We have four aqueous solutions labelled as:
A. \(0.1\, \ M\, \ NaCl\)
B. \(0.01\, \ M\, \ NaCl\)
C. \(0.01\, \ M\, \ BaCl_2\)
D. \(0.01\, \ M\, \ Sucrose\)
Choose the correct increasing order of van't Hoff factor from the options given below:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \(i_D < i_A < i_B < i_C\)
The van’t Hoff factor is the number of particles one formula unit actually gives in solution.
D. 0.01 M sucrose: a non-electrolyte, i = 1 (smallest).
A. 0.1 M NaCl: ideal value 2, but in the more concentrated solution ion pairing (interionic attraction) is greater, so i is below 2 (about 1.87).
B. 0.01 M NaCl: more dilute, so i is closer to 2 (about 1.94).
C. 0.01 M BaCl2: \( \ce{BaCl2} \) → \( \ce{Ba^{2+}} \) + \( \ce{2Cl^{-}} \), ideal i = 3; the actual value is near 3 (largest).
NCERT (2026-27 edition):
Abnormal Molar Masses – “… Table 1.4 depicts values of the factor, i for several strong electrolytes. For KCl, NaCl and MgSO4, i values approach 2 as the solution becomes very dilute. As expected, the value of i gets close to 3 for K2SO4.”
| Salt | 0.1 m | 0.01 m | 0.001 m | i for complete dissociation |
|---|---|---|---|---|
| NaCl | 1.87 | 1.94 | 1.97 | 2.00 |
| KCl | 1.85 | 1.94 | 1.98 | 2.00 |
| MgSO4 | 1.21 | 1.53 | 1.82 | 2.00 |
| K2SO4 | 2.32 | 2.70 | 2.84 | 3.00 |