# Video: Applying Knowledge of Oxygen-Oxygen Bond Distances, and Atomic Radii of Hydrogen Relative to Oxygen

For statements I and II, state for each if they are true or false. I) The oxygen–oxygen bond distance in O₂ is larger than the oxygen–oxygen bond distance in H₂O₂. II) The atomic radius of H is bigger than the atomic radius of O. If both are true, state if II is a correct explanation for I.

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### Video Transcript

For statements one and two, state for each if they are true or false. 1) The oxygen–oxygen bond distance in O₂ is larger than the oxygen–oxygen bond distance in H₂O₂. 2) The atomic radius of H is bigger than the atomic radius of O. If both are true, state if two is a correct explanation for one.

O₂ is the chemical formula for the oxygen molecule. The element oxygen is found in group 16 of the periodic table. So, we should recall that oxygen atoms have six valiance electrons each. We can start constructing the Lewis structure for O₂ by first working out that we have 12 electrons to play with. And we place the oxygen atoms side-by-side. We then use two electrons to form a single bond between our oxygen atoms. And then, we place lone pairs.

But we only had 10 electrons, which means five lone pairs, which means that one of our oxygens is missing two electrons from its full octet. To remedy this, we use one of the lone pairs on the other oxygen to form a double bond between the two atoms. So, the O₂ molecule has a double bond between the two oxygen atoms. Now, let’s have a look at H₂O₂, which is the molecular formula for hydrogen peroxide.

A molecule of hydrogen peroxide contains two hydrogen atoms, which each contribute one valence electron. And the two oxygen atoms contribute six electrons each. So, in total, we have 14 electrons to place in our Lewis structure. We place our oxygens in the middle, since they can form more bonds than hydrogen can, and a hydrogen on each end. And then, we use six electrons to form single bonds between the atoms in a line.

These single bonds satisfy the valence shell of hydrogen, which has a maximum occupancy of two. And we introduced the eight remaining electrons as lone pairs on each of the oxygens. The valence shells of all the atoms in hydrogen peroxide are satisfied. And we’ve used up all the electrons. So, we know that there’s a single bond between the two oxygen atoms in a molecule of hydrogen peroxide. So, what’s this got to do with the oxygen–oxygen bond distance?

If we look deeper into the O₂ molecule, we’ll see two oxygen nuclei. And the electrons of both atoms are blurred together in a big electron cloud. The double bond isn’t some solid pole that connects the nuclei; it’s actually a complex interaction between the nuclei and the electron cloud. So, when we talk about the bond distance, we’re really talking about the distance between the two nuclei because that’s the only distance we can reasonably measure.

In the O₂ molecule, there are four electrons in the double bond, which means there are strong forces of attraction between the nuclei and the electrons in-between. While in the single oxygen–oxygen bond in hydrogen peroxide, there are only two electrons. So, we’d actually expect the single oxygen–oxygen bond in hydrogen peroxide to be longer than the double bond in oxygen. Therefore, statement one is false. The oxygen–oxygen bond distance in O₂ is smaller than the oxygen–oxygen bond distance in H₂O₂.

Statement two suggests that the atomic radius of hydrogen is bigger than the atomic radius of oxygen. Now, atoms aren’t actually hard spheres, so measuring their radius is quite tricky. But there are things that will suggest that one type of atom will be bigger or smaller than another. And the simple rule of thumb is that the more occupied electron shells there are, the bigger the atom will be.

The atomic number of hydrogen is one, so every hydrogen atom contains one proton in its nucleus and one electron in the surrounding space. So, the electron configuration of a hydrogen atom in its ground state is 1s1. So, for a hydrogen atom, there’s a single electron in the first electron shell. Oxygen has an atomic number of eight, so oxygen atoms have eight protons in their nuclei and eight electrons in the surrounding space. The electron configuration for an oxygen atom in its ground state is 1s2 2s2 2p4. So, an atom of oxygen has electrons in the second electron shell. So, on this basis, we’d expect the atomic radius of a hydrogen atom to be smaller than the atomic radius of oxygen. And therefore, statement two is false.

Now, you may have noticed that the nucleus of oxygen has a much bigger charge, having eight protons in it versus hydrogen’s one. So, the first electron shell of oxygen is actually much smaller and denser than the first electron shell in hydrogen. However, the second electron shell, where the other electrons are in oxygen, is much, much bigger than the first. So, an oxygen atom is still bigger than a hydrogen atom. Neither of statements one and two were true, so we don’t have to address the last part of the question.