If the density of a gas is kept constant but the root mean square velocity of the gas molecules is doubled, then how much will the pressure of the gas increase?
Answer
Based on the molecular kinetic theory of gases the formula of pressure $P =\frac{1}{3} \text {mC} ^2$ when the density is kept constant then it is clear that $P \propto C ^2_{rms}$ that's why to make double of $C _{ rms }$ the pressure will be $2^2$ hence 4 times of it.
There are equal number of molecules of hydrogen and oxygen in a box. If a tiny hole is made in the box, which gas will leak out rapidly and why?
Answer
$C _\text {{rms}} \propto \frac{1}{\sqrt{ M }}$ because the molecular weight M of hydrogen is less than the molecular weight of oxygen. Therefore hydrogen will leak rapidly.
Why cannot an ideal gas be converted or liquid state?
Answer
To convert a gas in to solid or liquid state, it is necessary to have a force of attraction between the molecules, whereas there is no force of attraction between the molecules of an ideal gas, due to which the ideal gas cannot be converted in to solid or liquid.
If the number of molecules in a vessel is halved. What will be the change in pressure?
Answer
If the number of gas molecules in a closed vessel is halved so the number of collisions of molecules on this unit area of the vessel will be halved, due to which the pressure will be half as compared to before.
Two gases are at the same temperature, can we conclude that the r.m.s. of gas molecules? Will the velocities be the same? Why?
Answer
No, if the temperatures are the same then $\frac{3}{2} \text {kT}$, and $\frac{1}{2}\text {mc}^2$ will be same but the value of m is different in different gases. Hence C will also be different.
The root mean square velocity $\text {C}_\text {{rms}}$ of the molecules of a diatomic gas at room temperature is 1930 m/s. If found write the name of gas.
According to this rule, in thermal equilibrium the total kinetic energy of a moving system remains equally distributed among different degrees of freedom the value of energy corresponding to each degree of freedom is kT/2, where k = Boltzmann constant and T = absolute temperature.
If the absolute temperature of a gas is quadrupled, how many times will the root mean square velocity of its molecules increases? How many times will its total energy increase?
Answer
$\therefore{ } C _{ rms } \propto \sqrt{ T }$ Therefore, by increasing T, 4 times, it will double and $E \propto T$ i.e. energy will become four times.
Q If the velocities of four molecules of a gas are $\sqrt{3}, 3,4,6 ~\text {m / sec}$ respectively, then write the value of their root mean square velocity.
Answer
$\begin{aligned} C _{ rms } & =\left(\frac{ C _1^2+ C _2^2+ C _3^2+ C _4^2}{4}\right)^{\frac{1}{2}} \\ & =\left(\frac{(\sqrt{3})^2+(3)^2+(4)^2+(6)^2}{4}\right)^{\frac{1}{2}} \\ C_{ rms } & =\left(\frac{3+9+16+36}{4}\right)^{\frac{1}{2}}=\left(\frac{64}{4}\right)^{\frac{1}{2}} \\ C_{ rms } & =\text {4 m / sec }\end{aligned}$
What will be the ratio between the root mean square velocities and kinetic energies of gas at 270 K and 30K?
Answer
$\begin{array}{l}\frac{\left( C _{ rms }\right)_1}{\left( C _{rms}\right)_2}=\sqrt{\frac{ T _1}{T_2}}=\sqrt{\frac{270}{30}}=\sqrt{\frac{9}{1}}=3: 1 \\ \frac{ E _1}{ E _2}=\frac{ T _1}{T_2}=\frac{270 K}{30 K}=\frac{9}{1}=9: 1\end{array}$
What will be the ratio of root mean square forces of hydrogen and oxygen molecules at the same temperature?
Answer
$\frac{\left( C _{\text {rms }}\right)_{ H _2}}{\left( C _{\text { rms} }\right)_{ O _2}}=\sqrt{\frac{( M )_{ O _2}}{( M )_{ H _2}}}=\sqrt{\frac{32}{2}}=\frac{4}{1}=4: 1$
If a usual made of porous walls is filled with a mixture of two gases and it is kept in a vaccum chamber, then why does the lighter gas come out first? Write the reason.
Answer
Because the value of velocity of molecules of light gas is higher than that of molecules of heavy gases. $\frac{\left(C_{\text {rms }}\right)_1}{\left(C_{\text {rms }}\right)_2}=\sqrt{\frac{ M _2}{ M _1}}$
Generally, monatomic gases are ideal gases. Hydrogen, nitrogen, oxygen and helium gases are considered ideal gases because all of them are liquified with difficulty. These gases behave like real gases and ideal gases at high temperature and low pressure.
The value of the square root of the mean square speed of the molecules of a gas is called the root mean square speed. $C _{ rms }=\left[\frac{ C _1{ }^2+ C _2{ }^2+ C _3{ }^2+\ldots C _n{ }^2}{n}\right]^{\frac{1}{2}}$
What is R in the gas equation PV = nRT? Value of R write in liter atmosphere per Kelvin per mole.
Answer
R is a constant, which is called molar gas constant or gas constant. $\begin{aligned} R & =8.3 \text { joule } / mol - K \\ & =8.3 \text { Newton meter } / mol - K \\ & =8.3 \frac{\text { Newton }}{ m ^2} m^3 / mol - K \\ & =\frac{8.3}{1.03 \times 10^5} \times 10^3 \\ & \text { liter-Atmosphere } / mol - K \end{aligned}$ $\left[\because\right.$ 1 Atmosphere $=1.013 \times 10^5$ Newton $/ m ^2$ and $1 m^3=10^3$ liter] So, $R =0.821$ liter Atmosphere Kelvin 'mol'.
Doubling the pressure at constant temperature for a gas but the molecular weight, what will be the effect on velocity?
Answer
According to the following formula, the root mean square velocity depends on temerpature and not on pressure. $C _{ rms }=\sqrt{\frac{3 RT }{ M }}$ Therefore doubling the pressure will have no effect.