Embibe Experts Solutions for Chapter: Gaseous State, Exercise 1: EXERCISE

To an evacuated vessel with movable piston under external pressure of $1 \mathrm{atm}., 0.1 \mathrm{mol}$ of $\mathrm{He}$ and $1.0 \mathrm{mol}$ of an unknown compound (vapour pressure $0.68 \mathrm{atm}$ at $0°\mathrm{C}$) are introduced. Considering the ideal gas behaviour, determine the total volume (in litre) of the gases at $0°\mathrm{C}$.

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 $0.5 \mathrm{atm}$?

A tube of length $50 \mathrm{cm}$ is containing a gas in two sections separated by a mercury column of length $10 \mathrm{cm}$ as shown in figure. The open end of tube is just inside the $\mathrm{Hg}$ surface in container. Find the pressure of gas in two sections. [assume atmospheric pressure $=75 \mathrm{cm}$ of $\mathrm{Hg}$ $\text{column}$]

Which of the lines in the figure reflect correctly on the log scale, the temperature dependent of the root mean square velocity of the molecules.

In a basal metabolism measurement timed at $6$ $\mathrm{minutes}$, a patient exhaled $52.5 \mathrm{L}$ of air measured over water at $20°\mathrm{C}$. The vapour pressure of water at $20°\mathrm{C}$ is $17.5 \mathrm{torr}$. The barometric pressure was $750 \mathrm{torr}$. The exhaled air analyzed $16.75$ volume $\%$ oxygen and the inhaled air $20.32$ volume $\%$ oxygen. Both on a dry basis neglecting any solubility of the gases in water and any difference in the total volumes of inhaled and exhaled air, calculate the rate of oxygen consumption by the patient in $\mathrm{mL}$ ($\mathrm{STP}$) per minute.

The closed cylinder shown in the figure has a freely moving piston separating chambers $1$ and $2$. Chamber $1$ contains $25 \mathrm{mg}$ of ${\mathrm{N}}_2$ gas, and chamber $2$ contains $40 \mathrm{mg}$ of helium gas. When equilibrium is established, what will be the ratio ${\mathrm{L}}_1/{\mathrm{L}}_2$? What is the ratio of the number of moles of ${\mathrm{N}}_2$ to the number of moles of $\mathrm{He}$? (Molecular weights of ${\mathrm{N}}_2$ and $\mathrm{He}$ are $28$ and $4$).

The density of a mixture of ${\mathrm{O}}_2$ and ${\mathrm{N}}_2$ at NTP is $1.3 \mathrm{g} {\mathrm{litre}}^{-1}$. Calculate the partial pressure of ${\mathrm{O}}_2$.

Given a one meter long glass tube closed at one end having a uniform cross-section containing a mercury column of $10 \mathrm{cm}$ length, at a distance of $39 \mathrm{cm}$ from the closed end. By what distance would this column move down, if the tube is held vertically with the open end downwards. [Take atmospheric pressure to be $78 \mathrm{cm}$ of $\mathrm{Hg}.$]