Water

The formula for boiling point elevation is given by: where:
is the boiling point elevation,
is the ebullioscopic constant,
is the molality of the solution,
is the van't Hoff factor (number of particles produced per formula unit).
Given that , , and the solute 'X' dimerizes in water to the extent of 80%, the van't Hoff factor . Now, molality is given by: The mass of the solvent is 100g, or 0.1kg. The number of moles of 'X' is: where is the molar mass of 'X'. Substitute into the boiling point elevation formula: Simplifying:
Thus, the molar mass of 'X' is 26 g/mol.

The correct option is (A) : 26

To solve this problem, we need to identify the method that cannot remove permanent hardness from water.

1. Understanding Hardness in Water:
Hardness in water is caused by the presence of dissolved minerals, mainly calcium (Ca²⁺) and magnesium (Mg²⁺) ions. There are two types of hardness:

• Temporary hardness: Caused by dissolved bicarbonates (Ca(HCO₃)₂, Mg(HCO₃)₂) that can be removed by boiling.
• Permanenent hardness: Caused by dissolved sulphates and chlorides (such as CaSO₄, MgSO₄) and cannot be removed by boiling. This requires special treatments like ion exchange, washing soda, or other methods.

2. Analyzing Each Method:
Let’s evaluate each option to see if it can remove permanent hardness:

• Option (A) "Using washing soda": Washing soda (Na₂CO₃) is commonly used to remove both temporary and permanent hardness. It reacts with the calcium and magnesium ions to form insoluble carbonates, effectively removing the hardness. This method works for both types of hardness.
• Option (B) "Calgon's method": Calgon (sodium hexametaphosphate) is effective in removing both temporary and permanent hardness by forming a soluble complex with calcium and magnesium ions, making them unavailable for causing hardness. This method can remove permanent hardness.
• Option (C) "Clark's method": Clark's method involves adding lime (Ca(OH)₂) to water to precipitate calcium as calcium carbonate, which removes permanent hardness. This is an effective method for removing permanent hardness.
• Option (D) "Ion exchange method": The ion exchange method uses resins to exchange calcium and magnesium ions with sodium ions, effectively removing both temporary and permanent hardness. This method is widely used in water softening.

Final Answer:
All the methods mentioned (washing soda, Calgon's method, Clark's method, and ion exchange) are capable of removing permanent hardness. Therefore, the answer is (C) "Clark's method," which is not the correct method as it only removes temporary hardness.

Composition of Water Gas

Water gas is a mixture of gases produced by the reaction of carbon with steam at high temperatures. Let's analyze the given options to determine the correct composition of water gas:

Options:

1. Option C:
   This option lists the reactants, not the products of the water gas reaction.
2. Option D:
   This is the correct composition of water gas, consisting of carbon monoxide and hydrogen.
3. Option A:
   This option incorrectly includes nitrogen, which is not a product of the water gas reaction.
4. Option B:
   Methane ( ) is not the product of the water gas reaction; it is a solid (k) which is not relevant here.

Conclusion:

The correct answer is Option D: , as this correctly identifies the composition of water gas.