Thermodynamics

What this chapter is about

Thermodynamics is the branch of chemistry that deals with energy changes during physical and chemical processes. At Class 11, you study how heat and work are exchanged between a system and its surroundings, and how to predict whether a process will occur on its own. This knowledge helps you understand why reactions release or absorb heat, why ice melts at 0 °C, and why some reactions are spontaneous while others are not.

You will learn to define a thermodynamic system, distinguish between different types of energy transfers, and apply the first law of thermodynamics to calculate internal energy changes. The concept of enthalpy simplifies heat calculations at constant pressure, the condition under which most laboratory and everyday reactions occur. You will also meet entropy and Gibbs energy, which together decide spontaneity.

After working through this chapter, you should be able to write thermochemical equations, use Hess's law to find unknown enthalpy changes, interpret bond-enthalpy data, and apply the Gibbs equation to predict whether a reaction is feasible at a given temperature.

Key ideas

• System and surroundings: The part of the universe under study is the system; everything outside it is the surroundings. A system may be open (exchanges mass and energy), closed (exchanges only energy), or isolated (exchanges neither).

• State functions: Properties like internal energy (U), enthalpy (H), entropy (S) and temperature (T) depend only on the current state, not on the path taken. Work (w) and heat (q) are path functions.

• First law of thermodynamics: Energy can neither be created nor destroyed; it only changes form. Mathematically, ΔU = q + w, where ΔU is change in internal energy, q is heat absorbed by the system, and w is work done on the system.

• Work in expansion: For a gas expanding against external pressure, w = −P_ext × ΔV. Work done by the system is negative; work done on the system is positive.

• Enthalpy (H): Defined as H = U + PV. At constant pressure, the heat absorbed equals the enthalpy change: q_p = ΔH. This makes enthalpy the practical quantity for reactions in open beakers.

• Standard enthalpy of formation (Δ_f H°): Enthalpy change when one mole of a compound forms from its elements in their standard states (usually 1 bar, 25 °C). For any element in its most stable form, Δ_f H° = 0.

• Hess's law: The total enthalpy change for a reaction is the same whether it occurs in one step or several. This allows calculation of enthalpy changes that cannot be measured directly.

• Entropy (S) measures the randomness or disorder of a system. A spontaneous process in an isolated system increases total entropy.

• Gibbs energy (G): G = H − TS. At constant T and P, ΔG = ΔH − TΔS. If ΔG < 0, the process is spontaneous; if ΔG = 0, equilibrium exists; if ΔG > 0, the process is non-spontaneous.

Formulas and facts to remember

1. First law: ΔU = q + w (energy conservation for any system).

2. Work of expansion: w = −P_ext × ΔV, with P in Pa and V in m³ giving w in J.

3. Enthalpy at constant pressure: ΔH = q_p.

4. Standard enthalpy of reaction from formation enthalpies: Δ_r H° = Σ Δ_f H°(products) − Σ Δ_f H°(reactants).

5. Hess's law: ΔH for overall reaction = sum of ΔH values for individual steps.

6. Bond enthalpy approximation: Δ_r H ≈ Σ (bond enthalpies of bonds broken) − Σ (bond enthalpies of bonds formed).

7. Gibbs equation: ΔG = ΔH − TΔS (T in kelvin).

8. Spontaneity criterion: ΔG < 0 means the reaction can proceed on its own under those conditions.

Worked examples

### Example 1 – Applying the first law

A gas absorbs 500 J of heat and expands, doing 200 J of work on the surroundings. Find the change in internal energy.

Solution

Heat absorbed, q = +500 J (positive because absorbed).

Work done by the system on the surroundings = 200 J, so work done on the system w = −200 J.

Using ΔU = q + w:

ΔU = 500 + (−200) = 300 J.

The internal energy of the gas increases by 300 J.

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### Example 2 – Enthalpy of reaction from formation data

Calculate the standard enthalpy of combustion of methane using the following standard enthalpies of formation:

Δ_f H° (CH₄) = −74.8 kJ mol⁻¹, Δ_f H° (CO₂) = −393.5 kJ mol⁻¹, Δ_f H° (H₂O, l) = −285.8 kJ mol⁻¹. For O₂, Δ_f H° = 0.

Solution

Balanced equation: CH₄(g) + 2 O₂(g) → CO₂(g) + 2 H₂O(l)

Δ_r H° = [1 × (−393.5) + 2 × (−285.8)] − [1 × (−74.8) + 2 × 0]

= (−393.5 − 571.6) − (−74.8)

= −965.1 + 74.8

= −890.3 kJ mol⁻¹.

The combustion releases 890.3 kJ per mole of methane, explaining why natural gas is an effective cooking fuel.

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### Example 3 – Predicting spontaneity with Gibbs energy

For a reaction, ΔH = −120 kJ mol⁻¹ and ΔS = −150 J K⁻¹ mol⁻¹. Determine whether the reaction is spontaneous at 300 K and at 1000 K.

Solution

First convert ΔS to the same unit as ΔH: ΔS = −0.150 kJ K⁻¹ mol⁻¹.

At 300 K: ΔG = ΔH − TΔS = −120 − (300 × −0.150) = −120 + 45 = −75 kJ mol⁻¹.

ΔG < 0, so the reaction is spontaneous at 300 K.

At 1000 K: ΔG = −120 − (1000 × −0.150) = −120 + 150 = +30 kJ mol⁻¹.

ΔG > 0, so the reaction is non-spontaneous at 1000 K.

This illustrates that an exothermic reaction with a decrease in entropy may become non-spontaneous at higher temperatures.

Common mistakes

• Confusing sign of work: remember w is positive when work is done on the system, not when the gas expands → always check who does work on whom.

• Using ΔH where ΔU is required: ΔH = q only at constant pressure; at constant volume, q = ΔU → identify the conditions before applying a formula.

• Forgetting to convert J to kJ or vice-versa when mixing ΔH (often kJ) with TΔS (often J) → keep units consistent before adding.

• Taking Δ_f H° of an element compound as zero: only elements in their most stable standard form have Δ_f H° = 0, not all elements in any form → write the specific state.

• Believing all exothermic reactions are spontaneous: spontaneity depends on both ΔH and TΔS via Gibbs energy → always calculate ΔG.

Quick revision

• ΔU = q + w: energy in = energy stored + energy out.

• At constant pressure, heat exchanged equals ΔH.

• Hess's law lets you add enthalpy changes like algebra.

• ΔG = ΔH − TΔS decides spontaneity; negative means go.

• Standard enthalpy of formation for any element in its reference state is zero.

• Entropy increases when gases form or disorder rises.