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 $$\mathrm{CaCl}_2$$, theoretically, if it fully dissociates, it breaks down into one $$\mathrm{Ca}^{2+}$$ ion and two $$\mathrm{Cl}^-$$ 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:

$M = \frac{n}{V}$

where:

$$n$$ is the number of moles of solute,
$$V$$ is the volume of the solution in liters.

The number of moles of $$\mathrm{CaCl}_2$$ can be calculated as follows:

$n = \frac{mass}{molar~mass} = \frac{3.42~\mathrm{g}}{111~\mathrm{amu~g/mol}}$

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

$n = \frac{3.42}{111} \approx 0.0308~\mathrm{mol}$

Then, we convert $$2500~\mathrm{ml}$$ to liters:

$V = 2500~\mathrm{ml} = 2.5~\mathrm{L}$

Now, we calculate the molarity ($$M$$):

$M = \frac{0.0308}{2.5} = 0.01232~\mathrm{M}$

Using the van't Hoff equation for osmotic pressure ($$\Pi$$):

$\Pi = i M R T$

where:

$$\Pi$$ is the osmotic pressure,
$$i$$ is the van't Hoff factor,
$$M$$ is the molarity,
$$R$$ is the ideal gas constant ($$0.0821~\mathrm{L \cdot atm \cdot K^{-1} \cdot mol^{-1}}$$),
$$T$$ is the temperature in Kelvin. To convert $$27^\circ C$$ to Kelvin: $$T = 27 + 273.15 = 300.15~\mathrm{K}$$.

Given that $$\Pi = 0.75~\mathrm{atm}$$, we can rearrange the formula to solve for $$i$$:

$i = \frac{\Pi}{M R T}$

Substituting the given and calculated values:

$i = \frac{0.75}{0.01232 \times 0.0821 \times 300.15}$

$i = \frac{0.75}{0.01232 \times 0.0821 \times 300.15} \approx \frac{0.75}{0.301972632} \approx 2.484$

Therefore, the van't Hoff factor ($$i$$) for the given solution is approximately 2.484. This suggests that $$\mathrm{CaCl}_2$$ does not completely dissociate into three ions for every formula unit. The answer closest to our calculation is:

Option C: 2.47

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