Let's proceed stepwise, strictly using **quantitative physicochemical properties** relevant for classifying the bases below:

### **Candidate Substances:**
> **['KOH', 'nothing', 'Et3N', 'K3PO4', 'LiOtBu', 'CsF', 'NaOH', 'NaHCO3']**

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## **Step 1: Summarize the Most Relevant [Specified_physicochemical_Properties] for Bases**

For inorganic and organic bases, the most **quantitative, universally available database properties** for categorization are:

1. **pK_b / pK_a (of the conjugate acid):** Indicates base strength.
2. **State at room temp:** Solid, liquid, or gas (helps distinguish between organic/inorganic and practical use).
3. **Solubility in water:** (g/L or M) — important for operational base activity.
4. **Functional group count:** For organic bases (e.g., number of basic nitrogen atoms).

Other properties like "polarity" or "hydrogen-bond donor count" are less central for bases, unless distinguishing highly polar vs. nonpolar organic bases.

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## **Step 2: Gather Quantitative Data for Each Substance**

| Substance | pKa of Conjugate Acid* | State | Water Solubility | Notes |
|-----------|------------------------|-------|------------------|-------|
| **KOH**  | ~15.7 (H2O)            | Solid | Very High (~1100 g/L) | Strong inorganic base |
| **NaOH** | ~15.7 (H2O)            | Solid | Very High (~1000 g/L) | Strong inorganic base |
| **K3PO4**| ~12.4 (H2PO4-)         | Solid | High (~20 g/L)   | Moderate inorganic base |
| **CsF**  | ~3.2 (HF)              | Solid | High (~3 g/mL)   | Fluoride weakly basic, but basicity mainly from F– |
| **NaHCO3**| ~6.3 (H2CO3)           | Solid | High to moderate | Weak inorganic base (bicarbonate) |
| **Et3N** | ~10.7 (Et3NH+)         | Liquid| 112 g/L          | Strong organic base |
| **LiOtBu**| ~18.0 (tBuOH)         | Solid | Slightly soluble | Strong, hindered organic base |
| **nothing**| ---                   | ---   | ---              | Not a substance |

\*The pKa listed is for the conjugate acid (higher = stronger base).

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## **Step 3: Choose the Best Quantitative Classification Scheme**

The most **clear, quantitative basis for basification strength** is **pKa of the conjugate acid**. This allows for **objective grouping** as typically done in chemical databases:

- **Strong Base:** pKa(conj. acid) ≥ 14  
- **Moderate Base:** 7 < pKa(conj. acid) < 14  
- **Weak Base:** pKa(conj. acid) ≤ 7  

This approach is **standard**, objective, and clearly supported by quantitative data.

We can also indicate organic vs. inorganic in each group, but it is secondary here.

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## **Step 4: Assign Groups**

### **Group 1. Strong Bases** (pKa of conjugate acid ≥ 14)
- **KOH** (conjugate acid: H₂O, pKa = 15.7)
- **NaOH** (conjugate acid: H₂O, pKa = 15.7)
- **LiOtBu** (conjugate acid: tBuOH, pKa = 18.0)
  - *Note: Et₃N (pKa = 10.7) does **not** qualify as "strong" by the above quantitative standard, though often called strong among organic amines.*

### **Group 2. Moderate Bases** (7 < pKa < 14)
- **Et₃N** (conjugate acid: Et₃NH⁺, pKa = 10.7)
- **K₃PO₄** (conjugate acid: H₂PO₄⁻, pKa ≈ 12.4)
- **CsF** (conjugate acid: HF, pKa ≈ 3.2 — *Note: This would technically be "weak", but F⁻ is strongly basic in aprotic solvents*)

### **Group 3. Weak Bases** (pKa ≤ 7)
- **NaHCO₃** (conjugate acid: H₂CO₃, pKa = 6.3)
- **CsF** (on strict pKa of HF, but see above explanation regarding solvent effects)

### **Unclassifiable or Not a Base**
- **nothing**: Not a chemical substance.

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## **Step 5: Note Ambiguities**
- **CsF:** By water pKa (HF), it is a "weak" base, but in organic solvents or by basic utility (F⁻ as a desilylating base), it's used as a "strong" base. The database method sorts it as "weak" based on pKa, and it should be flagged as straddling categories.

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## **Final Table: Classified per Quantitative pKa**

| Group            | Substance(s)                 | Justification                          |
|------------------|-----------------------------|----------------------------------------|
| **Strong Bases** | KOH, NaOH, LiOtBu           | pKa(conj.acid) ≥ 14                    |
| **Moderate Bases** | K₃PO₄, Et₃N                | 7 < pKa(conj.acid) < 14                |
| **Weak Bases**   | NaHCO₃, (CsF*)              | pKa(conj.acid) ≤ 7 *(see note above)*  |
| **Not Classified** | nothing                    | Not a substance                        |

### **Summary:**
By prioritizing quantitative database pKa values of the conjugate acid, the candidate substances clearly separate into **no more than three groups**: *Strong, Moderate, and Weak Bases*, with only "nothing" not fitting any group. Ambiguities like CsF are justified based on the definition of basicity through pKa.

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**If you want an alternative grouping (e.g., by solubility or state), specify and I can recalculate.**