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 = ${\displaystyle \frac{\text{given mass}}{\text{molar mass}}}$
Here, we are given 48 g of Mg, therefore it is the given mass.
Thus, number of moles of Mg in 48 g = ${\displaystyle \frac{48}{24}}=2mol$
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.