Dissociation of Salts and Ions in Solution: Mathematical Analysis of NaCl and MgCl2

In the study of chemical reactions, it is crucial to understand how substances dissociate in solution and the number of ions they produce. This analysis is particularly important when comparing different salts, such as sodium chloride (NaCl) and magnesium chloride (MgCl2). By understanding the dissociation process through mathematical calculations, we can determine if (frac{1}{2}) mole of NaCl and (frac{1}{3}) mole of MgCl2 result in the same number of ions.

Understanding the Dissociation of NaCl and MgCl2

To begin, let's examine the dissociation of each salt:

Dissociation of Sodium Chloride (NaCl)

NaCl dissociates into one sodium ion (Na ) and one chloride ion (Cl-) per formula unit:

NaCl → Na Cl-

Therefore, the total number of ions produced by one mole of NaCl is:

Total ions from NaCl 1 Na 1 Cl- 2 ions per mole

Dissociation of Magnesium Chloride (MgCl2)

MgCl2 dissociates into one magnesium ion (Mg2 ) and two chloride ions (Cl-) per formula unit:

MgCl2 → Mg2 2 Cl-

Therefore, the total number of ions produced by one mole of MgCl2 is:

Total ions from MgCl2 1 Mg2 2 Cl- 3 ions per mole

Calculating the Number of Ions in Specific Moles

Now, let's calculate the total number of ions produced by (frac{1}{2}) mole of NaCl and (frac{1}{3}) mole of MgCl2.

Calculation of Total Ions for NaCl

For (frac{1}{2}) mole of NaCl:

Total ions from NaCl (frac{1}{2}) moles × 2 ions/mole 1 ion

Calculation of Total Ions for MgCl2

For (frac{1}{3}) mole of MgCl2:

Total ions from MgCl2 (frac{1}{3}) moles × 3 ions/mole 1 ion

Both (frac{1}{2}) mole of NaCl and (frac{1}{3}) mole of MgCl2 produce the same total number of ions, which is 1 ion per mole.

Understanding Atom Count in Different Quantities

It is also beneficial to compare the number of atoms in similar quantities:

NaCl Particles

For half a dozen (i.e., 6/2 3) NaCl particles:

Total atoms 3 Na atoms 3 Cl atoms 6 atoms

MgCl2 Particles

For one third of a dozen (i.e., 6/3 2) MgCl2 particles:

Total atoms 2 Mg atoms 4 Cl atoms 6 atoms

Both quantities contain the same total number of atoms, which is 6 atoms.

When considering the molar quantities, we can draw the same conclusion:

Molar Quantities

For 0.5 moles of NaCl:

Total atoms 0.5 moles of Na 0.5 moles of Cl 1 mole of atoms

For one third of a mole of MgCl2:

Total atoms 0.333 moles of Mg 0.667 moles of Cl 1 mole of atoms

Both molar quantities contain the same total number of ions and atoms.

In conclusion, (frac{1}{2}) mole of NaCl and (frac{1}{3}) mole of MgCl2 produce the same number of ions, and both contain the same number of total atoms when considering their dissociation in solution.