## Solution 1:

Here room the $\ceH-X-H$ shortcut angles and also the $\ceH-X$ shortcut lengths:\beginarraylcc\textmolecule & \textbond angle/^\circ & \textbond length/\pupm\\\hline\ceH2O & 104.5 & 96 \\\ceH2S & 92.3 & 134 \\\ceH2Se& 91.0 & 146 \\\hline\endarray

The classic textbook explanation would certainly argue that the orbitals in the water molecule is near to being $\cesp^3$ hybridized, however due to lone pair - lone pair electron repulsions, the lone pair-X-lone pair angle opens up up slightly in bespeak to alleviate these repulsions, thereby forcing the $\ceH-X-H$ angle to contract slightly. So rather of the $\ceH-O-H$ angle being the perfect tetrahedral edge ($109.5^\circ$) that is slightly reduced to $104.5^\circ$. On the various other hand, both $\ceH2S$ and also $\ceH2Se$ have no orbit hybridization. The is, The $\ceS-H$ and also $\ceSe-H$ bonds usage pure $\cep$-orbitals from sulfur and selenium respectively. 2 $\cep$-orbitals are used, one because that each that the 2 $\ceX-H$ bonds; this leaves an additional $\cep$-orbital and also an $\ces$-orbital to host the 2 lone bag of electrons. If the $\ceS-H$ and $\ceSe-H$ bonds offered pure $\cep$-orbitals us would intend an $\ceH-X-H$ interorbital edge of $90^\circ$. We see from the over table that us are an extremely close come the measured values. We can fine track our answer by saying that in bespeak to mitigate repulsion between the bonding electron in the 2 $\ceX-H$ bonds the angle opens up up a little wider. This explanation would be regular with the $\ceH-S-H$ angle gift slightly bigger than the matching $\ceH-Se-H$ angle. Due to the fact that the $\ceH-Se$ link is longer then the $\ceH-S$ bond, the interorbital electron repulsions will be much less in the $\ceH2Se$ situation alleviating the require for the bond edge to open up as much as it did in the $\ceH2S$ case.

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The only brand-new twist on all of this the some universities are now teaching is the water is no really $\cesp^3$ hybridized, the $\cesp^3$ explanation does no fit with all of the experimentally observed data, most notably the photoelectron spectrum. The an easy concept presented is that "orbitals just hybridize in solution to bonding." for this reason in water, the orbitals in the two $\ceO-H$ bond are approximately $\cesp^3$ hybridized, yet one lone pair resides in a practically pure p-orbital and the various other lone pair is in a about $\cesp$ hybridized orbital.

## Solution 2:

The concern asks why water has actually a larger angle than other hydrides the the type $\ceXH2$ in details $\ceH2S$ and also $\ceH2Se$. There have actually been other comparable questions, so an effort at a general answer is given below.There are, of course, numerous other triatomic hydrides, $\ceLiH2$, $\ceBeH2$, $\ceBeH2$, $\ceNH2$, etc.. It transforms out that some are linear and some are V shaped, yet with various bond angles, and also that the same basic explanation deserve to be offered for every of these cases.

It is clear that together the bond angle because that water is neither $109.4^\circ$, $120^\circ$, nor $180^\circ$ the $\cesp^3$, $\cesp^2$ or $\cesp$ hybridisation will not explain the shortcut angles. Furthermore, the UV photoelectron spectrum the water, which procedures orbital energies, needs to be described as go the UV absorb spectra.

The way out that this problem is come appeal to molecular orbital theory and to build orbitals based ~ above $\ces$ and $\cep$ orbitals and also their overlap as bond angle changes. The orbital diagram was cleared up a lengthy time earlier is now referred to as a Walsh chart (A. D. Walsh J. Chem. Soc. 1953, 2262; DOI: 10.1039/JR9530002260). The figure below sketches such a diagram, and the next few paragraphs describe the figure.

The shading suggests the authorize (phase) that the orbital, "like come like" being bonding otherwise not bonding. The energies are relative as space the shape of the curves. ~ above the left space the orbitals arranged in stimulate of increasing energy for a direct molecule; ~ above the right those for a bending molecule. The orbitals labelled $\Pi_\mathrmu$ are degenerate in the linear molecule but not therefore in the bent ones. The labels $\sigma_\mathrmu$, $\sigma_\mathrmg$ describe sigma bonds, the $\mathrmg$ and also $\mathrmu$ subscripts describe whether the combined MO has a center of turning back $\mathrmg$ (gerade) or no $\mathrmu$ (ungerade) and also derive indigenous the irreducible representations in the $D_\mathrm\infty h$ allude group. The labels on the right-hand side refer to representations in the $C_\mathrm2v$ suggest group.

Of the three $\Pi_\mathrmu$ orbitals one develops the $\sigma_\mathrmu$, the various other two space degenerate and non-bonding.One the the $\cep$ orbitals lies in the plane of the diagram, the various other out that the plane, in the direction of the reader.

When the molecule is bend this orbital stays non-bonding, the various other becomes the $\ce3a_1$ orbital (red line) whose power is substantially lowered as overlap v the H atom"s s orbital increases.To occupational out even if it is a molecule is linear or bent all the is crucial is to placed electrons into the orbitals. Thus, the following thing is to do a perform of the number of possible electrons and also see what diagram predicts.\beginarrayrcll \textNr. & \textShape & \textmolecule(s) & \text(angle, configuration) \\ \hline 2 & \textbent & \ceLiH2+ & (72,~\textcalculated)\\ 3 & \textlinear & \ceLiH2, \ceBeH2+ &\\ 4 & \textlinear & \ceBeH2, \ceBH2+ &\\ 5 & \textbent & \ceBH2 & (131, \ce<2a_1^2 1b_2^2 3a_1^1>)\\ 6 & \textbent & \ce^1CH2 & (110, \ce<1b_2^2 3a_1^2>)\\ & & \ce^3CH2 & (136, \ce<1b_2^2 3a_1 1b_1^1>)\\ & & \ceBH2^- & (102)\\ & & \ceNH2+ & (115, \ce<3a_1^2>)\\ 7 & \textbent & \ceNH2 & (103.4, \ce<3a_1^2 1b_1^1>)\\ 8 & \textbent & \ceOH2 & (104.31, \ce<3a_2^2 1b_1^2>)\\ & & \ceNH2^- & (104)\\ & & \ceFH2^+ &\\ \hline\endarray

Other hydrides show comparable effects relying on the variety of electrons in $\ceb2$, $\cea1$ and $\ceb1$ orbitals; for example:\beginarrayll \ceAlH2 & (119, \ce) \\ \cePH2 & (91.5, \ce) \\ \ceSH2 & (92)\\ \ceSeH2 & (91)\\ \ceTeH2 & (90.2)\\ \ceSiH2 & (93)\\\endarray

The agreement with experiment is qualitatively good, but, of food the bond angles cannot it is in accurately identified with such a an easy model only general trends.

The photoelectron spectrum (PES) of water mirrors signals native $\ce2a1$, $\ce1b2$, $\ce3a1$, $\ce1b1$ orbitals, ($21.2$, $18.7$, $14.23$, and $\pu12.6 eV$ respectively) the critical being non-bonding as displayed by the lack of structure. The signal from $\ce3b2$ and $\ce3a1$ orbitals display vibrational framework indicating that these space bonding orbitals.

The variety of UV and visible absorption by $\ceBH2$, $\ceNH2$, $\ceOH2$ space $600 - 900$, $450 - 740$, and also $150 - \pu200 nm$ respectively. $\ceBH2$ has a little HOMO-LUMO power gap between $\ce3a1$ and $\ce1b1$ together the floor state is contempt bent. The an initial excited state, is predicted to be straight as its configuration is $\ce1b_2^2 1b_1^1$ and also this is it was observed experimentally.

$\ceNH2$ has a HOMO-LUMO power gap indigenous $\ce3a_1^2 1b_1^1$ to $\ce3a_1^1 1b_1^2$, for this reason both ground and also excited states must be bent, the excited state edge is approx $144^\circ$. Contrasted to $\ceBH2$, $\ceNH2$ is much more bent for this reason the HOMO-LUMO power gap should be larger as observed.

$\ceOH2$ has actually a HOMO-LUMO power gap indigenous $\ce3a_1^2 1b_1^2$ to $\ce3a_1^2 1b_1^1 4a_1^1$, i.e. One electron promoted from the non-bonding orbital to the an initial anti-bonding orbital. The excited molecule remains bent largely as result of the solid effect of 2 electrons in $\ce3a1$ counteracting the single electron in $\ce4a1$. The bond angle is nearly unchanged in ~ $107^\circ$, but the energy gap will certainly be bigger than in $\ceBH2$ or $\ceNH2$, again as observed.

The bond angle of $\ceNH2$, $\ceNH2-$ and also $\ceNH2+$ are all very similar, $103^\circ$, $104^\circ$, and also $115^\circ$ respectively. $\ceNH2$ has actually the construction $\ce3a_1^2 1b_1^1$ whereby the $\ceb1$ is a non bonding orbital, thus including one electron makes tiny difference, remove one means that the $\ce3a_1$ orbital is not stabilised together much and also so the bond edge is opened a little.

The singlet and also triplet state $\ceCH2$ molecules present that the singlet has actually two electron in the $\ce3a1$ orbital and has a smaller sized angle than the triplet state with just one electron here and also one in the non-bonding $\ceb1$, therefore the triplet floor state bond angle is meant to be bigger than the singlet.

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As the size of the central atom increases, its cell core becomes much more shielded by main point electrons and also it becomes less electronegative. For this reason going under the regular table the $\ceX-H$ bond becomes less ionic, an ext electron density is approximately the $\ceH$ atom for this reason the $\ceH$ nucleus is better shielded, and also thus the $\ceX-H$ bond is longer and weaker. Thus, together usual through trends within the same household in the regular table, the result is, basically, one of atomic size.

Molecules v heavier central atom, $\ceSH2$, $\cePH2$, etc. All have bond angles around $90^\circ$. The to decrease in electronegativity destabilises the $\Pi_\mathrmu$ orbital elevating its energy. The $\ces$ orbitals of the heavier central atoms space larger and lower in energy than those of oxygen, thus these orbitals overlap v the $\ceH$ atom"s $\ces$ orbital an ext weakly. Both this factors aid to stabilise the linear $3\sigma_\mathrmg$ orbital and hence the $\ce4a1$ in the bending configuration. This orbit belongs come the very same symmetry varieties as $\ce3a1$ and also thus they can interact by a second order Jahn-Teller interaction. This is proportional come $1/\Delta E$ where $\Delta E$ is the energy gap between the two orbitals mentioned. The result of this communication is to raise the $\ce4a1$ and decrease the $\ce3a1$ in energy. Thus in going down the collection $\ceOH2$, $\ceSH2$, $\ceSeH2$, etc. The bond angle must decrease i m sorry is what is observed.

Example have actually been provided for $\ceXH2$ molecules, but this technique has likewise been provided to understand triatomic and tetra-atomic molecule in general, such as $\ceNO2$, $\ceSO2$, $\ceNH3$, etc..