Explanation:

To find the value of X, we need to understand the concepts of molality and mole fraction.

Molality:
Molality is a measure of the concentration of a solute in a solvent. It is defined as the number of moles of solute per kilogram of solvent. The formula for molality is:

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

Mole Fraction:
Mole fraction is a way to express the concentration of a component in a mixture. It is the ratio of the number of moles of a component to the total number of moles in the mixture. The formula for mole fraction is:

Mole Fraction (χ) = (moles of component) / (total moles in mixture)

In this problem, we are given that the mole fraction of the compound in benzene is 0.2.

Calculating the Value of X:
To calculate the value of X, we can use the relationship between molality and mole fraction. The mole fraction of the compound can be expressed as:

χ = (moles of compound) / (moles of compound + moles of benzene)

We are also given that the compound is present in an X molal solution in benzene. This means that for every kilogram of benzene, there are X moles of the compound.

Using these relationships, we can set up the following equation:

0.2 = X / (X + 1)

Solving this equation will give us the value of X.

Solving the Equation:
To solve the equation, we can multiply both sides by (X + 1):

0.2(X + 1) = X

0.2X + 0.2 = X

0.8 = 0.8X

X = 1

Therefore, the value of X is 1.

RELATION BETWEEN MOLE FRACTION AND MOLALITY:-
m=xb(solute) X 1000 / xa(solvent) X M.M of solvent
WHERE, xb= Mole fraction of solute xa= Mole fraction of solvent M.M= molecular mass of solvent
NOW, m= 0.2 X 1000 / 0.8 X 78. (since, 1-0.2=0.8) = 200/62.4 = 3.20512 molal
REMEBER THAT FORMULA , THATS EASIEST AND FASTEST WAY TO SOLVE QUESTIONS RELATED WITH MOLALITY AND MOLE FRACTION.