Let's evaluate each statement:
1. value is same for a gas in any solvent: This is incorrect. The Henry's law constant varies with the type of solvent. It is specific to the gas-solvent combination.
2. Higher the value, more the solubility of gas: This is incorrect. According to Henry's law, a higher value corresponds to a lower solubility of the gas. The solubility of a gas in a solvent is inversely proportional to .
3. K_H value increases on increasing the temperature of the solution: This is correct. As the temperature increases, the solubility of gases generally decreases, which causes the Henry's law constant to increase. This is because gases become less soluble at higher temperatures.
4. Easily liquefiable gases usually have lesser K_H values: This is incorrect. Gases that are easily liquefiable, such as ammonia, generally have higher solubility in a solvent, which corresponds to a lower value.
Therefore, the correct answer is (C): value increases on increasing the temperature of the solution.