Getting the depth right

A question that often comes up in face to face workshops is a really good one that is also difficult to answer! The question is usually ‘what depth do I need to go into?’ and it will be with regards to one of the new areas of the course.

My initial feeling was to relate the syllabus statement to the learning objectives. For example, in topic 11.3 (measurement and data processing – spectroscopic identification of organic compounds) we see that under application and skills, one of the statements is ‘Determination of the IHD from a molecular formula.’ Now, ‘determine’ is an objective 3 command term so, to me, it would seem (logical?) that this would indicate the level of depth …. Although I have since been told that this is not the case – I do still feel that it is a useful rule of thumb in helping to gauge things.

Let me explain through an example using topic 14.1, Chemical bonding and structure – further aspects of covalent bonding and structure – in particular, ‘Explanation of the wavelength of light required to dissociate oxygen and ozone’ – this is something that is new to the course and so it would be fair to ask, how much depth do I need to include?

For example, is it suffice to teach the following:

As the O₂ double bond energy is 498 kJ mol ^-1 (from the data book) and the O₃ bond energy will be somewhere in-between the O=O double bond and the O-O single bond (144 kJ mol ^-1) the wavelength of radiation needed to break the O₂ double bond will be smaller (and hence higher in energy) than the amount of energy needed to break the O₃ bond? This is why Ozone dissociates more readily than O₂.

This, I felt was deep enough until I thought about how this explanation related to the command term. All I have really addressed here is the objective 1 term, ‘state’.

In order to ‘explain’ and to do this statement credit I needed to first take the above explanation a step further and show my students through calculations (objective 2) how the wavelength needed to dissociate the O₂ double is smaller than that of the ozone bond.

The calculations involve some tricky numbers but are just relay derived from rearranging and combining equations:

c =λv can be rearranged to give v = c / λ

As E = hv we can substitute c / l for v to give

E = hc /λ

Which can be rearranged to give λ = hc / E

Now, if the energy to break a O=O bond is 498 kJ mol ^-1, we can determine the energy to break one bond by dividing by 6.02 x 10 ²³ (to give 8.27 x 10 ^-22 kJ = 8.27 x 10 -19 J).

This means that the wavelength of light to break one bond will be l = (6.63 x 10 ^-34) (3 x 10 ⁸) / 8.27 x 10 ^-19 = 2.4 x 10 ^{– 7} m (x 1,000,000,000) = 241nm.

The ozone bond is a resonance hybrid, so if one makes the assumption that the energy needed to break this is the midpoint of the O=O double bond (498 kJ mol ^-1) and O-O single bond (144 kJ mol ^-1) is 321 kJ mol -1 the same calculation can be used to give a value of 1.989 x 10 ^-25 / 5.33 x 10 ^{– 19} = 3.73 x 10 ^-7m =373nm.

Now we can clearly see that 241 nm is smaller (and hence higher in energy) than 373 nm.

This explanation – I am sure you will agree is much more worthy of an objective three command term as implied by the syllabus statement!

By the way, the actual value of light needed to break ozone is 330nm, which implies that more energy is needed to break the delocalised bond in ozone. This implies that the bond in ozone resembles the double bond more than the single bond. What really stumps me is why? I am sure the explanation is simple enough ……. if you know, I’d be really grateful to read your thoughts!