User: 

do formal charge determine whether something is cation or anion

Assistant:  FormalFormal charge helps determine the distribution of charge within a molecule or ion on individual atoms, but it does **not directly determine whether the entire species is a cation or anion**. 

Here's why:

- **Formal charge** is a bookkeeping tool used to estimate the charge on individual atoms within a molecule or ion by assuming equal sharing of electrons in covalent bonds. It helps identify the most stable Lewis structure and predict the reactivity or site of reactivity in molecules.

- The **overall charge** of a molecule or ion (whether it is a cation, anion, or neutral) depends on the sum of the charges of all atoms (including formal charges and any extra electrons or missing electrons due to ionization).

### Example:
- In the sulfate ion, \(\mathrm{SO_4^{2-}}\):
  - The formal charges on sulfur and oxygen atoms may be assigned based on the Lewis structure.
  - But overall, the ion carries a \(-2\) charge (making it an anion), irrespective of individual formal charges.

- In the ammonium ion, \(\mathrm{NH_4^{+}}\):
  - The nitrogen atom usually carries a formal positive charge.
  - The entire species is a cation with a net +1 charge.

### Summary:
- **Formal charges help understand charge distribution within a molecule/ion.**
- **The net sum of these charges (plus any ionic charge) defines whether the species is a cation, anion, or neutral.**

If you want to know whether a species is an anion or cation, you look at its overall charge rather than just individual formal charges.
User: formal charrge of an individual element? For example, in CH3, i see formal charge of +1 on carbon. That means its cation?
Assistant:  GreatGreat question!

Let's clarify how formal charge on **an individual atom** relates to the overall charge of a molecule or ion.

---

### Formal charge on an atom:

- Formal charge is a hypothetical charge assigned to an individual atom in a molecule based on electron counting.  
- It is calculated as:

\[
\text{Formal charge} = (\text{valence electrons in free atom}) - (\text{non-bonding electrons}) - \frac{1}{2} (\text{bonding electrons})
\]

- It **does not mean that atom is necessarily a free cation or anion**, just that its electron distribution in the molecule makes it electron-rich or electron-poor relative to the neutral atom.

---

### Case of \(\mathrm{CH_3}\):

- \(\mathrm{CH_3}\) (methyl radical) is usually neutral overall.
- If you calculate formal charges in the methyl radical (\(\mathrm{CH_3}\)):

  - Carbon starts with 4 valence electrons.
  - In \(\mathrm{CH_3}\), carbon forms 3 bonds with hydrogen and has one unpaired electron.
  - The radical unpaired electron counts as half an electron in bonding/nonbonding for formal charge calculation.  
  - Usually, the formal charge on carbon in \(\mathrm{CH_3}\) radical is **0** because the carbon has 3 bonds and 1 unpaired electron, balancing the count.

- Sometimes if a specific Lewis structure is drawn showing carbon with 4 bonds and an extra proton around it, carbon might have a **formal charge +1**, but that structure typically represents the methyl cation (\(\mathrm{CH_3}^+\)), **not the neutral methyl radical**.

---

### So:

- If the **entire molecule/ion's net charge is zero**, the species is neutral, even if individual atoms have formal charges (like +1 or -1) that sum to zero overall.
- If the **sum of formal charges on all atoms is +1**, the species is a cation (e.g., \(\mathrm{CH_3}^+\)) — it has an overall positive charge.
- If the **sum is -1**, it's an anion.
  
---

### Summary for your example:

- If carbon has formal charge +1 in \(\mathrm{CH_3}\), it means the **species as a whole is a cation** (\(\mathrm{CH_3}^+\), methyl cation), **not neutral**.
- The formal charge of carbon alone does not tell whether the atom itself is an isolated ion, but reflects its electron deficiency relative to neutral carbon within the overall species.
- You need to look at the **sum of formal charges** on **all atoms** to determine the overall charge (cation/anion/neutral).

---

If you want, I can help by calculating formal charges for \(\mathrm{CH_3}\), \(\mathrm{CH_3}^+\), and \(\mathrm{CH_3}^-\). Would you like that?
User: so if you have CH3 the most likely structure is 3 single bonds and 1 single electron on carbon?
Assistant:  ExactlyExactly! For the neutral methyl radical \(\mathrm{CH_3}\):

- Carbon forms **3 single bonds** with three hydrogen atoms.
- Carbon has **one unpaired electron** (a radical electron).
- This gives carbon 3 bonding pairs and 1 single (unpaired) electron.

### Key points:

- The unpaired electron is not paired with another electron in a bond; it makes the molecule a **radical**.
- The formal charge on carbon in this species is usually **0**:
  - Valence electrons of neutral carbon = 4
  - Non-bonding electrons = 1 (the unpaired electron)
  - Bonding electrons = 6 (3 bonds × 2 electrons each)
  
  Calculate formal charge:
  
  \[
  \text{FC} = 4 - 1 - \frac{6}{2} = 4 - 1 - 3 = 0
  \]

- So carbon is **neutral** in terms of formal charge here.
- The molecule as a whole is neutral but a radical because of the unpaired electron.

---

### Summary for neutral \(\mathrm{CH_3}\):

- 3 single C–H bonds
- 1 unpaired electron on carbon (makes it a radical)
- Overall charge = 0 (neutral species)
- Carbon formal charge = 0

---

If you had \(\mathrm{CH_3}^+\) (methyl cation):

- Carbon would have 3 single bonds to H and **no unpaired electron**
- Formal charge on carbon = +1
- Overall molecule charge = +1 (cation)

If you had \(\mathrm{CH_3}^-\) (methyl anion):

- Carbon would have 3 single bonds plus 1 lone pair (2 electrons)
- Formal charge on carbon = -1
- Overall molecule charge = -1 (anion)

---

Would you like me to show formal charge calculations for those charged species too?
User: do methyl cations adn methyl anions in this structure appear too or no
Assistant:  GreatGreat question! Let's discuss whether **methyl cations (\(\mathrm{CH_3}^+\))** and **methyl anions (\(\mathrm{CH_3}^-\))** exist with the structures we've talked about.

---

### Methyl cation (\(\mathrm{CH_3}^+\)):

- **Structure:** Carbon bonded to three hydrogens with no lone pairs; it has only 6 valence electrons around carbon (electron-deficient).
- **Geometry:** Trigonal planar, with an empty p orbital.
- **Existence:** Yes, methyl cations are known and important intermediates in organic chemistry (carbocations).  
- They are **very reactive** and rarely isolated under normal conditions but can be observed in superacids, gas phase, or in some stabilized environments.
- You can draw \(\mathrm{CH_3}^+\) as carbon with three single bonds to H and a formal charge +1 on carbon.

---

### Methyl anion (\(\mathrm{CH_3}^-\)):

- **Structure:** Carbon bonded to three hydrogens plus one lone pair (giving carbon a full octet with 8 electrons).
- **Geometry:** Tetrahedral.
- **Existence:** Yes, methyl anions also exist but are highly reactive and strong bases.
- In fact, methyl anion is a foundational example of a **carbanion**.
- Usually they exist transiently or are stabilized by metals in organometallic compounds (such as methyl lithium or methyl magnesium bromide).
- You can draw \(\mathrm{CH_3}^-\) as carbon with three bonds to hydrogen and one lone pair, with a formal charge -1 on carbon.

---

### Summary:

- Both methyl cation and methyl anion **do appear** as valid species with the structures discussed.
- They are generally **reactive intermediates** or exist under special/stabilized conditions.
- Their structures differ mainly in the number of electrons around carbon and resulting geometry.
- Neutral methyl radical (\(\mathrm{CH_3}\)) is different: it has an unpaired electron instead of a full positive or negative charge.

---

If you want, I can also help show how these species behave in reactions or their relative stabilities!
User: but do radical carbon appear most frequently?
Assistant: Good question!

### Do carbon-centered radicals (like the methyl radical, \(\mathrm{CH_3}\cdot\)) appear most frequently?

**It depends on the context**, but generally:

- **Carbon radicals do appear frequently**, especially as reactive intermediates in many organic reactions (like combustion, polymerization, photochemical reactions, and radical chain mechanisms).
- However, **carbon radicals are typically short-lived** due to their high reactivity. They tend to quickly react or combine to form more stable species.
- In everyday stable organic molecules, **carbon radicals are much less common** than neutral molecules or ions because radicals are usually very reactive and transient.

---

### Relative frequency comparison:

| Species              | Occurrence                      | Stability                     |
|---------------------|--------------------------------|------------------------------|
| Neutral molecules (like methane \(\mathrm{CH_4}\))    | Very common, stable           | Very stable                  |
| Carbon cations (\(\mathrm{CH_3}^+\))                  | Common as reactive intermediates, rare isolated | Electron-deficient, thus reactive and unstable |
| Carbon radicals (\(\mathrm{CH_3}\cdot\))              | Common as intermediates in many reaction mechanisms | Reactive and moderately unstable, short-lived |
| Carbon anions (\(\mathrm{CH_3}^-\))                   | Occur in organometallic chemistry and strong bases, relatively less frequent | Strong bases, reactive but can be stabilized |

---

### Why radicals appear frequently in reaction mechanisms?

Radicals are often generated by homolytic bond cleavage (breaking bonds evenly), for example by:

- Heat or light (photochemical reactions)
- Radical initiators (like peroxides)
- Oxidation or reduction reactions

Once formed, these radicals rapidly engage in chain reactions or recombinations.

---

### So:

- **Carbon radicals such as \(\mathrm{CH_3}\cdot\) do occur frequently in chemical processes as transient intermediates.**
- But **in stable, isolated molecules, radicals are very rare** because of their high reactivity.
- On the other hand, neutral molecules or ionic species dominate the “stable” world you encounter in most chemistry or everyday substances.

---

If you want, I can give examples of reactions where the methyl radical is important, or explain more about the stability of radicals versus cations or anions!
User: don't these structures violate the octet rule
Assistant: