The number of lone pairs on a linear molecule's central atom can vary, but a linear molecule MUST have atoms arranged in a straight line. This arrangement is dictated by the central atom's electron pair geometry.
Here's a breakdown:
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Two Bonded Atoms, No Lone Pairs: In the simplest case, a linear molecule has a central atom bonded to two other atoms with no lone pairs on the central atom. Examples include carbon dioxide (CO2) and beryllium chloride (BeCl2). These molecules are linear because the two bonding pairs repel each other equally, resulting in a 180-degree bond angle.
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Linear with Lone Pairs: It's also possible to have a linear molecule where the central atom does have lone pairs. The key is that the electron pair geometry around the central atom must be linear, trigonal bipyramidal, or octahedral, and the lone pairs must be positioned such that the bonded atoms are forced into a linear arrangement.
- Trigonal Bipyramidal Electron Geometry: This occurs when there are five regions of electron density (bonding or lone pairs) around the central atom. If three of these are lone pairs and two are bonding pairs, the molecule will be linear. A classic example is the triiodide ion (I3-), where the central iodine atom has two bonding pairs and three lone pairs, resulting in a linear shape.
- Octahedral Electron Geometry: This occurs when there are six regions of electron density around the central atom. If four of these are lone pairs and two are bonding pairs, the molecule will be linear. Xenon difluoride (XeF2) exemplifies this.
Therefore, a linear molecule can have 0 lone pairs (on the central atom), or it can have 3 lone pairs (on the central atom, with a trigonal bipyramidal electron geometry), or it can have 4 lone pairs (on the central atom, with an octahedral electron geometry). The number of lone pairs dictates the geometry, but the shape ends up linear because of the positioning of the lone pairs.
