In two vessels of 1 litre each at the same temperature 1 g of H2 and 1 g of CH4 are taken, for

step 1 Hello students. In this question, we have two vessels, each of volume 1 liter and have the same

In two vessels of 1 litre each at the same temperature 1 g...

In two vessels of 1 litre each at the same temperature $1 \mathrm{~g}$ of $\mathrm{H}_{2}$ and $1 \mathrm{~g}$ of $\mathrm{CH}_{4}$ are taken, for these: (a) $V_{\mathrm{rms}}$ values will be same (b) Kinetic energy per mol will be same (c) Total kinetic energy will same (d) Pressure will be same

In two vessels of 1 litre each at the same temperature $1 \mathrm{~g}$ of $\mathrm{H}_{2}$ and $1 \mathrm{~g}$ of $\mathrm{CH}_{4}$ are taken, for these:
(a) $V_{\mathrm{rms}}$ values will be same
(b) Kinetic energy per mol will be same
(c) Total kinetic energy will same
(d) Pressure will be same

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Key Concepts

Root Mean Square Speed

The root mean square speed represents the square root of the average of the squared speeds of gas particles and is given by the expression sqrt(3RT/M). This shows that at a constant temperature, the rms speed is inversely proportional to the square root of the molar mass, meaning lighter molecules travel faster on average than heavier ones.

Average Kinetic Energy per Mole

According to kinetic theory, the average kinetic energy per mole of gas is given by (3/2)RT. This relationship demonstrates that at a fixed temperature the kinetic energy per mole is constant for all ideal gases, regardless of the type or mass of the molecules.

Total Kinetic Energy

Total kinetic energy is the cumulative kinetic energy of all molecules within a system. While the average kinetic energy per particle (or per mole) is dictated by the temperature, the total kinetic energy depends on the number of particles present, linking microscopic energy contributions to macroscopic quantities.

Pressure in Gases

In the kinetic theory framework, pressure arises from the bombardment of gas molecules against the walls of their container. This pressure is influenced by both the molecular speeds (and thus kinetic energies) and the number of molecules per unit volume, connecting microscopic motion with the observable macroscopic pressure in a gas sample.

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