At 283K a saturated solution of solid X can be prepared by dissolving $ 21.0{\text{ g}} $ of it in $ 100{\text{ g}} $ of water. The maximum amount of X which can be dissolved in $ 100{\text{ g}} $ of water at 313K is $ 62.0{\text{g}} $ . An attempt is made to dissolve $ 50.0{\text{ g}} $ of X n $ 100{\text{ g}} $ of water at 313K.
1. All the $ 50.0{\text{ g}} $ of X will dissolve at 313K
2. At 313K, $ 29.0{\text{ g}} $ of X will remain undissolved
3. Solubility of X decreases with an increase in temperature.
4. On cooling the solution of X from 313K to 283K then $ 21.0{\text{ g}} $ of X will crystallize out.
Which of the following statements are correct?
(A) 1 and 2
(B) 1 and 4
(C) 2 and 3
(D) 1, 3 and 4

Hint: To answer this question, you must recall the concept of saturation. In simple words, we can say that the point of saturation of a salt is the point at which more salt cannot be dissolved into the solution. If more salt is added, it will result in the formation of a precipitate.

Complete step by step solution
Saturation is said to be achieved in a solution when an equilibrium is established between the salt present in solid form and that present in the dissolved form. The amount of salt dissolved in a saturated solution is the maximum amount that can be dissolved in the given amount of solvent at the given temperature. In the question, it is given that at 283K temperature, the maximum amount of salt that can be added to $ 100{\text{ g}} $ of water is $ 21.0{\text{ g}} $ . And at 313K, the amount of the salt X that can be dissolved in $ 100{\text{ g}} $ of water is $ 62.0{\text{g}} $ . Thus, we can see that the solubility of X is increasing with an increase in the temperature.
So when at 313K, $ 50.0{\text{ g}} $ of X is added in $ 100{\text{ g}} $ of water, all of it will dissolve. When the solution is cooled from a temperature of 313K to 273K, the solubility decreases and $ 29{\text{ g}} $ of the salt separates out as solid.
The correct statements are 1 and 4.
Thus, the correct answer is B.

Note
When a salt dissolves in a solution, its constituent atoms or ions solvate and diffuse throughout the solution independently. However, this is not a unidirectional process. When the dissolved atoms or ions collide with a particle of an undissolved salt particle, it adheres to the particle and results in the crystallization. The dissolution and crystallization process are in equilibrium in a saturated solution.