Chemical Thermodynamics and Energetics — MHT-CET Chemistry

Formulas (1)

• Isothermal, Isochoric, Isobaric, Adiabatic and Reversible · What each process fixes
  $$\text{isochoric: } w = 0;\quad \text{isothermal (ideal): } \Delta U = 0;\quad \text{adiabatic: } q = 0;\quad \text{isobaric: } q_P = \Delta H$$

Reference tables (1)

Watch out for (2)

• Heat capacity as intensive
  → Systems, Intensive Versus Extensive, State Versus Path
• 'Isothermal' read as 'no heat exchange'
  → Isothermal, Isochoric, Isobaric, Adiabatic and Reversible

Formulas (5)

• ΔU = q + w and the Sign Convention · First law
  $$\Delta U = q + w,\qquad q_{\text{absorbed}} > 0,\quad w_{\text{on system}} > 0$$
• Work Against a Constant External Pressure: w = −P_ext ΔV · PV work
  $$w = -P_{\text{ext}}\,\Delta V,\qquad 1\ \text{dm}^3\,\text{bar} = 100\ \text{J},\quad 1\ \text{L atm} = 101.3\ \text{J}$$
• ΔU From Heat Absorbed and an Expansion · First law with expansion work
  $$\Delta U = q - P_{\text{ext}}\,\Delta V$$
• Work in a Gas-Phase Reaction: w = −Δn_g RT · Reaction work
  $$w = -\Delta n_g\,RT$$
• Reversible Isothermal Work: −2.303 nRT log(V₂/V₁) · Maximum (reversible) work
  $$w_{\text{rev}} = -2.303\,nRT\log_{10}\frac{V_2}{V_1} = -2.303\,nRT\log_{10}\frac{P_1}{P_2}$$

Watch out for (5)

• 'Work done BY the system' entered as positive
  → ΔU = q + w and the Sign Convention
• Leaving the answer in dm³ bar when joules are asked
  → Work Against a Constant External Pressure: w = −P_ext ΔV
• Adding the work instead of subtracting it
  → ΔU From Heat Absorbed and an Expansion
• Counting liquids and solids in Δn
  → Work in a Gas-Phase Reaction: w = −Δn_g RT
• Using the pressure ratio the same way as the volume ratio
  → Reversible Isothermal Work: −2.303 nRT log(V₂/V₁)

Formulas (2)

• Enthalpy, Heat at Constant Pressure and Phase Changes · Enthalpy
  $$H = U + PV,\qquad \Delta H = q_P,\qquad \Delta H_{\text{vap}} = \frac{q}{n}$$
• ΔH = ΔU + Δn_g RT · ΔH and ΔU
  $$\Delta H = \Delta U + \Delta n_g\,RT$$

Watch out for (2)

• Dividing the heat by the grams
  → Enthalpy, Heat at Constant Pressure and Phase Changes
• Counting liquid water as a gas
  → ΔH = ΔU + Δn_g RT

Formulas (3)

• Enthalpy of Formation and the Reaction Enthalpy From It · Reaction enthalpy from formation enthalpies
  $$\Delta_r H^\circ = \sum \nu_p\,\Delta_f H^\circ_{\text{products}} - \sum \nu_r\,\Delta_f H^\circ_{\text{reactants}}$$
• Hess's Law and the Enthalpy of Solution · Hess's law; enthalpy of solution
  $$\Delta H_{\text{overall}} = \sum \Delta H_{\text{steps}},\qquad \Delta_{\text{soln}}H = \Delta_L H + \Delta_{\text{hyd}}H$$
• Bond Enthalpy: Bonds Broken Minus Bonds Formed · Reaction enthalpy from bond enthalpies
  $$\Delta_r H = \sum \Delta H_{\text{broken}} - \sum \Delta H_{\text{formed}}$$

Watch out for (3)

• Reporting the equation's ΔH as the formation enthalpy
  → Enthalpy of Formation and the Reaction Enthalpy From It
• Subtracting hydration from lattice enthalpy
  → Hess's Law and the Enthalpy of Solution
• Using a whole N₂ for the formation enthalpy of NH₃
  → Bond Enthalpy: Bonds Broken Minus Bonds Formed

Formulas (2)

• Predicting the Sign of ΔS · Rule of thumb
  $$\Delta n_g > 0 \Rightarrow \Delta S > 0;\qquad \Delta n_g < 0 \text{ or gas} \to \text{liquid/solid} \Rightarrow \Delta S < 0$$
• ΔS = q_rev/T, ΔS_surr = −ΔH/T and ΔS_total · Entropy of surroundings and total
  $$\Delta S_{\text{surr}} = -\frac{\Delta H_{\text{sys}}}{T},\qquad \Delta S_{\text{total}} = \Delta S_{\text{sys}} - \frac{\Delta H_{\text{sys}}}{T}$$

Watch out for (2)

• Counting moles without looking at phases
  → Predicting the Sign of ΔS
• Dividing kilojoules by kelvin
  → ΔS = q_rev/T, ΔS_surr = −ΔH/T and ΔS_total

Formulas (2)

• ΔG = ΔH − TΔS and the Sign Table · Gibbs energy
  $$\Delta G = \Delta H - T\Delta S$$
• ΔG = 0: Boiling Points, Transition Temperatures and K · Equilibrium conditions
  $$T_{\text{eq}} = \frac{\Delta H}{\Delta S},\qquad \Delta G^\circ = -2.303\,RT\log_{10} K$$

Watch out for (2)

• Subtracting joules from kilojoules
  → ΔG = ΔH − TΔS and the Sign Table
• Inverting to T = ΔS/ΔH
  → ΔG = 0: Boiling Points, Transition Temperatures and K