Embibe Experts Solutions for Chapter: States of Matter: Gases and Liquids, Exercise 2: EXERCISE-2

What is the mass of ${\mathrm{H}}_2\mathrm{O}$ present in air in $10$ litre closed vessel with $80\%$ relative humidity at $1 \mathrm{atm}$ and $300 \mathrm{K}$ ?

Given: Vapour pressure of ${\mathrm{H}}_2\mathrm{O}$ is $30$ torr at $300 \mathrm{K}$.

Volume of air at $8.21$. atm & $300 \mathrm{K}$ containing $21\%$ of oxygen by volume is required to competely burn $100 \mathrm{g}$ of carbon sample containing $16\%$ inert material, is :

Berthelot proposed the following empirical relation to explain the real behaviour of the real gases :

$\left(\mathrm{P}+\frac{\mathrm{a}}{{\mathrm{TV}}^2}\right)(\mathrm{V}-\mathrm{b})=\mathrm{RT}$

If the Berthelot equation of state be one of the forms of virial equation for 1 mole real gas is as under:

$\mathrm{PV}=\mathrm{RT}\left[1+\frac{\mathrm{A}}{\mathrm{V}}+\frac{\mathrm{B}}{{\mathrm{V}}^2}+\frac{\mathrm{C}}{{\mathrm{V}}^3}+\dots . \mathrm{to} \mathrm{higher} \mathrm{powe} \mathrm{rof} \mathrm{n}\right]$

where A, B and C are constants which are known as second, third and fourth virial coefficients respectively. Then what will be the correct value of Boyle's temperature i.e., ${\mathrm{T}}_{\mathrm{B}}$ i.e., the temperature at which $\mathrm{PV}=\mathrm{RT}$ i.e., ideal gas equation is obeyed?

The van der Waal's constants of a gas are: $\mathrm{a}=0.751{\mathrm{dm}}^6 \mathrm{atm}{ \mathrm{mol}}^{-2}$ and $\mathrm{b}=0.0226{\mathrm{dm}}^3{ \mathrm{mol}}^{-1}.$ Which of the following is correct?

The critical compressibility factor has the value :-

The van der Waal's constant ' $\mathrm{b}$ ' for gas is $0.0329{\mathrm{dm}}^3{ \mathrm{mol}}^{-1}$. The radius of one molecule is :-

Consider the following statements:

The coefficient $\mathrm{B}$ in the virile equation on state

${\mathrm{PV}}_{\mathrm{m}}=\mathrm{RT}\left(1+\frac{\mathrm{B}}{{\mathrm{V}}_{\mathrm{m}}}+\frac{\mathrm{C}}{{\mathrm{V}}_{\mathrm{m}}^2}+\dots \dots ..\right)$

a : is independent of temperature

b : is equal to zero at boyle temperature

c : has the dimension of molar volume

Which of the above statements are correct.

Consider the following statements: If the vander Waal's parameters of two gases are given as

$\begin{array}{ll} \mathrm{a}(\mathrm{atm}\mathrm{lit} \left.{}^2{ \mathrm{mol}}^{-2}\right)& \left.\mathrm{b} (\mathrm{lit} {\mathrm{mol}}^{-1}\right)\\ \mathrm{Gas}\mathrm{X}: 6.5& 0.056\\ \mathrm{Gas}\mathrm{Y}: 8.0& 0.011\end{array}$

then $\mathrm{a}:{\mathrm{V}}_{\mathrm{C}}\left(\mathrm{X}\right)<{\mathrm{V}}_{\mathrm{C}}\left(\mathrm{Y}\right)$

$\mathrm{b}:{\mathrm{P}}_{\mathrm{C}}\left(\mathrm{X}\right)<{\mathrm{P}}_{\mathrm{C}}\left(\mathrm{Y}\right)$

$\mathrm{c}:{\mathrm{T}}_{\mathrm{c}}\left(\mathrm{X}\right)<{\mathrm{T}}_{\mathrm{c}}\left(\mathrm{Y}\right)$

Select correct alternate: