Embibe Experts Solutions for Chapter: States of Matter: Gases and Liquids, Exercise 3: EXERCISE-3

A toy balloon originally had $1.00\mathrm{}\mathrm{g}$ of helium gas and had a radius of $10.0\mathrm{}\mathrm{c}\mathrm{m}$. During night, $0.25\mathrm{}\mathrm{g}$ of the gas effused from the balloon. Assuming ideal gas behaviour under these constant pressure and temperature conditions, what was the radius of the balloon the next morning?

$12 \mathrm{g}{ \mathrm{N}}_2, 4 \mathrm{g} {\mathrm{H}}_2,$ and $9 g O_2$ are put into a one litre container at $27°\mathrm{C}.$ What is the total pressure.

At room temp, ${\mathrm{NH}}_3$ gas at one $\mathrm{atm}$ & $\mathrm{HCl}$ gas at $\text{'}\text{'}\mathrm{P}\text{'}\text{'}$ $\mathrm{atm}$ are allowed to effuse through identical pin holes to the opposite ends of a glass tube $1 \mathrm{m}$ long & uniform cross-section. A white deposit is observed at a distance of $60 \mathrm{cm}$ from the $\mathrm{HCl}$ end. What is $\text{'}\text{'}\mathrm{P}\text{'}\text{'}.$

At what temperature in ${}^{\circ }\mathrm{C},$ the ${\mathrm{U}}_{\mathrm{ms}}$ of  ${\mathrm{SO}}_2$ is equal to the average velocity of ${\mathrm{O}}_2$ at $27°\mathrm{C}.$

Calculate the temperature at which the root mean square velocity, average velocity and most probable velocity of oxygen gas are all equal to $1500{ \mathrm{ms}}^{-1}.$

The vapour pressure of two pure liquids, $\mathrm{A}$ and $\mathrm{B}$, that form an ideal solution are $300$ and $800$ torr, respectively, at temperature $\mathrm{T}$. A mixture of the vapour of $\mathrm{A}$ and $\mathrm{B}$ for which the amount fraction of $\mathrm{A}$ is $0.25$ is slowly compressed at temperature $\mathrm{T}$. Calculate:
(a) The composition of the first drop of the condensate,
(b) The total pressure when this drop is formed,
(c) The composition of the solution whose normal boiling point is $\mathrm{T}$. $\left[{\mathrm{P}}_{\mathrm{atm}}=760 \text{torr}\right]$
(d) The pressure when only the last bubble of vapour remains.
(e) The composition of the last bubble.

At $20°\mathrm{C}$, two balloons of equal volume and porosity are filled to a pressure of $2 \mathrm{atm}$. One is with $14 \mathrm{kg} {\mathrm{N}}_2$ and other is with $1 \mathrm{kg}$ of ${\mathrm{H}}_2$. The ${\mathrm{N}}_2$ balloon leaks to a pressure of $0.5 \mathrm{atm}$ in $1$ hour. How long will it take for ${\mathrm{H}}_2$ balloon to reach a pressure of $0.5 \mathrm{atm}$?

The vander waals constant for ${\mathrm{O}}_2$ are $\mathrm{a}=1.36 \mathrm{atm}{ \mathrm{L}}^2{ \mathrm{mol}}^{-2}$ and $\mathrm{b}=0.0318 \mathrm{L}{ \mathrm{mol}}^{-1}.$ Calculate the temperature at which ${\mathrm{O}}_2$ gas behaves, ideally for longer range of pressure.