Mole fraction of a component in a solution is defined as the ratio of the number of moles of that component to the total number of moles of all components in the solution.

Given that the mole fraction of I2 in CCl4 is 0.2, we can write the equation:

moles of I2 / (moles of CCl4 + moles of I2) = 0.2

Let's assume the moles of I2 is x and the moles of CCl4 is y. We can rewrite the equation as:

x / (x + y) = 0.2

To find the molality value, we need to calculate the moles of solute (I2) per kilogram of solvent (CCl4).

Molality (m) is defined as the moles of solute per kilogram of solvent. It can be calculated using the formula:

m = moles of solute / mass of solvent (in kg)

In this case, we need to calculate the moles of I2 per kilogram of CCl4. The molar mass of I2 is 253.8 g/mol and the molar mass of CCl4 is 153.8 g/mol.

Let's assume the mass of CCl4 is M grams. We can calculate the moles of I2 as:

x = 0.2 * (x + y) (Multiplying both sides by (x + y))

x = 0.2x + 0.2y (Distributing)

0.8x = 0.2y (Subtracting 0.2x from both sides)

y = 4x (Dividing both sides by 0.2)

Now, we can substitute this value of y in terms of x in the equation for molality:

m = x / (M/1000) (Converting mass of CCl4 from grams to kilograms)

m = (x * 1000) / M

To find the value of x, we need an additional equation. Since we don't have any other information, we cannot determine the exact value of the molality without more data.

Therefore, none of the given options (A. 1.62, B. 0.8, C. 1.54, D. 1.8) can be considered as the correct answer without additional information.