Dragos Rule
How do we predict the stability and geometry of covalent hydrides? Why are some hydrides stable and while others are unstable and decompose easily? We will get these answers by studying Drago's rule. Drago’s Rule helps in understanding the bonding in hydrides of Group 13 and 14 elements, particularly in predicting whether $d-p \pi$ bonding or back-donation will occur or not.
Drago's rule is an empirically based concept applied with an understanding of bond angles and molecular geometries of some hydrides; particularly, those that contain the elements of groups 15 and 16 from the periodic table are considered. This is admitted to include elements in the third period and lower, like phosphorus, arsenic, antimony, sulfur, selenium, and tellurium.
Drago's rule
Drago’s Rule is a principle in inorganic chemistry used to predict the bonding behavior of hydrides, particularly of Group 13 (B, Al, Ga) and Group 14 (C, Si, Ge, etc.) elements. Dragos rule explains the bond angles of hydrides of groups 14, 15, and 16 and 2nd members of each of these three groups.
According to Drago's rule, if the central atom is less electronegative and has a low tendency to form multiple bonds, and the hydrogen atoms are not strongly electronegative, then the hybridization of the central atom is not necessary for bond formation. Instead, the bonds are formed using pure atomic orbitals without mixing.
In Drago’s rule, when the various conditions are satisfied as mentioned below, then the energy difference will be very high between the participating atomic orbitals, and hence no mixing of orbitals or hybridization takes place.
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At least one lone pair must be present on the central atom.
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The central atom must be off or below the 3rd period.
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The electronegativity of the surrounding atoms must be less than or equal to 2.1.
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For these hydrides, hybridization does not take place, and thus bonding takes place only through pure atomic p orbitals, like in PH3, and hence the bond angle will be approximately $90^0$.
For example, the bond angle for $\mathrm{H}_2 \mathrm{O}$ is 104.50 but for $\mathrm{S}_2 \mathrm{H}, \mathrm{Se}_2 \mathrm{H}$, and $\mathrm{Te}_2 \mathrm{H}$, the bond angles are approximately $90^0$.
Conditions and Implications of the Drago Rule
The following must be met for Drago's rule to be valid in a good number of cases:
1. Lone Pairs: The central atom has to contain a lone pair of electrons.
2. Element Group: It has to be a member of groups 13 through 16, be on the third period, and be on.
3. Electronegativity: The centrality of the atom, concerning electronegativity, should be 2.5 or less.
In such cases, the sum of sigma bonds and lone pairs on the central atom becomes four. Hybridization is hence not required, and atomic orbitals may directly participate in bond formation. This leads to odd molecular geometries that do not ideally fall into conventional theories of hybridization.
Bond Angle
Bond angle is the angle between two bonds that form between two atoms. The figure given below illustrates the concept.
Real-Life Applications and Relativity
Drago's rule has a huge impact on describing the behavior of so many molecules in such diverse areas. Take for instance the compound phosphine, PH3. The central phosphorus atom contains a lone pair of electrons. As we all have an idea, it falls under group 15 in the periodic table. In addition, its electronegativity is 2.19. Applying Drago's rule, it could easily be derived that the s-character percent in P-H bonds is less, about 6%. Hence, the lone pair in the compound remains in an orbital that is highly rich in s-character. This is something that never happens in a hybridized orbital. This causes the bond angle to be about 90°, which again deviates from the idealized geometry of a tetrahedron.
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Some Solved Examples
Example 1: Why is NH3 a stronger Lewis base than PH3?
1) (correct)In NH3 lone pair is present in one of the sp3 hybridized orbitals, while in PH3 lone pair is present in pure s-orbital.
2)In NH3 lone pair is present in a pure s-orbital, while in PH3 lone pair is present in one of the sp3 hybridized orbitals.
3)In NH3 lone pair is present in one of the sp3d hybridised orbitals, while in PH3 lone pair is present in pure s-orbital
4)None
Solution
In NH3 lone pair is present in one of the sp3 hybridized orbitals, while in PH3 lone pair is present in pure s-orbital.
Hence, the lone pair donation capacity of NH3 is stronger than PH3.
Therefore, option number(1) is correct.
Example 2: As the s-character of a hybridized orbital decreases, the bond angle:
1) Decreases (correct)
2) Increases
3) Does not change
4) Becomes zero
Solution
As the s-character of hybridized orbitals decreases, the bond angle also decreases. In sp3 hybridisation: s-character (1/4), bond angle 109°. In sp2 hybridization: s-character (1/3), bond angle 120°. In sp hybridization: s-character (1/2), bond angle 180°.
Hence, the answer is option (1).
Example 3: The HCH bond angle in {HCHO} is nearly equal to:
1) $120^0$ (correct)
2) $90^{\circ}$
3) $60^0$
4) $ 180^0$
Solution
The hybridization of HCHO is sp2
The bond angle in HCHO is close to 120o Facing repulsion by the lone pair of Oxygen.
Hence, option number (1) is correct
Example 4: Which one of the following compounds has the smallest bond angle in its molecule?
1) $\mathrm{SO}_2 \mathrm{SO} 2$
2) $\mathrm{OH}_2 \mathrm{OH} 2$
3) $\left(\mathrm{SH}_2\right)$ (correct) $\mathrm{SH}_2$
4) $\mathrm{NH}_3 \mathrm{NH}-$
Solution:
The repulsion force acts on bonds due to a lone pair present on the central atom, then the bond angle between multiple bonds decreases.
As the number of lone pairs increases bond angle decreases.
As the size of the central atom increases and lone pairs are also present then the bond angle decreases more.
| Molecule | Bond angle | Number of Lone pairs |
| $\mathrm{SO}_2$ | $119.5^0$ | 1 |
| $\mathrm{H}_2 \mathrm{O}$ | $104.5^0$ | 2 |
| $\mathrm{H}_2 \mathrm{S}$ | $92.5^0$ | 2 |
| $\mathrm{NH}_3$ | $107^0$ | 1 |
O and S have two lone pair.
Atom size S > O
So, $\mathrm{H}_2 \mathrm{S}$has the smallest bond angle.
Hence, the answer is the option (3).
Example 5: The dipole moments of CCl4, CHCl3 and CH4 are in the order:
1) (Correct)$\mathrm{CH}_4=\mathrm{CCl}_4<\mathrm{CHCl}_3$$\mathrm{CH}_4=\mathrm{CCl}_4<\mathrm{CHCl}_3$CH4=CCl4<CHCl3
2)$\mathrm{CHCl}_3<\mathrm{CH}_4=\mathrm{CCl}_4$CHCl3<CH4=CCl4
3)$\mathrm{CH}_4<\mathrm{CCl}_4<\mathrm{CHCl}_3$CH4<CCl4<CHCl3
4)$\mathrm{CCl}_4<\mathrm{CH}_4<\mathrm{CHCl}_3$CCl4<CH4<CHCl3
Solution
Let us first look at the structures of the given compounds
Clearly $\mu \neq 0$ of $\mathrm{CHCl}_3$
Therefore, Option(1) is correct.
$\mathrm{CH}_4=\mathrm{CCl}_4<\mathrm{CHCl}_3$
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Conclusion
In a nutshell, one such principle that aids inorganic chemistry in obtaining knowledge about molecular geometries and bond angles of certain hydride molecules is Drago's rule. Therefore, it can be done that much predictions and explanations of the behavior of these molecules under different contexts by the chemist, based on an understanding of the conditions under which this rule operates and its implications.
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Frequently Asked Questions (FAQs)
Drago's Rule helps predict the likelihood and strength of acid-base reactions. It suggests that reactions between hard-hard or soft-soft pairs will be more favorable and result in stronger bonds compared to hard-soft combinations.
Ion size is an important factor in Drago's Rule. Generally, smaller ions tend to be harder, while larger ions tend to be softer due to differences in charge density and polarizability.
Charge density is closely related to hardness in Drago's Rule. Species with high charge density (high charge in a small volume) tend to be harder, while those with low charge density tend to be softer.
Drago's Rule can help predict solubility trends. For example, hard acids like Na+ tend to form more soluble compounds with hard bases like Cl-, while soft acids like Ag+ form less soluble compounds with soft bases like I-.
In Drago's Rule, polarizability is a key factor in determining whether a species is hard or soft. Hard acids and bases have low polarizability, while soft acids and bases have high polarizability.
Cu+,Ag+,Hg2+, and Pt2+ are examples of soft acids. They are larger, less charged, and more polarizable than hard acids.
I-, RS- (thiolate), and CN- are examples of soft bases. They are larger, less electronegative, and more polarizable than hard bases.
Drago's Rule helps explain the stability of coordination compounds by predicting which ligands (bases) will form stronger bonds with certain metal ions (acids) based on their relative hardness or softness.
Drago's Rule complements Lewis acid-base theory by providing a framework to predict the strength of Lewis acid-base interactions based on the hardness or softness of the species involved.
F−,OH−,Cl−, and H2O are examples of hard bases. They are small, highly electronegative, and have low polarizability.
Drago's Rule is a principle in chemistry that helps predict the strength of acid-base interactions. It states that hard acids prefer to bind with hard bases, while soft acids prefer to bind with soft bases. This rule is based on the concept of hard and soft acids and bases (HSAB).
Drago's Rule was developed by Ralph Pearson and further refined by Robert S. Drago. It's an extension of Pearson's HSAB (Hard and Soft Acids and Bases) theory.
Hard acids and bases are typically small, highly charged species with low polarizability. They form strong ionic bonds and have a low tendency to share electrons.
Soft acids and bases are usually larger, less charged species with high polarizability. They form weaker covalent bonds and have a higher tendency to share electrons.
Electronegativity is often correlated with hardness in Drago's Rule. Highly electronegative elements tend to form hard acids or bases, while less electronegative elements often form soft acids or bases.
Hard-hard interactions are typically stronger because they involve ionic bonding between species with complementary charge densities. This results in strong electrostatic attractions.
Drago's Rule helps predict the stability of metal-ligand complexes by indicating which combinations of metals (acids) and ligands (bases) will form the strongest bonds based on their relative hardness or softness.
Drago's Rule refines the concept of Lewis acid strength by categorizing acids as hard or soft. This helps predict not just the strength of acid-base interactions, but also their nature (ionic vs. covalent).
In organic chemistry, Drago's Rule can help predict the reactivity of various functional groups. For example, it can explain why certain nucleophiles (bases) prefer to react with specific electrophiles (acids).
Yes, some species can exhibit borderline behavior, acting as hard or soft depending on the reaction partner. These are often transition metal ions or species with intermediate properties.
In coordination chemistry, Drago's Rule helps predict the stability of metal-ligand complexes. Hard metal ions tend to form more stable complexes with hard ligands, and soft metal ions with soft ligands.
While Drago's Rule primarily predicts stability and strength of interactions, it can indirectly inform reaction rates. Hard-hard or soft-soft interactions often proceed faster than hard-soft interactions.
Drago's Rule refines Lewis acid-base theory by categorizing Lewis acids and bases as hard or soft, which helps predict the strength and nature of their interactions.
Generally, elements on the left side of the periodic table tend to form harder acids and bases, while elements on the right side (especially lower down) tend to form softer acids and bases.
Drago's Rule explains that metal complexes formed between hard metals and hard ligands, or soft metals and soft ligands, tend to be more stable than those formed between hard metals and soft ligands or vice versa.
Higher oxidation states generally lead to harder acids, while lower oxidation states tend to produce softer acids. This is due to changes in charge density and polarizability.
Drago's Rule explains chemical symbiosis, where hard-hard or soft-soft combinations lead to more stable and synergistic interactions, analogous to biological symbiosis.
Yes, Drago's Rule can help predict substitution reaction outcomes by indicating which incoming group (nucleophile) is more likely to successfully replace the leaving group based on their relative hardness or softness.
Pi-backbonding is more common in soft acid-soft base interactions, as explained by Drago's Rule. Soft metal centers and soft ligands are more likely to engage in pi-backbonding due to their higher polarizability.
Drago's Rule helps explain the stability of organometallic compounds by predicting which metal-carbon bonds will be more stable based on the hardness or softness of the metal and the carbon-based ligand.
Drago's Rule is essentially an application and extension of the HSAB principle, providing a more quantitative approach to predicting acid-base interactions based on hardness and softness.
Yes, Drago's Rule can explain halogen reactivity trends. Fluorine, being the hardest halogen, reacts more readily with hard bases, while iodine, the softest halogen, reacts more readily with soft bases.
Electronegativity often correlates with hardness in Drago's Rule. Highly electronegative elements tend to form harder acids or bases, influencing the nature and strength of chemical bonds they form.
Drago's Rule can help predict nucleophilicity and electrophilicity. Soft nucleophiles (bases) tend to react more readily with soft electrophiles (acids), while hard nucleophiles prefer hard electrophiles.
Yes, Drago's Rule can explain solubility trends of metal hydroxides. Hard metal ions form more insoluble hydroxides with the hard OH- ion, while softer metal ions form more soluble hydroxides.
Drago's Rule complements ligand field theory by providing insights into the strength of metal-ligand interactions based on their hardness or softness, which influences the splitting of d-orbitals.
Drago's Rule helps predict which ligands will form more stable complexes with specific metal ions based on their relative hardness or softness, guiding the design and understanding of coordination complexes.
In redox reactions, Drago's Rule can help predict the likelihood of electron transfer. Soft species are generally more easily oxidized or reduced than hard species due to their higher polarizability.
Yes, Drago's Rule explains trends in coordination compound formation. Hard metal ions prefer hard ligands like F- or O-donors, while soft metal ions prefer soft ligands like S-donors or phosphines.
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