Do all the molecules in a 1 -mole sample of CH4(g) have the same kinetic energy at 273 K? Do all

step 1 Problem 33 essentially has two parts. The first asking, do all the molecules in one mole of meth

Do all the molecules in a 1 -mole sample of CH4(g) have the...

Do all the molecules in a 1 -mole sample of $\mathrm{CH}_{4}(g)$ have the same kinetic energy at 273 $\mathrm{K}$? Do all molecules in a 1 -mole sample of $\mathrm{N}_{2}(g)$ have the same velocity at 546 $\mathrm{K}$ ? Explain.

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Key Concepts

Kinetic Molecular Theory

This theory explains that gas molecules are in constant, random motion and that at a given temperature, the average kinetic energy of all molecules is determined solely by that temperature. However, it also implies that individual molecules do not all have the same kinetic energy or velocity at any moment because their speeds naturally vary due to constant collisions and interactions.

Average Kinetic Energy and Temperature

The average kinetic energy of gas molecules is directly proportional to the absolute temperature (expressed by the equation (3/2)kT for ideal gases). This means that, irrespective of the gas type, all molecules in a sample at a given temperature share the same average kinetic energy; however, this does not mean each molecule has the identical kinetic energy.

Maxwell-Boltzmann Distribution

This concept describes the statistical distribution of speeds (and hence kinetic energies) among molecules in a gas. It shows that even though the average kinetic energy is fixed at a certain temperature, the speeds of molecules follow a distribution where many molecules move slower or faster than the average, meaning not all molecules have the same velocity.

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