Introduction: Hydrochloric acid is a strong acid that is highly soluble in water. It is commonly used in various industrial processes, laboratory experiments, and as a cleaning agent. The concentration of hydrochloric acid in a solution is typically expressed in terms of weight percent or molarity. The mole fraction is another way to express the concentration of a solute in a solution.

Formula: The mole fraction (X) of a solute in a solution is defined as the ratio of the number of moles of the solute to the total number of moles of all the components in the solution.

Calculation: To calculate the mole fraction of HCl in a solution of hydrochloric acid in water containing 36% HCl by weight, we need to follow the steps below:

1. Assume 100 g of the solution
2. Calculate the weight of HCl present in the solution
- 36% HCl by weight means 36 g of HCl in 100 g of the solution
3. Calculate the weight of water present in the solution
- 100 g of the solution - 36 g of HCl = 64 g of water
4. Calculate the number of moles of HCl present in the solution
- Moles of HCl = Weight of HCl / Molar mass of HCl
- Molar mass of HCl = 36.46 g/mol
- Moles of HCl = 36 g / 36.46 g/mol = 0.987 mol
5. Calculate the number of moles of water present in the solution
- Moles of water = Weight of water / Molar mass of water
- Molar mass of water = 18.015 g/mol
- Moles of water = 64 g / 18.015 g/mol = 3.550 mol
6. Calculate the total number of moles in the solution
- Total moles = Moles of HCl + Moles of water = 0.987 mol + 3.550 mol = 4.537 mol
7. Calculate the mole fraction of HCl in the solution
- Mole fraction of HCl = Moles of HCl / Total moles
- Mole fraction of HCl = 0.987 mol / 4.537 mol = 0.2175

Therefore, the mole fraction of HCl in a solution of hydrochloric acid in water containing 36% HCl by weight is 0.2175.