Bond enthalpies — estimating ΔH_rxn from bond energies

2.5.9 · Chemistry › Thermodynamics (Chemical)

Bond enthalpy KIYA hota hai?

Working formula KAISE derive karte hain (first principles se)

Humein $\Delta H_{rxn}$ chahiye. Enthalpy ek state function hai, toh hum reactants aur products ke beech koi bhi path le sakte hain. Imaginary atomic path choose karo:

1. Path step 1 — reactants ko atomize karo. Reactants ke har bond todo → free gaseous atoms. Needed energy $=\sum (\text{bond enthalpies of reactant bonds})=+{\sum }_{\text{reactants}}\Delta H_{bonds}$

2. Path step 2 — products banao. Un free atoms se products ke har bond banao. Released energy $=-\sum (\text{bond enthalpies of product bonds})=-{\sum }_{\text{products}}\Delta H_{bonds}$

Kyunki enthalpy path-independent hai (Hess's law), dono steps add karne par reaction enthalpy milti hai:

Worked Example 1 — Ethene ka Hydrogenation

${\text{H}}_2\text{C}={\text{CH}}_2+{\text{H}}_2⟶{\text{H}}_3\text{C}-{\text{CH}}_3$

Bond values (kJ/mol): C=C 614, C–H 413, H–H 436, C–C 348.

Bonds broken (reactants):

• 1 × C=C = 614 — Kyun? Ethene mein double bond khatam karna hoga.
• 4 × C–H = 1652 — Kyun? Ethene ke 4 C–H bonds.
• 1 × H–H = 436 — Kyun? Add hone wala H₂.
• Total broken = $614+1652+436=2702$

Bonds formed (product ethane):

• 1 × C–C = 348 — Kyun? Double single ban gaya.
• 6 × C–H = 2478 — Kyun? Ethane mein 6 C–H bonds hote hain.
• Total formed = $348+2478=2826$

$\Delta H_{rxn}=2702-2826=-124\text{kJ/mol}$

Negative kyun? Humne C=C + H–H destroy kiya aur C–C + 2 extra C–H banaye — net stronger bonding ⟹ exothermic. ✅ (forecast se match karta hai)

Worked Example 2 — Methane ka Combustion

${\text{CH}}_4+2{\text{O}}_2⟶{\text{CO}}_2+2{\text{H}}_2\text{O}$

Values: C–H 413, O=O 498, C=O 799, O–H 463.

Broken: 4 C–H + 2 O=O $=4(413)+2(498)=1652+996=2648$ 2 O=O kyun? O₂ par coefficient 2 hai, har ek mein ek double bond hai.

Formed: 2 C=O (CO₂ mein) + 4 O–H (2 H₂O × 2 each) $=2(799)+4(463)=1598+1852=3450$ 4 O–H kyun? Do water molecules, har ek mein do O–H bonds.

$\Delta H_{rxn}=2648-3450=-802\text{kJ/mol}$

(Experimental ≈ −802 to −890; gap isliye hai kyunki table values averages hain aur yahan H₂O gas hai, liquid nahi.)

YEH sirf estimate kyun hai

Active Recall

Connections

• Hess's Law — woh state-function principle jis par yeh derivation rely karti hai.
• Standard Enthalpy of Formation — zyada accurate alternative method.
• Enthalpy and the First Law of Thermodynamics
• Exothermic vs Endothermic Reactions
• Lewis Structures — bonds sahi count karne ke liye zaroori.
• Resonance Energy — estimation error ka ek hissa explain karta hai.

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