1. Definition of Azeotrope:
An azeotrope is a mixture of two or more liquids that boil at a constant temperature and have a fixed composition, such that the vapor produced has the same composition as the liquid mixture. Azeotropes behave like pure substances during boiling and cannot be separated into their individual components by simple distillation.
2. Azeotrope formed by Negative Deviation from Raoult's Law:
When a mixture exhibits a negative deviation from Raoult's law, the intermolecular forces between the molecules of the two liquids are stronger than those in the individual components. As a result, the boiling point of the mixture is lower than that predicted by Raoult's law, and the vapor has a different composition than the liquid. This leads to the formation of a minimum boiling azeotrope.
Example:
An example of an azeotrope formed by a negative deviation from Raoult's law is the mixture of hydrochloric acid (HCl) and water. This mixture forms a minimum boiling azeotrope with a boiling point of 108°C and a composition of approximately 20% HCl and 80% water.
A substance 'X' (1.5 g) dissolved in 150 g of a solvent 'Y' (molar mass = 300 g mol$^{-1}$) led to an elevation of the boiling point by 0.5 K. The relative lowering in the vapour pressure of the solvent 'Y' is $____________ \(\times 10^{-2}\). (nearest integer)
[Given : $K_{b}$ of the solvent = 5.0 K kg mol$^{-1}$]
Assume the solution to be dilute and no association or dissociation of X takes place in solution.
Rishika and Shivika were partners in a firm sharing profits and losses in the ratio of 3 : 2. Their Balance Sheet as at 31st March, 2024 stood as follows:
Balance Sheet of Rishika and Shivika as at 31st March, 2024
| Liabilities | Amount (₹) | Assets | Amount (₹) |
|---|---|---|---|
| Capitals: | Equipment | 45,00,000 | |
| Rishika – ₹30,00,000 Shivika – ₹20,00,000 | 50,00,000 | Investments | 5,00,000 |
| Shivika’s Husband’s Loan | 5,00,000 | Debtors | 35,00,000 |
| Creditors | 40,00,000 | Stock | 8,00,000 |
| Cash at Bank | 2,00,000 | ||
| Total | 95,00,000 | Total | 95,00,000 |
The firm was dissolved on the above date and the following transactions took place:
(i) Equipements were given to creditors in full settlement of their account.
(ii) Investments were sold at a profit of 20% on its book value.
(iii) Full amount was collected from debtors.
(iv) Stock was taken over by Rishika at 50% discount.
(v) Actual expenses of realisation amounted to ₹ 2,00,000 which were paid by the firm. Prepare Realisation Account.
A carpenter needs to make a wooden cuboidal box, closed from all sides, which has a square base and fixed volume. Since he is short of the paint required to paint the box on completion, he wants the surface area to be minimum.
On the basis of the above information, answer the following questions :
Find \( \frac{dS}{dx} \).