The observed osmotic pressure for a 0.10 M 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$$^{-1}$$)

The osmotic pressure ($$\pi$$) is related to the Van't Hoff factor ($$i$$) by the formula: $$\pi = i \times C \times R \times T$$ where: - $$C$$ is the molar concentration (0.10 M), - $$R$$ is the gas constant (0.082 L atm K⁻¹ mol⁻¹), - $$T$$ is the temperature in Kelvin. First, convert the temperature from Celsius to Kelvin: $$T = 25 + 273 = 298 \text{ K}$$ The observed osmotic pressure is given as 10.8 atm. To find the experimental (observed) Van't Hoff factor ($$i_{\text{experimental}}$$), rearrange the formula: $$i_{\text{experimental}} = \frac{\pi_{\text{observed}}}{C \times R \times T}$$ Substitute the known values: $$i_{\text{experimental}} = \frac{10.8}{0.10 \times 0.082 \times 298}$$ Calculate the denominator step by step: - First, compute $$0.10 \times 0.082$$: $$0.10 \times 0.082 = 0.0082$$ - Next, multiply by $$T$$: $$0.0082 \times 298$$ Break it down: $$0.0082 \times 300 = 2.46$$ $$0.0082 \times 2 = 0.0164 \quad \text{(since 298 = 300 - 2)}$$ $$2.46 - 0.0164 = 2.4436$$ So, the denominator is 2.4436. Now, divide: $$i_{\text{experimental}} = \frac{10.8}{2.4436} \approx 4.42$$ (Detailed division: 2.4436 × 4 = 9.7744; 10.8 - 9.7744 = 1.0256; 1.0256 ÷ 2.4436 ≈ 0.4195; thus, 4 + 0.4195 = 4.4195 ≈ 4.42) Next, determine the expected Van't Hoff factor ($$i_{\text{expected}}$$) for complete dissociation of Fe(NH₄)₂(SO₄)₂. The compound dissociates in water as follows: $$\text{Fe(NH}_4\text{)}_2\text{(SO}_4\text{)}_2 \rightarrow \text{Fe}^{2+} + 2\text{NH}_4^+ + 2\text{SO}_4^{2-}$$ This produces a total of 5 ions (one Fe²⁺, two NH₄⁺, and two SO₄²⁻). Therefore, for complete dissociation, the expected Van't Hoff factor is 5. The experimental value is 4.42, which is less than 5, indicating incomplete dissociation or possible ion pairing in the solution. Comparing with the options: - A: 4 and 4.00 - B: 3 and 5.42 - C: 5 and 4.42 - D: 5 and 3.42 The values 5 (expected) and 4.42 (experimental) match option C. Hence, the correct answer is Option C.