Bonds

• holds atoms together
• change the properties
• care about nature of bond and resulting shapes
  • example: graphene vs polyethylene
  • insert hexagon vs chain

Ionic Bond §

• complete transfer of one or more electrons from one atom to another
• has dipoles
• formed between 2 atoms of differing electronegativity ($\Delta \text{EN}>2$)
• example: $NaCl$. electron goes from Na to. Cl
  • IE of Na is 495.8
  • IE of Cl is 1251.2
  • Cl is 3p orbital but less energy than Na because increased number of protons, but not increased principle quantum number (distance from nucleus)
• atoms that form ions w/ noble gas configurations are very stable
  • NaCl is example once again
  • Na -> Ne, Cl -> Ar
    • $Na\to N{a}^{+}+e^{-}$, $Cl+e^{-}=C{l}^{-}$
  • 8 electorns in valence shell
  • octet rule: atoms with 8 electrons around them are stable
  • general rule
    • Group 1 likes to lose electron -> $A^{+}$
    • Group 2 likes to lose 2 electrons -> $A^{2+}$
    • Group 3 likes to lose 3 electrons -> $A^{3+}$
    • Group 6 likes to gain 2 electrons -> $A^{2-}$
    • Group 7 likes to gain electron -> $A^{-}$

To calculate the change of energy when K bonds with F,

$$\begin{array}{c}K\to K^{+}+e^{-},\Delta E=I{E}_1=419\frac{kJ}{mol}\\ e^{-}+F\to F^{-},\Delta E=-EA=-328\frac{kJ}{mol}\\ V_{\infty }=\Delta E_{\infty }\\ V(R_{KF})=\frac{q_K{q}_F}{4\pi {ϵ}_0{R}_{KF}}+V_{\infty }\end{array}$$

Basically, the potential energy for a distance of $R_{KF}$ between the two ions in terms of Joules per ion pair is the above. To get it in $\frac{kJ}{mol}$, we need to multiply by Avogadro’s number and divide by 1000.

$$V(R_{KF})=\frac{q_K{q}_F(}{4\pi {ϵ}_0{R}_{KF}}\left(\frac{N_A}{10^3}\right)+V_{\infty }$$

Covalent Bonds §

• $\Delta \text{EN}<0.4$
• electrons are shared evenly

Polar-Covalent Bonds §

• gray area between ionic and covalent
• somewhat closer to one atom than another

Let’s consider the simple molecule H2

• forms of energy
  • potential: energy due to position or composition
  • kinetic: motion

Energy §

Let’s consider the simple molecule $H_2$.

Potential Energy §

• energy due to composition or position

$$V=V_{en}+V_{ee}+V_{nn}$$

• $V_{en}$ is attractive
• $V_{ee}+V_{nn}$ are repulsive

$$V=\frac{e^2}{4\pi {ϵ}_0}\left(\frac{1}{r_{1a}}+\frac{1}{r_{2a}}+\frac{1}{r_{1B}}+\frac{1}{r_{2B}}\right)+\frac{e^2}{4\pi {ϵ}_0}\left(\frac{1}{r_{12}}\right)+\frac{e^2}{4\pi {ϵ}_0}\left(\frac{1}{R_{AB}}\right)$$

Total Energy §

$$E=\sum {\text{KE}}_e+\sum {\text{KE}}_n+V$$

Morse Potential §

Morse potential curve describes the potential energy in a diatomic bond as a function of the radius. The basic version looks like the diagram below.

When the $r<r_{eq}$, the repulsion force between the electrons of one atom and another and the repulsion of the nuclei of each atom generate high potential energy. Then, as $r>r_{eq}$ the attractive force between the electrons of one atom and the nucleus of the other is what increases potential energy.

Below is a diagram for an ionic bond.

• strong ionic bond
• the potential energy is less at $r_{eq}$ since the bond is super stable
• $r_{eq}$ is shorter because stronger bond
• potential energy is larger because of energy required to ionize both ions in the bond

Bond Descriptors §

Bond Length §

• distance between 2 atoms
• shorter -> stronger

Energy §

• $\Delta E_d$ larger = more stable
• reproducible from molecule to molecule
• C-O $\Delta E_d$ is $\pm 10\%$
• O-H $\Delta ϵ=465\frac{kJ}{mol}$

Order §

• number of shared electrons between 2 pairs of atoms
• more electrons = stronger = shorter distance

Polarity §

• absolute value of the difference in electronegativity between 2 bonded atoms
  • large difference > 2 => ionic
  • small < 0.4 => covalent
  • in between 0.4 -> 2 => polar covalent
• $H^{\delta +}-F^{\delta -}$: $\Delta =|2.2-3.98|=1.78$
• $\delta$
  • fraction of charge on each atom
  • $q=\delta e$ is total charge
  • $\delta$ is 1 and 0 for ionic bond
  • measurable
    • $\mu =(\frac{R}{0.2082\mathcal{A}})\delta$ is dipole moment in debye
    • $R$ is bond length in $\mathcal{A}$
    • for HF, $\mu =1.82\text{D},R=0.917\mathcal{A}⟹\delta =1.82\text{D}(\frac{0.2082\mathcal{A}}{0.917\mathcal{A}}=0.41$ ionic

Oxidation Number/States §

• oxidation numbers: fictitious charges on each atom in molecule
  • $C{r}^{3+}$ good for you, $C{r}^{6+}$ gives you cancer
  • $C{o}^{3+}\to C{o}^{4+}+e^{-}$ powers phones

Rules §

1. number of atoms in neutral molecular must add to charge of ion (0 if neutral)
2. alkali-metal atoms = +1, alkaline earth atoms = +2 b/c noble gas
3. $F=-1$ above all (unless $F_2$) and halogens = $-1$ because noble gas (unless other halides or $O$)
4. $H=+1$ unless alkali metal then $H=-1$
5. $O=-2$ unless with $F$ (rule 3)

Bonding in Different Families §

Different families of elements bond differently.

1. Bonding in organic molecules
2. Bonding in Transition Metals