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Testing concepts using the H3+ ion

Monday 18 October 2021


The trihydrogen cation is one of the most abundant molecular species in the universe. It is also one of the simplest and yet nowhere does it appear on the IB syllabus.

Model of the H3+ ion

For a bit of light relief and to widen their interest in chemistry, you might explain to your students the existence of the trihydrogen cation, H3+ and then ask them a few simple questions which will test their understanding of concepts that are very much part of the IB programme.

Some background information

The trihydrogen complex cation, H3+, was first discovered as long ago as 1911 when J.J Thompson was performing his cathode ray tube experiments and came across an ion with an e/m ratio of 1/3. He reasoned that it was unlikely to be C4+ so deduced that it must be H3+. In 1989 the trihydrogen complex ion was  detected in the ionosphere of Jupiter and it has subsequently been found on Saturn and Uranus in our own solar system and in many exoplanets of other solar systems.

However its main concentration is in interstellar space where there is high cosmic radiation. In the presence of this high energy gamma radiation hydrogen gas can lose an electron to form the dihydrogen ion, H2+. This ion then reacts with hydrogen to form H3+.

H2  → H2+ + e 

H2+ + H2 → H3+ + H

In the H3+ complex ion the three equivalent hydrogen atoms are bonded so that they make up the corners of an equilateral triangle:


1. The H3+ ion can act as a Brønsted−Lowry acid. State the conjugate base of the H3+ ion.

H2. (The equation for the dissociation is H3+ ⇄ H2 + H+)

2. The presence of the H3+ ion can be detected by infrared spectroscopy.

What can be deduced about the vibrations of the H3+ complex ion from this information?

At least one of the vibrations must involve a change in dipole moment for it to be IR active.

3. The H3+ ion has a triangular shape. Is it possible to draw a Lewis structure for the H3complex ion?

Not in the normal sense. Lewis structures show valence electrons and how they are paired to form either bonding pairs or non-bonding pairs of electrons The structure of H3+ consists of just two electrons covering three bonds, that is a two electron bond spread over three centres, instead of the usual two, i.e. a delocalized resonance hybrid type of structure.

4. (a) How many isotopic forms of H3+ can exist?

10. (Hydrogen can exist as 1H, 2H and 3H, so ten combinations are possible.)

(b) What will be the relative molar mass of the heaviest isotopic form of H3+?

9. (Due to 3H3+, where all three hydrogen atoms are tritium , i.e. contain two neutrons and one proton each)

5. The H−H bond length in the H3+ ion is 9.0 x 10−11 m. Explain how this compares to the H−H bond length in hydrogen gas.

The H−H bond length is slightly longer in H3+ as less electrons are involved in forming the bond compared to the single H−H bond in hydrogen gas (7.4 x 10−11 m).

6. The bond enthalpy of the H−H bond in H3+ has been calculated to be 4.5 eV (435 kJ mol−1). Comment on how this compares with the H−H bond enthalpy in hydrogen, H2.

The H−H bond enthalpy for hydrogen gas is given in the IB data booklet as 436 kJ mol−1. This is virtually identical to the H−H bond enthalpy in H3+. Although less electrons are involved in each H−H bond in H3+ compared to H2 and so the bond enthalpy might be expected to be less, the delocalized resonance structure appears to contribute significantly to the overall bond strength.


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