Which one of the following salts would have the same value of van't Hoff factor as that of \(Al(NO_3)_3\)?
Answer & explanation
Correct answer: option 2
The correct answer is option 2. \(K_3[Fe(CN)_6]\).
The van't Hoff factor (\(i\)) indicates the number of particles into which a solute dissociates in solution. It is crucial in colligative properties such as boiling point elevation and freezing point depression. The factor is calculated based on the dissociation of a solute in a solvent.
\(Al(NO_3)_3\)
Chemical Formula: \(Al(NO_3)_3\)
Dissociation in Water: \(Al(NO_3)_3 \rightarrow Al^{3+} + 3NO_3^-\)
Ions Formed: 1 \(Al^{3+}\) ion, 3 \(NO_3^-\) ions
Total Number of Ions: 1 + 3 = 4
van't Hoff Factor (\(i\)): 4
Analysis of Other Salts:
1. \(Al_2(SO_4)_3\)
Chemical Formula: \(Al_2(SO_4)_3\)
Dissociation in Water: \(Al_2(SO_4)_3 \rightarrow 2Al^{3+} + 3SO_4^{2-}\)
Ions Formed: 2 \(Al^{3+}\) ions, 3 \(SO_4^{2-}\) ions
Total Number of Ions: 2 + 3 = 5
van't Hoff Factor (\(i\)): 5
2. \(K_3[Fe(CN)_6]\)
Chemical Formula: \(K_3[Fe(CN)_6]\)
Dissociation in Water: \(K_3[Fe(CN)_6] \rightarrow 3K^+ + [Fe(CN)_6]^{3-}\)
Ions Formed: 3 \(K^+\) ions, 1 \([Fe(CN)_6]^{3-}\) ion
Total Number of Ions: 3 + 1 = 4
van't Hoff Factor (\(i\)): 4
3. \(K_2SO_4\)
Chemical Formula: \(K_2SO_4\)
Dissociation in Water: \(K_2SO_4 \rightarrow 2K^+ + SO_4^{2-}\)
Ions Formed: 2 \(K^+\) ions, 1 \(SO_4^{2-}\) ion
Total Number of Ions: 2 + 1 = 3
van't Hoff Factor (\(i\)): 3
4. \(KCl\)
Chemical Formula: \(KCl\)
Dissociation in Water: \(KCl \rightarrow K^+ + Cl^-\)
Ions Formed: 1 \(K^+\) ion, 1 \(Cl^-\) ion
Total Number of Ions: 1 + 1 = 2
van't Hoff Factor (\(i\)): 2
Thus, the salt that has the same van’t Hoff factor as \(Al(NO_3)_3\) is:2. \(K_3[Fe(CN)_6]\)