Physical Chemistry I - Chp. I - Fundamental Concepts of Thermodynamics

Concept and formulae.

formula for pressure

P = F/A

• P is pressure (Pa, or N m^-2, or kg m^-1 s^-2)

• F is force (N, or kg m s^-2)

• A is area (m²)

formula for hydrostatic pressure

p = hρg

• p is hydrostatic pressure (Pa, or N m^-2, or kg m^-1 s^-2)

• h is height of the fluid (m)

• ρ is the density of the fluid (kg m^-3)

• g is the acceleration due to gravity (9.8 m s^-2)

formula for the ideal gas law

PV = nRT

• P is pressure (atm)

• V is volume (L)

• n is amount of gas (mol)

• R is the universal gas constant (0.08206 atm L mol^-1 K^-1)

• T is the temperature (K)

formula for gas density law

PM = dRT

• P is pressure (atm)

• M is molar mass of gas (g mol^-1)

• d is the density of gas (g L^-1)

• R is the universal gas constant (0.08206 atm L mol^-1 K^-1)

• T is the temperature (K)

formula for combined gas law

P_AV_A/T_A = P_BV_B/T_B

• P_A is pressure of gas A (atm)

• V_A is volume of gas A (L)

• T_A is temperature of gas A (K)

• P_B is pressure of gas A (atm)

• V_B is volume of gas A (L)

• T_B is temperature of gas A (K)

equation for Dalton’s Law of Partial Pressures

P_total = Σ_nP_n

• P_total = total pressure exerted by all component gases

• P_n = partial pressure exerted by a component gas

equation for partial pressure

P_gas = P_totalχ_gas

• P_gas = partial pressure exerted by a component gas

• P_total = total pressure exerted by all component gases

• χ_gas = mole fraction of a component gas

equation for Graham’s Law of Effusion

rate effusion of gas A / rate effusion of gas B = √(M_B) / √(M_A)

• M_A is the molar mass of gas A

• M_B is the molar mass of gas B

equation for kinetic energy

ε_k = 0.5mv²

• ε_k is kinetic energy (J, or kg m s^-2)

• m is mass (kg)

• v is velocity (m s^-1)

equation for root mean squared speed

u_rms = √(ū²) = √[(u₁² + u₂² + u₃² … + u_n²) / n ]

• u_rms is root mean squared speed (m s^-1)

• ū² is mean squared speed (m² s^-2)

• u_n is velocity of a gas molecule (m s^-1)

• n is the number of gas molecules with known velocities

equation for compressibility factor

Z = V_{m,real gas} / V_{m,ideal gas} = (PV_m / RT)_measured

• Z is compressibility factor

• V_{m,real gas} is molar volume of real gas (L mol^-1)

• V_{m,ideal gas} is molar volume of ideal gas (L mol^-1)

• P is pressure (atm)

• V_m is molar volume (L mol^-1)

• R is universal gas constant (0.08206 atm L mol^-1 K^-1)

• T is temperature (K)

equation for a real gas ("van der Waals formula”)

(P + an²/V)(V - nb) = nRT

• P is pressure (atm)

• a is a constant based on gas identity describing strength of intermolecular attraction (L² atm mol^-1)

• n is amount of gas (mol)

• V is volume of gas (L)

• b is a constant based on gas identity describing size of gas molecules (L mol^-1)

• R is universal gas constant (0.08206 L atm mol^-1 K^-1)

• T is temperature (K)

equation for force

F = ma

• F is force (N, or kg m s^-2)

• m is mass (kg)

• a is acceleration (m s^-2)