Embibe Experts Solutions for Chapter: States of Matter: Gases and Liquids, Exercise 1: JEE Advanced Paper 1 - 2014

Liquids $\mathrm{A}$ and $\mathrm{B}$ form ideal solution for all compositions of $\mathrm{A}$ and $\mathrm{B}$ at ${25}^{\circ }C$. Two such solutions with $0.25$ and $0.50$ mole fractions of $\mathrm{A}$ have the total vapor pressures of $0.3$ and $0.4$ bar, respectively. What is the vapor pressure of pure liquid $\mathrm{B}$ in bar?

The qualitative sketches I, II and III given below show the variation of surface tension with molar concentration of three different aqueous solutions of KCl, $\mathrm{C}{\mathrm{H}}_3\mathrm{O}\mathrm{H}\mathrm{ }$ and $\mathrm{C}{\mathrm{H}}_3{\left(\mathrm{C}{\mathrm{H}}_2\right)}_{11}\mathrm{O}\mathrm{S}{\mathrm{O}}_3^{-}\mathrm{ }\mathrm{N}{\mathrm{a}}^{+}$ at room temperature. The correct assignment of the sketches is -

One mole of a monoatomic real gas satisfied the equation $\mathrm{p}\left(\mathrm{V}-\mathrm{b}\right)=\mathrm{R}\mathrm{T}$ where b is a constant. The relationship of interatomic potential V(r) and interatomic distance r for the gas is given by

In thermodynamics, the $\mathrm{P}-\mathrm{V}$ work done is given by $\mathrm{w}=-\int {\mathrm{dVP}}_{\mathrm{ext}}$. For a system undergoing a particular process, the work done is,

$\mathrm{w}=-\int \mathrm{dV}\left(\frac{\mathrm{RT}}{\mathrm{V}-\mathrm{b}}-\frac{\mathrm{a}}{{\mathrm{V}}^2}\right)$. This equation is applicable to a

Aluminium reacts with sulfuric acid to form aluminium sulfate and hydrogen. What is the volume of hydrogen gas in liters $\left(\mathrm{L}\right)$ produced at $300 \mathrm{K}$ and $1.0$ atm pressure, when $5.4 \mathrm{g}$ of aluminium and $50.0 \mathrm{mL}$ of $5.0 \mathrm{M}$ sulfuric acid are combined for the reaction? (Use molar mass of aluminium as $27.0 \mathrm{g} {\mathrm{mol}}^{-1}$, $\mathrm{R}=0.082 \mathrm{atm} \mathrm{L} {\mathrm{mol}}^{-1}{\mathrm{K}}^{-1}$)

If the distribution of molecular speeds of a gas is as per the figure shown below, then the ratio of the most probable, the average, and the root mean square speeds, respectively, is

Which of the following statement(s) (are) correct regarding the root-mean-square speed $\left({\mathrm{U}}_{\mathrm{r}\mathrm{m}\mathrm{s}}\right)$ and average translational kinetic energy $\left({\mathrm{E}}_{\mathrm{av}}\right)$ of a molecule in a gas at equilibrium?