COMEDK 2023 Shift 1 Paper

To find the van't Hoff factor (i) for the given solution, we first need to calculate the molarity of the solution. The van't Hoff factor is crucial in determining how many particles a compound dissolves into in solution. For CaCl2, theoretically, if it fully dissociates, it breaks down into one Ca2+ ion and two Cl−ions, suggesting a theoretical i of 3 . However, the actual i can differ based on how completely the solute dissociates in solution.
Let's start by calculating the molarity (M) of the solution. The formula to calculate molarity is:
M=‌

n

V

where:
n is the number of moles of solute,
V is the volume of the solution in liters.
The number of moles of CaCl2 can be calculated as follows:
n=‌

‌ mass ‌

‌ molar mass ‌

=‌

3.42g

111‌amu‌g∕mol

First, we calculate the number of moles (n) :
n=‌

3.42

111

≈0.0308‌mol
Then, we convert 2500‌ml to liters:
V=2500‌ml=2.5L
Now, we calculate the molarity (M) :
M=‌

0.0308

2.5

=0.01232M
Using the van't Hoff equation for osmotic pressure ( Π ):
Π=iMRT
where:
Π is the osmotic pressure, i is the van't Hoff factor, M is the molarity,
R is the ideal gas constant (0.0821L⋅atm⋅K−1⋅mol−1), T is the temperature in Kelvin. To convert 27∘C to Kelvin: T=27+273.15=300.15K
Given that Π=0.75‌atm, we can rearrange the formula to solve for i :
i=‌

Π

MRT

Substituting the given and calculated values:
‌i=‌

0.75

0.01232×0.0821×300.15

Therefore, the van't Hoff factor (i) for the given solution is approximately 2.484 . This suggests that CaCl2 does not completely dissociate into three ions for every formula unit. The answer closest to our calculation is:
Option C: 2.47