Question

What mass of NaCl would contain the same total number of ions as 245 g of ${\text{MgC}}{{\text{l}}_2}$?

Answer 1

Hint: According to the Avogadro, one mole of any substance has $\,6.02 \times {10^{23}}$ atoms, ions or molecules. This number $\,6.02 \times {10^{23}}$ is known as Avogadro number. This is denoted by the symbol $N_A$.

Complete step by step answer:
Use mole formula to determine the mole of magnesium chloride as follows:

${\text{Mole}}\,\, = \dfrac{{{\text{Mass}}}}{{{\text{Molar}}\,{\text{mass}}}}$
Molar mass of magnesium chloride is 95 g/mol.
Substitute 95 g/mol for molar mass and 245 g for mass.

${\text{Mole}}\,\, = \dfrac{{{\text{245}}\,{\text{g}}}}{{95\,{\text{g/mol}}}}$
${\text{Mole}}\,\, = 2.6\,{\text{mol}}$
Determine the number of ions in $2.6\,{\text{mol}}$ of magnesium chloride as follows:
One mole of magnesium chloride has three ions, one magnesium ion and two chloride ions.
$= 3\, \times \,2.6\,{\text{mol}} \times 6.02 \times {10^{23}}{\text{ions/mol}}$
$= 4.7 \times {10^{24}}\,{\text{ions}}$
So, the number of ions in magnesium chloride is $4.7 \times {10^{24}}\,{\text{ions}}$.
So, the number of ions present in sodium chloride is $4.7 \times {10^{24}}\,{\text{ions}}$.
One mole of sodium chloride has two ions, one sodium ion and one chloride ions.
So, the total number of ions in one mole of sodium chloride is,
$= 2\, \times \, \times 6.02 \times {10^{23}}{\text{ions/mol}}$
$= 1.2 \times {10^{24}}{\text{ions/mol}}$
So, the mole of sodium chloride is,
$= \dfrac{{4.7 \times {{10}^{24}}\,}}{{1.2 \times {{10}^{24}}}}$
$= 3.9\,{\text{mol}}$
So, mass of sodium chloride is,
Molar mass of magnesium chloride is $58.5\,{\text{g/mol}}$.
Substitute $58.5\,{\text{g/mol}}$ for molar mass and $3.9\,{\text{mol}}$ for mole.
${\text{3}}{\text{.9}}\,{\text{mol}}\,\, = \dfrac{{\text{Mass of sodium chloride}}}{{58.5\,{\text{g/mol}}}}$
${\text{Mass of sodium chloride}}\,{\text{ = }}\,{\text{3}}{\text{.9}}\,{\text{mol}}\,\, \times 58.5\,{\text{g/mol}}$
Mass of sodium chloride = 228 g

Therefore, the mass of sodium chloride is $228\,{\text{g}}$.

Note: The number of atoms present in 12 g of carbon-12 is known as one mole. The molar mass of the compound is the sum of the atomic mass of the atoms presents in the compound. Number of ions of a compound is determined by the ionization of ionic compounds in water. Sodium chloride dissociates in water as follows:
${\text{NaCl}}\, \to \,{\text{N}}{{\text{a}}^ + }\, + \,{\text{C}}{{\text{l}}^ - }$
And magnesium chloride dissociates as follows:
${\text{MgCl}}{\,_2} \to \,{\text{M}}{{\text{g}}^{2 + }}\, + 2\,{\text{C}}{{\text{l}}^ - }$.