $ \times $ Avogadro's number
Therefore, number of atoms in 48 g of Mg = 2 mol $ \times $ $6.022 \times {10^{23}}$atoms/mol= \[12.04 \times {10^{23}}\] atoms.
Thus, 48 g of Mg is equivalent to $12.04 \times {10^{23}}$ atoms.

Hence, option A is the correct answer.

Note: It should be noted that molar mass is the mass of 1 mole of a substance in grams. 1 mole of a particular substance contains Avogadro's number (also called Avogadro constant) of particles or entities (atoms/molecules) that is, $6.022 \times {10^{23}}$ particles. Therefore, we can also say that 1 mol of Mg contains $6.022 \times {10^{23}}$ atoms and then, consequently 2 moles of Mg will contain $12 \times {10^{23}}$ atoms.