Chemical Thermodynamics — JEE Mains Chemistry

Formulas (1)

• First law sign convention: ΔU = q + w · First law of thermodynamics
  $$\Delta U = q + w$$

Reference tables (1)

Watch out for (4)

• Sign-reversed textbook relations
  → State functions, intensive properties and the standard relations
• Same concentration, different Gibbs energy
  → State functions, intensive properties and the standard relations
• Adding the magnitudes
  → First law sign convention: ΔU = q + w
• Boiling water does work
  → First law sign convention: ΔU = q + w

Formulas (3)

• Reversible isothermal and adiabatic work · Reversible isothermal work
  $$w_{\mathrm{rev}} = -2.303\,nRT\log\frac{V_2}{V_1} = -2.303\,nRT\log\frac{p_1}{p_2}$$
• Work against a constant external pressure and free expansion · Work against a constant external pressure
  $$w = -p_{\mathrm{ext}}\,(V_2 - V_1)$$
• Work as an area on a p–V graph · Work around a cycle
  $$w_{\mathrm{net}} = -\oint p\,dV,\qquad |w_{\mathrm{net}}| = \text{area enclosed}$$

Watch out for (6)

• log for ln
  → Reversible isothermal and adiabatic work
• q and w with the same sign
  → Reversible isothermal and adiabatic work
• A change in volume does not mean work
  → Work against a constant external pressure and free expansion
• Reversible is the extreme in two different senses
  → Work against a constant external pressure and free expansion
• V on the vertical axis
  → Work as an area on a p–V graph
• A cycle is not always the biggest area
  → Work as an area on a p–V graph

Formulas (3)

• Heat capacity: Cp, Cv and q = nCΔT · Heat and heat capacity
  $$q = nC_m\Delta T,\qquad C_p - C_v = R$$
• Bomb calorimeter: heat at constant volume · Bomb calorimeter
  $$\Delta_c U = -\frac{C_{\mathrm{cal}}\,\Delta T}{n}$$
• ΔH and ΔU through the change in gas moles · Enthalpy and internal energy
  $$\Delta H = \Delta U + \Delta n_g RT$$

Watch out for (5)

• Cv for heat added at constant pressure
  → Heat capacity: Cp, Cv and q = nCΔT
• Bomb heat is ΔU, not ΔH
  → Bomb calorimeter: heat at constant volume
• Positive heat, negative ΔU
  → Bomb calorimeter: heat at constant volume
• Counting liquid water as a gas
  → ΔH and ΔU through the change in gas moles
• R in joules beside ΔH in kilojoules
  → ΔH and ΔU through the change in gas moles

Formulas (3)

• Reaction enthalpy from formation enthalpies · Reaction enthalpy from formation enthalpies
  $$\Delta_r H^\circ = \sum \nu\,\Delta_f H^\circ_{\mathrm{products}} - \sum \nu\,\Delta_f H^\circ_{\mathrm{reactants}}$$
• Formation enthalpy from combustion enthalpies · Formation enthalpy from combustion enthalpies
  $$\Delta_f H = \sum \nu\,\Delta_c H_{\mathrm{elements}} - \Delta_c H_{\mathrm{compound}}$$
• Hess's law: adding, reversing and scaling equations · Hess's law
  $$\Delta H_{\mathrm{target}} = \sum_i k_i\,\Delta H_i$$

Watch out for (6)

• The standard state is not 0 °C
  → Reaction enthalpy from formation enthalpies
• One mole of everything
  → Reaction enthalpy from formation enthalpies
• Flipping the combustion rule
  → Formation enthalpy from combustion enthalpies
• Which water?
  → Formation enthalpy from combustion enthalpies
• Heat on the product side
  → Hess's law: adding, reversing and scaling equations
• 22.4 L at room temperature
  → Hess's law: adding, reversing and scaling equations

Formulas (2)

• Enthalpies of phase change, solution, dilution and hydration · Hess cycles for phase changes and hydration
  $$\Delta_{\mathrm{sub}}H = \Delta_{\mathrm{fus}}H + \Delta_{\mathrm{vap}}H,\qquad \Delta_{\mathrm{hyd}}H = \Delta_{\mathrm{sol}}H_{\mathrm{anhydrous}} - \Delta_{\mathrm{sol}}H_{\mathrm{hydrate}}$$
• Enthalpy of neutralisation and the temperature rise · Temperature rise on neutralisation
  $$\Delta T = \frac{n_{\mathrm{H_2O}}\,|\Delta_{\mathrm{neut}}H|}{m\,c}$$

Watch out for (4)

• The sign of a heat of dilution
  → Enthalpies of phase change, solution, dilution and hydration
• Kilojoules beside joules in a heating path
  → Enthalpies of phase change, solution, dilution and hydration
• Only one solution's volume
  → Enthalpy of neutralisation and the temperature rise
• More acid is not more heat
  → Enthalpy of neutralisation and the temperature rise

Formulas (2)

• Reaction enthalpy from bond enthalpies · Reaction enthalpy from bond enthalpies
  $$\Delta_r H = \sum BE_{\mathrm{broken}} - \sum BE_{\mathrm{formed}}$$
• Average bond enthalpy and atomisation cycles · Average bond enthalpy from formation enthalpies
  $$\overline{BE} = \frac{\Delta_f H(\mathrm{A},g) + n\,\Delta_f H(\mathrm{B},g) - \Delta_f H(\mathrm{AB}_n,g)}{n}$$

Watch out for (4)

• Formed minus broken
  → Reaction enthalpy from bond enthalpies
• Bond enthalpies are for gases
  → Reaction enthalpy from bond enthalpies
• The sign on a lattice enthalpy
  → Average bond enthalpy and atomisation cycles
• Per mole of compound
  → Average bond enthalpy and atomisation cycles

Formulas (2)

• Entropy change and Gibbs energy of a reaction · Entropy and Gibbs energy of reaction
  $$\Delta_r S^\circ = \sum \nu S^\circ_{\mathrm{products}} - \sum \nu S^\circ_{\mathrm{reactants}},\qquad \Delta_r G^\circ = \Delta_r H^\circ - T\Delta_r S^\circ$$
• Temperature at which ΔG changes sign · Temperature at which ΔG changes sign
  $$\Delta G = 0\ \Rightarrow\ T = \frac{\Delta H}{\Delta S}$$

Reference tables (1)

Watch out for (6)

• Exothermic is not enough
  → Spontaneity from the signs of ΔH and ΔS
• Swapping the two derivatives of G
  → Spontaneity from the signs of ΔH and ΔS
• ΔS in joules, ΔH in kilojoules
  → Entropy change and Gibbs energy of a reaction
• Heating entropy needs the 1/T
  → Entropy change and Gibbs energy of a reaction
• A factor of a thousand
  → Temperature at which ΔG changes sign
• Below, not above
  → Temperature at which ΔG changes sign

Formulas (2)

• Standard Gibbs energy and the equilibrium constant · Gibbs energy and the equilibrium constant
  $$\Delta G^\circ = -RT\ln K = -2.303\,RT\log K$$
• Graphs of log K against 1/T and of G against extent · log K against 1/T
  $$\log K = -\frac{\Delta H^\circ}{2.303R}\cdot\frac{1}{T} + \frac{\Delta S^\circ}{2.303R}$$

Watch out for (4)

• A positive ΔG° is not 'no reaction'
  → Standard Gibbs energy and the equilibrium constant
• Moles are not partial pressures
  → Standard Gibbs energy and the equilibrium constant
• Dropping the minus sign
  → Graphs of log K against 1/T and of G against extent
• Reading the slope
  → Graphs of log K against 1/T and of G against extent