Thermodynamics and Gas Laws Review

Flashcards covering key concepts and formulas from lecture notes on gas laws and thermodynamics, presented in a vocabulary style.

Ideal Gas Law

pV = nRT

Dalton’s Law of Partial Pressures

ptotal = Σ pi, with pi = yi p_total

Molar volume at STP (1 bar, 273 K)

V_m ≈ 22.7 L mol⁻¹

Average Molar Kinetic Energy

〈E_k〉 = (3/2)RT

Root-mean-square speed (c_rms)

c_rms = √(3RT/M)

Mean speed (c̄)

c̄ = √(8RT/πM)

Most probable speed (c_mp)

c_mp = √(2RT/M)

Compressibility Factor Z

Z = pV_m/(RT); ideal gas if Z=1

van der Waals equation

(p + a n²/V²)(V − nb) = nRT

van der Waals constants (a and b) from critical constants

b = RTc/(8pc), a = 27R²Tc²/(64pc)

Virial expansion form

Z = 1 + B(T)/V_m + …

First Law of Thermodynamics

∆U = q + w

Work at constant external pressure

w = −p_ext ∆V

Work reversible isothermal (ideal gas)

w = −nRT ln(V₂/V₁)

Change in Internal Energy (∆U) for isothermal ideal gas

∆U = 0

Change in Enthalpy (∆H) for isothermal ideal gas

∆H = 0

Adiabatic reversible relation (pressure and volume)

pV^γ = const

Adiabatic reversible relation (temperature and volume)

TV^(γ−1) = const

Adiabatic work expression

w = ∆U = nC_V∆T

Definition of Enthalpy H

H = U + pV

Heat at constant pressure (q_p)

q_p = ∆H

Heat at constant volume (q_V)

q_V = ∆U

Mayer’s relation (ideal gas)

Cp − Cv = R

Enthalpy change (∆H) for ideal gas formula

∆H = n ∫ C_p dT

Internal energy change (∆U) for ideal gas formula

∆U = n ∫ C_v dT

Standard enthalpy of reaction formula

∆rH° = Σν ∆fH°(products) − Σν ∆_fH°(reactants)

Hess’s Law

Add reactions, add enthalpies

Kirchhoff’s Law formula

∆rH(T₂) ≈ ∆rH(T₁) + ∆C_p ∆T

Relation between ∆H and ∆U for ideal-gas reactions

∆H − ∆U = ∆n_g RT

Internal pressure (π_T)

πT = (∂U/∂V)T

Thermal expansion coefficient (α)

α = (1/V)(∂V/∂T)_p

Isothermal compressibility (κ_T)

κT = −(1/V)(∂V/∂p)T

Joule–Thomson coefficient (µ_JT)

µJT = (∂T/∂p)H = (V/C_p)(Tα − 1)

Assumption defining an ideal gas

No intermolecular interactions; molecules occupy no volume; elastic collisions.

Compressibility factor Z > 1

Indicates repulsions dominate (gas is less compressible).

Compressibility factor Z < 1

Indicates attractions dominate (gas is more compressible).

Origin of pressure in kinetic theory

From molecular collisions transferring momentum to container walls.

Why average molar kinetic energy depends only on T

Because temperature measures average kinetic energy, independent of pressure or volume.

First Law of Thermodynamics (in words)

Energy is conserved: the change in internal energy equals heat supplied plus work done on the system.

Reason for maximum reversible work

External pressure is always infinitesimally less than system pressure, so the system does the most work possible without losing equilibrium.

Distinction between isothermal and adiabatic expansion

Isothermal: T constant, ∆U=0, heat exchange balances work. Adiabatic: no heat exchange, T drops as system does work.

Why ∆U is only a function of T for ideal gases

Because ideal gas internal energy depends only on kinetic energy, which is temperature dependent.

Why ∆H ≈ ∆U for condensed phases

Because the pV term is negligible relative to the large energies of chemical bonds.

Significance of Hess’s Law

Enthalpy is a state function, independent of path.

Significance of Kirchhoff’s Law

Reflects the temperature dependence of reaction enthalpy due to differences in heat capacities of reactants and products.

Meaning of ∆H − ∆U = ∆n_gRT

The difference between enthalpy and internal energy changes comes from expansion work of changing gas moles.

Information conveyed by internal pressure (π_T)

How internal energy changes with volume at constant T; measures intermolecular interactions.

Information conveyed by thermal expansion coefficient (α)

Fractional change in volume per degree rise at constant pressure.

Information conveyed by isothermal compressibility (κ_T)

Fractional change in volume per unit pressure drop at constant T.

Information conveyed by Joule–Thomson coefficient (µ_JT)

Whether a real gas cools or heats upon expansion at constant enthalpy.