The Gas Phase

Standard Temperature and Pressure (STP)

1 atm = 760 mmHg ≡ 760 torr = 101,325 Pa; 0 C or 273.15 K

standard conditions

25˚C or 298 K, 1 atm, 1 M concentrations; used when measuring standard enthalpy, entropy, Gibbs free energy, and electromotive force

Boyle’s Law

PV = k or P1V1 = P2V2

Charles’s Law

V / T = k or V1 / T1 = V2 / T2

Gay-Lussac’s Law

P / T = k or P1 / T1 = P2 / T2

Avogadro’s Principle

n / V = k or n1 / V1 = n2 / V2

Combined Gas Law

Integrates Boyle’s Law, Charles’s Law, and Gay Lussac’s Law (P1V1) / T1 = (P2V2) / T2

Ideal Gas Law

PV = nRT

Real Gases

Decreasing the volume of a sample of gas makes it behave less ideally because the individual gas particles are in closer proximity in a smaller volume. (They are more likely to engage in intermolecular interactions.)

Deviations due to pressure

As the pressure of a gas increases, the particles are pushed closer and closer together. At moderately high pressure, a gas’s volume is less than would be predicted by the ideal gas law due to intermolecular attraction.

Deviations due to temperature

As the temperature of a gas decreases, the average velocity of the gas molecules decreases and the attractive intermolecular forces become increasingly significant. As the temperature of a gas is reduced, intermolecular attraction (a) causes the gas to have a smaller volume than would be predicted. At extremely low temperatures, the volume of the gas particles themselves (b) causes the gas to have a larger volume than would be predicted.

Van der Waals equation of state

accounts for the deviations from ideality that occur when a gas does not closely follow the ideal gas law (P + n²a/V² )(V – nb) = nRT ; 1 mole of gas at STP = 22.4 L

Dalton’s law of partial pressures

states that the total pressure of a gaseous mixture is equal to the sum of the partial pressures of the individual components PT = PA + PB + PC +… PA = PTXA where XA = T n n A (moles of A) (total moles)

Kinetic molecular theory of gases

an explanation of gaseous molecular behavior based on the motion of individual molecules

Average molecular speeds

K = 1/2mv² = 3/2 kbT

Root-mean-square speed

Urms = sqrt(3RT/M)