A tightly sealed 25.0 litre acetone drum was found to have...

A tightly sealed $25.0$ litre acetone drum was found to have $15.4$ litre acetone (I) at $780 \mathrm{~mm} \mathrm{Hg}$ pressure and $18^{\circ} \mathrm{C} .$ Suddenly during transporlation the drum was dented and its internal volume was found to decrcase hy $4.6$ litre. If vapour pressure of acetone at $18^{\circ} \mathrm{C}$ is $400 \mathrm{~mm}$ of $\mathrm{Hg}$. cilculate the pressure inside the drum after denting.

Key Concepts

Vapor Pressure Equilibrium

This concept refers to the state in which a volatile liquid and its vapor coexist at a given temperature, such that the vapor exerts a fixed pressure (the vapor pressure) regardless of the volume of the container, provided that some liquid remains. The vapor pressure is an intrinsic property of the liquid at a specific temperature and governs the maximum pressure the vapor can exert under equilibrium conditions.

Boyle’s Law and the Pressure?Volume Relationship

Boyle’s law states that for a given mass of gas at constant temperature, the pressure is inversely proportional to the volume. When the volume of a sealed container decreases, the pressure of any non?condensable gases it contains will increase in proportion to the reduction in volume, assuming no gas is added or removed.

Dalton’s Law of Partial Pressures

Dalton’s law explains that in a mixture of gases, the total pressure is the sum of the pressures that each gas would exert if it occupied the container alone. In systems containing a volatile liquid, the overall pressure is made up of the vapor pressure of the liquid (which stays fixed at equilibrium) and the pressure due to any other non?condensable gases, each responding to changes in volume according to Boyle’s law.

Phase Equilibrium in Sealed Systems

In a sealed container with both a volatile liquid and its vapor, the liquid and vapor maintain a phase equilibrium where the vapor pressure remains at the defined value for that temperature. When the container’s volume changes, any additional compression increases the pressure of non?condensable gases while the vapor’s partial pressure stays anchored at the liquid’s vapor pressure until conditions force additional phase change to restore equilibrium.

Transcript

Please give Ace some feedback