The observed osmotic pressure for a `0.10M` solution of `Fe(NH_(4))_(2)(SO_(4))_(2)` at `25^(@)C` is `10.8 atm`. The expected and experimental (observed) values of Van't Hoff factor (i) will be respectively: `(R = 0.082 L atm k^(-) mol^(-1))`

Options

A. 3 and `5.42`
B. 5 and `3.42`
C. 4 and `4.00`
D. 5 and `4.42`

Explanation

To solve the problem, we need to calculate the expected and observed Van't Hoff factor (i) for the given solution of `Fe(NH4)2(SO4)2`.

### Step 1: Understand the formula for osmotic pressure
The osmotic pressure (π) is given by the formula:
\[ \pi = i \cdot c \cdot R \cdot T \]
where:
- \( \pi \) = osmotic pressure
- \( i \) = Van't Hoff factor
- \( c \) = concentration of the solution (in molarity)
- \( R \) = ideal gas constant (0.0821 L atm K⁻¹ mol⁻¹)
- \( T \) = temperature in Kelvin

### Step 2: Identify the values given in the problem
From the problem statement:
- Observed osmotic pressure (π) = 10.8 atm
- Concentration (c) = 0.10 M
- Temperature (T) = 25°C = 298 K
- Gas constant (R) = 0.0821 L atm K⁻¹ mol⁻¹

### Step 3: Calculate the observed Van't Hoff factor (i)
Rearranging the osmotic pressure formula to solve for \( i \):
\[ i = \frac{\pi}{c \cdot R \cdot T} \]

Substituting the values:
\[ i = \frac{10.8 \, \text{atm}}{0.10 \, \text{mol/L} \cdot 0.0821 \, \text{L atm K}^{-1} \text{mol}^{-1} \cdot 298 \, \text{K}} \]

Calculating the denominator:
\[ 0.10 \cdot 0.0821 \cdot 298 = 2.475 \]

Now, substituting back into the equation for \( i \):
\[ i = \frac{10.8}{2.475} \approx 4.36 \]

### Step 4: Calculate the expected Van't Hoff factor (i)
Now, we need to find the expected Van't Hoff factor for `Fe(NH4)2(SO4)2`.

When `Fe(NH4)2(SO4)2` dissolves in water, it dissociates into:
- 1 Fe²⁺ ion
- 2 NH4⁺ ions
- 2 SO4²⁻ ions

So, the total number of ions produced is:
\[ 1 \, (\text{Fe}^{2+}) + 2 \, (\text{NH}_4^+) + 2 \, (\text{SO}_4^{2-}) = 5 \]

Thus, the expected Van't Hoff factor \( i \) is 5.

### Final Results:
- Expected \( i = 5 \)
- Observed \( i \approx 4.36 \)

### Summary:
The expected and experimental (observed) values of the Van't Hoff factor (i) are respectively:
- Expected \( i = 5 \)
- Observed \( i \approx 4.36 \)