Enthalpy H = U + PV; ΔH for reactions at constant P

2.5.5 · Chemistry › Thermodynamics (Chemical)

Overview

Enthalpy (H) ek state function hai jo system ki total heat content measure karta hai. Isko define kiya jaata hai H = U + PV ke roop mein, jahan U internal energy hai, P pressure hai, aur V volume hai. Chemical reactions mein jo constant pressure par hoti hain (jyadatar lab conditions), ΔH directly surroundings ke saath exchange hone wali heat ke barabar hoti hai.

Enthalpy Ki Zaroorat Kyun Hai?

H = U + PV define kyun karein? Kyunki jab P constant hota hai, ΔH mein change perfectly heat exchange ko capture karta hai, jisse thermochemistry experiments seedhe aur aasaan ho jaate hain.

First Principles Se Derivation

Yeh kyun kaam karta hai: PV term automatically expansion work ko account karta hai. Jab aap constant-pressure calorimeter mein heat flow measure karte ho, tum directly ΔH measure kar rahe ho.

Har Term Ka Physical Meaning

Chemical Reactions Ke Liye ΔH

Yeh sign convention kyun? Jab products mein reactants se kam enthalpy hoti hai, toh "missing" energy surroundings mein heat ke roop mein release ho jaati hai — exothermic.

Worked Examples

Worked example Example 2: Thermal Decomposition

$CaCO_{3} (s) \to CaO (s) + CO_{2} (g) Δ H ° = + 178 kJ/mol$

Question: Ek student open crucible mein CaCO₃ ko heat karta hai. Kya yeh 25°C par spontaneous hai?

Analysis: Step 1: Energy requirement identify karein $Δ H ° > 0 \Rightarrow endothermic$ Iska kya matlab hai? System ko surroundings se continuous heat input ki zaroorat hai.

Step 2: Spontaneity consider karein 25°C par yeh reaction non-spontaneous hai (ΔG > 0) kyunki:

Bada positive ΔH (unfavorable)
Gas formation se entropy increase hoti hai jo help karta hai, lekin low T par kaafi nahi

Yeh step kyun? Spontaneity ΔG = ΔH - TΔS par depend karta hai, sirf ΔH par nahi.

Step 3: High temperature par (>800°C), TΔS term dominate karta hai → ΔG negative ho jaata hai → spontaneous

Answer: 25°C par spontaneous nahi; ~1000 K tak heating chahiye

Worked example Example 3: ΔH aur ΔU Ko Relate Karna

Reaction ke liye: $N_{2} (g) + 3 H_{2} (g) \to 2 NH_{3} (g) Δ H ° = - 92.4 kJ/mol$

Question: 298 K par ΔU° calculate karein.

Solution:

Step 1: Relationship use karein $Δ H = Δ U + Δ (P V)$

Constant T aur P par ideal gases ke liye: $Δ (P V) = Δ n_{g a s} R T$

Kyun? Ideal gas law se: PV = nRT, isliye Δ(PV) = Δn·RT jab T constant ho.

Step 2: Δn_gas calculate karein $Δ n_{g a s} = n_{products} - n_{reactants} = 2 - (1 + 3) = - 2 mol$ Yeh step kyun? Gas moles decrease hote hain, isliye system kam expansion work karta hai.

Step 3: Δ(PV) calculate karein $Δ (P V) = (- 2) (8.314) (298) = - 4955 J = - 4.96 kJ$

Step 4: ΔU solve karein $Δ U = Δ H - Δ (P V) = - 92.4 - (- 4.96) = - 87.4 kJ/mol$

ΔU kam negative kyun hai? Enthalpy decrease ka kuch part reduced gas volume (system par compression work) se aata hai, sirf internal energy decrease se nahi.

Answer: ΔU° = -87.4 kJ/mol

Common Mistakes

Memory Aids

Active Recall Practice

Recall Feynman Technique: 12 Saal Ke Bachche Ko Samjhao

Socho tumhare paas ek water balloon hai. Andar ka paani internal energy U ki tarah hai — molecules ki sari jiggly motion. Ab, balloon ek certain size tak phula hua hai, bahar ki hawa ke against push kar raha hai. Woh "pushing energy" jo balloon ko phula ke rakhne ke liye chahiye, woh PV part ki tarah hai.

Enthalpy total hai: paani ki energy PLUS woh energy jo balloon ko air pressure ke against bahar push kar ke rakhne mein stored hai.

Jab tum ek open beaker mein chemical reaction karte ho (jaise baking soda aur vinegar mix karna), toh yeh normal air pressure par hoti hai — bilkul waise jaise humara balloon room mein hai. Jo heat tum feel karte ho (beaker warm ya cold hona) exactly enthalpy change ΔH hai.

Kyun? Kyunki constant air pressure par, jo heat flow tum measure karte ho usme internal energy change aur kisi gas bubble ke expand hone ka kaam dono include hote hain. Enthalpy inhe bundle kar deta hai!

Exothermic (ΔH negative) = tumhari reaction deflating balloon ki tarah hai, warmth release karti hai. Endothermic (ΔH positive) = tumhari reaction room se heat kheenchti hai, jaise balloon phulana tumhe blow karna padta hai (energy add karni padti hai).

Connections Internal Energy U and First Law — H ko U ke terms mein define kiya jaata hai

PV Work and Expansion — Enthalpy definition mein PV kyun aata hai
Hess's Law — ΔH ek state function hai, path-independent
Standard Enthalpy of Formation — Tabulated data se ΔH_rxn banana
Calorimetry — ΔH ki experimental measurement
Entropy and Gibs Free Energy — ΔH spontaneity ka ek piece hai (ΔG = ΔH - TΔS)
Bond Enthalpies — Bond energies se ΔH estimate karna

Flashcards

#flashcards/chemistry

Enthalpy H ki definition kya hai? :: H = U + PV, jahan U internal energy hai, P pressure hai, V volume hai

Constant pressure par ΔH kiske barabar hota hai?

ΔH = q_P (constant pressure par surroundings ke saath exchange hone wali heat)

Constant-pressure reactions ke liye enthalpy internal energy se zyada useful kyun hai?

Constant P par, ΔH directly measurable heat flow ke barabar hota hai, PV work ko automatically account karta hai

Exothermic reaction mein ΔH ka sign kya hota hai?

ΔH < 0 (system surroundings ko heat release karta hai)

Endothermic reaction mein ΔH ka sign kya hota hai?

ΔH > 0 (system surroundings se heat absorb karta hai)

N₂ + 3H₂ → 2NH₃ reaction ke liye, agar ΔH = -92 kJ/mol hai, toh kya ΔU zyada ya kam negative hai?

Kam negative (ΔU ≈ -87 kJ/mol) kyunki Δn_gas < 0 matlab compression work partially internal energy decrease ko offset karta hai

Ideal gas reactions ke liye ΔH aur ΔU mein kya relationship hai?

ΔH = ΔU + Δn_gas·RT, jahan Δn_gas = (gaseous products ke moles) - (gaseous reactants ke moles)

Agar reaction ke baad beaker hot feel hoti hai, toh ΔH positive hai ya negative?

ΔH negative hai (exothermic); system ne surroundings ko heat release ki, beaker warm hua

Kis condition mein ΔH heat flow ke barabar NAHI hota?

Jab pressure constant nahi hota (jaise constant volume processes jahan q_V = ΔU hota hai)

Bomb calorimeter kaun si thermodynamic quantity measure karta hai?

ΔU (constant volume par internal energy change)

Coffee-cup calorimeter kaun si thermodynamic quantity measure karta hai?

ΔH (constant pressure par enthalpy change)