Arrange nitrogen dioxide molecule `(NO_(2)),` nitronium ion `(NO_(2)^(+))` and nitriteion `(NO_(2)^(-))` in incrasing order of bond angle and explain the order.

Explanation

`NO_(2)^(-)` ion: Total number of electrons in the valence shell of the N-atom of the ion=[5 valence electrons of N-atom +2 electrons of O-atom linked by a double bond +1 electrons of O-atom linked by a single bond]=[8 electrons or 4 electron pairs]=[`2sigma`-bond-pairs+1 lone pair+1`pi`-bond pair]. since `pi`-bond pair plays no role in determining the shape of the molecule, according to VSEPR theory, the three electron pairs will be oriented towards the corners of an equilateral triangle and the shape of the ion having one lone-paiir angular. in this case, the lone pair-bond pair repulsion is greater than the repulsion between two bond pairs of the two bonds having partial double bond character due to resonance. as a result, the O-N-O bond angle `(115^(@))` is less than the expected regular trigonal shape with greater O-N-O bond angle `(120^(@))`.

`NO_(2)` molecule: total number of electrons in the valence shell of the N-atom of the molecule =[5 valence electron of N-atom +2 electrons of O-atom linked by a double bond+zero electron of the O-atom linked by a co-ordinate covalent bond]=7 electrons=[3 electron pair+1 odd electron]=[`1sigma`- bond pair+1 coordinate `sigma`-bond pair+`1pi`-bond pair`+1`odd electron]. according to VSEPR theory, two bond pairs and the odd electron are arranged trigonally in a plane so, the shape of `NO_(2)` molecule having an odd electron is angular. in this case, the repulsive force between the bond pairs of two bonds having parrtial double bond character is greater than the repulsive force acting between the bond pairs and the odd electron. As a result, the value of O-N-O bond angle `(135^(@))` is greater than that of the regular planar trigonal shape `(120^(@))`.

`NO_(2)^(+)` ion: Total number of electrons in the valence shell of the N-atom of the ion=5 electrons of N-atom +4 electrons of two O-atoms linked by two double bonds-1 electron for the positive charge=8 electrons=4 electron pairs=`2sigma`- bond pairs+`2pi`-bond pairs. the two `pi`-bond pairs have no contribution towards the shape of theion. according to VSEPER theory, the two bond pairs are oriented in opposite directions. hence, the shape of the `NO_(2)^(+)` ion is linear and the value of O-N-O bond angle is `180^(@)`.
therefore, the increasing order of O-N-O bond angle of the given species is `NO_(2)^(-) lt NO_(2) lt NO_(2)^(+)`.