Physical Chemistry - Lecture Notes on Gases

Flashcards covering key physical chemistry concepts on gas properties, empirical gas laws, kinetic theory of gases, van der Waals equation, and molar heat capacities.

What physical characteristics distinguish gases from solids and liquids?

Solids have well-defined shapes and are difficult to compress; liquids are free-flowing and bounded by self-formed surfaces; gases expand freely to fill their containers, have relatively low density and viscosity, diffuse readily, and distribute uniformly throughout any container.

What are the terms for the phase transitions from solid directly to gas, and from gas to liquid?

The transition from the solid state to the gaseous state is called sublimation, while the transition from the gaseous state to the liquid state is called liquefaction or condensation.

Under what thermodynamic conditions can water exist in a stable equilibrium across ice, liquid water, and water vapor simultaneously?

Water exists in a stable equilibrium in three states (ice, liquid water, and water vapor) near $0^\text{o}\text{C}$ and low pressure.

What is an equation of state, and what equation describes an ideal gas?

An equation of state is a mathematical relationship between macroscopic variables of a system. An ideal gas is described by the Clapeyron-Mendeleev equation $pv = nRT$.

How is the universal gas constant $R$ physically defined in terms of work?

The universal gas constant $R$ is equal to the work performed during the expansion of one mole of an ideal gas at constant pressure when its temperature increases by $1\text{ K}$.

What are the physical definitions of Boyle's law and the Gay-Lussac-Joule law?

Boyle's law states that in a gas held at constant temperature, volume is inversely proportional to pressure. The Gay-Lussac-Joule law states that the internal energy of an ideal gas depends only on temperature and does not depend on volume or pressure.

What does Dalton's law state regarding a mixture of ideal gases?

Dalton's law states that the total pressure of a gas mixture occupying a definite volume is equal to the sum of the partial pressures of the constituent gases: $p = \text{p}_1 + \text{p}_2 + \text{p}_3 + \text{...} = \text{p}_i$.

How is mole fraction defined, and how is it used to compute the partial pressure of a component in an ideal gas mixture?

Mole fraction is the ratio of the number of moles of a given component to the total moles of the mixture ($\frac{n_i}{n}$). The partial pressure of any component is equal to the total pressure multiplied by its mole fraction ($p_i = \frac{n_i}{n} \times p$).

What three core assumptions form the basis of the kinetic theory of gases?

(i) Molecules are in continuous chaotic movement in all directions, colliding with each other and container walls; (ii) dimensions of molecules are negligible compared with the distance between them; (iii) attractive forces between molecules are negligible.

How does kinetic theory explain gas pressure and temperature on a microscopic level?

Gas pressure registers the average change of momentum experienced by molecules as they collide with and rebound from container walls. Temperature is proportional to the average kinetic energy of the molecules (or the square of their average velocity).

What is the fundamental equation of the kinetic theory of gases for one mole of gas?

The fundamental equation is $pV = \frac{1}{3} N_A m \bar{u}^2 = \frac{1}{3} M \bar{u}^2$, where $N_A$ is Avogadro's number, $m$ is the mass of one molecule, $M$ is molecular weight, and $\bar{u}$ is the root mean square velocity.

How is the mean translational kinetic energy of gas molecules related to temperature and Boltzmann's constant?

The mean translational kinetic energy is $\bar{E} = \frac{1}{2} m \bar{u}^2 = \frac{3}{2} \frac{RT}{N_A} = \frac{3}{2} kT$, where $k = \frac{R}{N_A}$ is the Boltzmann constant.

What physical quantity does the equation shown in this image calculate?

This equation calculates the root mean square velocity ($\bar{u}$) of ideal gas molecules at a given temperature, where $R$ is the universal gas constant, $T$ is absolute temperature, and $M$ is molecular weight.

What is the van der Waals equation of state for real gases?

The van der Waals equation is $(p + \frac{a}{V^2})(V - b) = RT$, where $a$ and $b$ are material parameters determined experimentally for each gas.

What physical mechanisms do the parameters $a$ and $b$ represent in the van der Waals equation?

The term $\frac{a}{V^2}$ acts as a correction for mutual attraction of molecules (internal pressure), while $b$ is a volume of exclusion correcting for the actual volume of molecules and short-range mutual repulsion.

How is the van der Waals volume parameter $b$ related to the molecular dimensions?

The parameter $b$ is approximately equal to four times the volume of the molecules as evaluated from their gas-kinetic radius.

How do experimental findings for van der Waals constants $a$ and $b$ differ from theoretical predictions?

Theoretically, $a$ and $b$ should be independent of temperature and pressure; however, experimental data show that $a$ depends on temperature and $b$ varies with volume.

Why is the molar heat capacity at constant pressure ($C_p$) greater than at constant volume ($C_V$) for an ideal gas?

$C_p$ is greater than $C_V$ because when temperature increases by $1\text{ K}$ at constant pressure, the gas performs work against external pressure equal to $nR(T+1) - nRT = nR$, making $C_p - C_V = nR$.