Question

Arrange the following molecules in order of increasing average molecular speed. H2 at 371K, NO2 at 339K, Ne at 371K, H2 at 425K Enter formulas and temperatures in the boxes below: 1 = slowest, 4 = fastest 1 at K 2 at K 3 at K 4 at K ???

Answer 1

1 - `NO_2` at 339 K
2 - `Ne` at 371 K
3 - `H_2` at 371 K
4 - `H_2` at 425 K

Explanation:

Kinetic Energy is directly related to temperature; the higher the temperature the higher the kinetic energy. Kinetic energy is also equal to `1/2 m*v^2`, so if we want a high velocity we want high temp and low mass. So let's list out approximate masses:

`m(H_2) ~~ 2`
`m(NO_2) ~~ 46`
`m(Ne) ~~ 20`

So we have `NO_2` at 339 K, the lowest temperature out of the mix, and the highest mass out of the mix, so this is moving the slowest.

In contrast, we have `H_2` at 425 K, the highest temperature out of the mix, and the lowest mass out of the mix, so this is moving the fastest.

Now we have `Ne` and `H_2` at 371 K, since they are at the same temperature they have the same kinetic energy. But `H_2` is lighter than `Ne` so it must be faster. To quantify this mathematically, let's assume (this is wrong but just as an assumption for an example) KE at 371 K is 100:

`100 = 1/2 * m * v^2`
`200 = m * v^2`
`sqrt(200/m) = v`
So `H_2` is about `v=10` and `Ne` is about `v = sqrt(10) ~~ 3`

So the order to recap is:
1 - `NO_2` at 339 K
2 - `Ne` at 371 K
3 - `H_2` at 371 K
4 - `H_2` at 425 K

Hope that makes it clearer!