We know from Chapter 18 that the average kinetic energy of...

We know from Chapter 18 that the average kinetic energy of an ideal gas atom or molecule at Kelvin temperature $T$ is $\frac{3}{2} k T$ . For what value of $T$ does this energy correspond to (a) the bond energy of the van der Waals bond in $\mathrm{He}_{2}\left(7.9 \times 10^{-4} \mathrm{eV}\right)$ and $(\mathrm{b})$ the bond energy of the covalent bond in $\mathrm{H}_{2}(4.48 \mathrm{eV}) ?(\mathrm{c})$ The kinetic energy in a collision between molecules can go into dissociating one or both molecules, provided the kinetic energy is higher than the bond energy. At room temperature $(300 \mathrm{K}),$ is it likely that $\mathrm{He}_{2}$ molecules will remain intact after a collision? What about $\mathrm{H}_{2}$ molecules? Explain.

Key Concepts

Temperature-Energy Conversion

This key idea involves converting energy units (such as electron volts) to temperature scales using the Boltzmann constant. It is essential for comparing the thermal energy available at a given temperature with the energy required to overcome bond energies in chemical species.

Molecular Collisions and Dissociation

In gases, collisions between molecules allow kinetic energy to be shared or transferred, potentially leading to chemical bond breakage if the collision energy exceeds the bond energy. This concept is critical in understanding the conditions under which molecules may dissociate and the effect of temperature on molecular stability.

Bond Energy

Bond energy refers to the amount of energy required to break a chemical bond between atoms. It serves as a benchmark for evaluating the stability of molecular bonds and is crucial in determining whether thermal collisions have enough energy to initiate bond dissociation.

Average Kinetic Energy of Gas Molecules

This concept establishes that the average kinetic energy of an ideal gas molecule is given by (3/2)kT, linking the microscopic thermal motion of particles with the macroscopic temperature of the system. It forms the basis for understanding how thermal energy is distributed among the particles in a gas.

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