Question

in which one of the following pairs has the same number of ions?
1) 1 mole of NaCl and 1 mole of MgCl2
2) 1/2 mole of NaCl and 1/2 mole of MgCl2
3)1/2mole of NaCl and 1/3 mole of MgCl2
4)1/3 mole of NaCl and 1/2 mole of MgCl2

Answer 1

Answer:

4th one has same number of ions

Answer 2

The pair that has the same number of ions is 1/2 mole of $NaCl$ and 1/3 mole of $\[MgC{l_2}\]$. Thus, the correct option is (3).

Explanation:

• One mole of a substance contains an Avogadro number of atoms, ions or molecules.
• 1 mole of NaCl contains 1 mole of sodium and 1 mole of chloride ions. Therefore, they contain an Avogadro number of sodium and chloride ions. Thus, the total number of ions $\[ = 2{N_A}\]$
• 1 mole of $\[MgC{l_2}\]$ contains 1 mole of Mg and 2 moles of chloride ions. Therefore, the total number of ions $\[ = 3{N_A}\]$
• Therefore, 1/2 mole of NaCl contains a total number of $\[{N_A}\]$ ions while 1/2 mole of $\[MgC{l_2}\]$ contains a total number of $\[1.5{N_A}\]$ ions.
• 1/3 mole of NaCl contains a total number of $\[0.66{N_A}\]$ ions while 1/3 mole of $\[MgC{l_2}\]$ contains a total number of $\[0.99{N_A} \approx 1{N_A}\]$ ions.
• Thus, the pair that has the same number of ions is 1/2 mole of $NaCl$ and 1/3 mole of $\[MgC{l_2}\]$ as both have a total number of $\[{N_A}\]$ ions.