How Does Thermal Energy Compare to Ionization Energy in a Flame?

[physicsnobrain]

Homework Statement

The energy of particles in a flame at a temperature T might be described by a
Boltzmann distribution. Temperature can be converted to energy (and thereby velocity)
using the gas constant R = 8.3145 J mol-1 K-1. Let us approximate thermal energy in the
flame by RT (squiggly lines mean approximately) where T is in degree Kelvin:
thermal energy ≈ RT
The first ionization energy for Li is 5.20 x 10 2 kJ/mol and the second ionization energy
is 7.29 x 103 kJ/mol. Assume that your Bunsen burner reached 869 ºC, and that nearly all
of Li atoms heated in your Bunsen burner had energies less than 4 x RT. Would you or
would you not expect significant ionization in the flame? Explain.

The Attempt at a Solution

The ionization energy for Li is the opposite of the ionization energy of the flame. The second Li ionization is fairly high, and as a result, I would expect that the ionization energy of the flame is not very significant because the Li ionization is high. Lithium is high on the list of reactive elements, they increase in reactivity going down, example, francium is much more reactive than lithium, I would expect a much larger ionization of flame from franciums ionization compared to lithium.
Am I correct?

 

[DrClaude]

The ionization energy for Li is the opposite of the ionization energy of the flame.

What does "ionization energy of the flame" mean?

Lithium is high on the list of reactive elements, they increase in reactivity going down, example, francium is much more reactive than lithium, I would expect a much larger ionization of flame from franciums ionization compared to lithium.

I don't understand what this has to do with the problem. You only have to consider lithium in the flame. Is it significantly ionized or not?

 

[physicsnobrain]

What does "ionization energy of the flame" mean?


I don't understand what this has to do with the problem. You only have to consider lithium in the flame. Is it significantly ionized or not?

no it is not significantly ionized. I said that.

 

[DrClaude]

no it is not significantly ionized. I said that.

But based on what? I would like to see some calculations...

 

[physicsnobrain]

But based on what? I would like to see some calculations...

well obviously R x T is wayyyyyyyyy less than 4(R)(T)

That is why

 

[DrClaude]

well obviously R x T is wayyyyyyyyy less than 4(R)(T)

You're comparing $RT$ with $4RT$? I think you misunderstood the statement of the problem. First, it says that $E_\mathrm{thermal} \approx RT$, then that $E_\mathrm{thermal}$ is at most $4RT$ (the energy follows a distribution, it is not a fixed value). So how does that compare to the ionization energy?