Library Guides: Chemistry Textbook: Summary

Summary

Key Equations

P = \frac{F}{A}

$P V = n R T$

$P_{T o t a l} = P_{A} + P_{B} + P_{C} + ... = Σ_{i} P_{i}$

$P_{A} = X_{A} \times P_{T o t a l} where X_{A} = \frac{n_{A}}{n_{T o t a l}}$

$rate of diffusion = \frac{amount of gas passing through an area}{unit of time}$

$\frac{rate of effusion of gas A}{rate of effusion of gas B} = \frac{\sqrt{m_{B}}}{\sqrt{m_{A}}} = \frac{\sqrt{ℳ_{B}}}{\sqrt{ℳ_{A}}}$

$u_{r m s} = \sqrt{\bar{u^{2}}} = \sqrt{\frac{u_{1}^{2} + u_{2}^{2} + u_{3}^{2} + u_{4}^{2} + \dots}{n}}$

${KE}_{avg} = \frac{3}{2} R T$

$u_{rms} = \sqrt{\frac{3 R T}{M}}$

Gas Pressure

Gases exert pressure, which is force per unit area. The pressure of a gas may be expressed in the SI unit of pascal or kilopascal, as well as in many other units including torr, atmosphere, and bar. Atmospheric pressure is measured using a barometer; other gas pressures can be measured using one of several types of manometers.

Gas Laws for Ideal Gases

The behavior of gases can be described by several laws based on experimental observations of their properties. The pressure of a given amount of gas is directly proportional to its absolute temperature, provided that the volume does not change (Amontons’s law). The volume of a given gas sample is directly proportional to its absolute temperature at constant pressure (Charles’s law). The volume of a given amount of gas is inversely proportional to its pressure when temperature is held constant (Boyle’s law). Under the same conditions of temperature and pressure, equal volumes of all gases contain the same number of molecules (Avogadro’s law).

The equations describing these laws are special cases of the ideal gas law, PV = nRT, where P is the pressure of the gas, V is its volume, n is the number of moles of the gas, T is its kelvin temperature, and R is the ideal (universal) gas constant.

Gas Mixtures and Reactions

The ideal gas law can be used to derive a number of convenient equations relating directly measured quantities to properties of interest for gaseous substances and mixtures. Appropriate rearrangement of the ideal gas equation may be made to permit the calculation of gas densities and molar masses. Dalton’s law of partial pressures may be used to relate measured gas pressures for gaseous mixtures to their compositions. Avogadro’s law may be used in stoichiometric computations for chemical reactions involving gaseous reactants or products.

Kinetic-Molecular Theory of Gases

The kinetic molecular theory is a simple but very effective model that effectively explains ideal gas behavior. The theory assumes that gases consist of widely separated molecules of negligible volume that are in constant motion, colliding elastically with one another and the walls of their container with average velocities determined by their absolute temperatures. The individual molecules of a gas exhibit a range of velocities, the distribution of these velocities being dependent on the temperature of the gas and the mass of its molecules.

Effusion and Diffusion of Gases

Gaseous atoms and molecules move freely and randomly through space. Diffusion is the process whereby gaseous atoms and molecules are transferred from regions of relatively high concentration to regions of relatively low concentration. Effusion is a similar process in which gaseous species pass from a container to a vacuum through very small orifices. The rates of effusion of gases are inversely proportional to the square roots of their densities or to the square roots of their atoms/molecules’ masses (Graham’s law).