Van't Hoff factors of aqueous solutions of `X`,`Y` and `Z` are `2.8`,`1.8` and `3.5` respectively. Which of the following statement(s) is (are) correct?
a.`BP:XltYltZ`
b.`FP:ZltXltY`
c.Osmotic pressure,X=Y=Z
d.`VP:YltXltZ`

Options

A. `b.p:XltYltZ`
B. `f.p.ZltXltY`
C. osmotic pressure: `X=Y=Z`
D. `v.p.:YltXltZ`

Explanation

To solve the problem, we need to analyze the given van't Hoff factors (i) for the solutions of substances X, Y, and Z, which are 2.8, 1.8, and 3.5 respectively. We will determine the relationships between boiling point (BP), freezing point (FP), osmotic pressure (OP), and vapor pressure (VP) based on these factors.

### Step 1: Understanding the van't Hoff factor
The van't Hoff factor (i) indicates the number of particles into which a solute dissociates in solution. The greater the van't Hoff factor, the greater the effect on colligative properties (boiling point elevation, freezing point depression, osmotic pressure, and vapor pressure lowering).

### Step 2: Analyzing the van't Hoff factors
- For X: i = 2.8
- For Y: i = 1.8
- For Z: i = 3.5

### Step 3: Determine the boiling point (BP)
Boiling point elevation is directly proportional to the van't Hoff factor. Therefore, the order of boiling points (BP) is:
- Z (3.5) > X (2.8) > Y (1.8)
So, the correct order is: BP: Z > X > Y

### Step 4: Determine the freezing point (FP)
Freezing point depression is inversely proportional to the van't Hoff factor. Thus, the order of freezing points (FP) is:
- Z (3.5) < X (2.8) < Y (1.8)
So, the correct order is: FP: Z < X < Y

### Step 5: Determine the osmotic pressure (OP)
Osmotic pressure is directly proportional to the van't Hoff factor. Therefore, the order of osmotic pressure (OP) is the same as that of boiling point:
- Z (3.5) > X (2.8) > Y (1.8)
So, the correct order is: OP: Z > X > Y

### Step 6: Determine the vapor pressure (VP)
Vapor pressure is inversely proportional to boiling point. Therefore, the order of vapor pressure (VP) is the reverse of the boiling point order:
- Z (3.5) < X (2.8) < Y (1.8)
So, the correct order is: VP: Z < X < Y

### Conclusion
Now, let's evaluate the statements:
- a. BP: X < Y < Z (Incorrect, the correct order is Z > X > Y)
- b. FP: Z < X < Y (Correct, the order is Z < X < Y)
- c. Osmotic pressure: X = Y = Z (Incorrect, the correct order is Z > X > Y)
- d. VP: Y < X < Z (Incorrect, the correct order is Z < X < Y)

### Final Answer
The only correct statement is:
- b. FP: Z < X < Y