Gases Chapter 10 Gases John Bookstaver St. Charles Community College St. Peters, MO  2006, Prentice Hall, Inc. Chemistry, The Central Science, 10th edition Theodore L. Brown; H. Eugene LeMay, Jr.; and Bruce E. Bursten

Gases Characteristics of Gases Gases share the following behaviors:  Gases expand to fill their containers.  Gases are highly compressible.  Gases have extremely low densities.  Gases exert pressure.

Gases Pressure = Force/Area Typical Pressure Units: lbs/in 2 and N/m 2 (pascal) (English)(metric) 95 lbs/in 2

Gases Pressure is the amount of force applied to an area. Pressure Atmospheric pressure is the weight of air per unit of area. P = FAFA

Gases Does the atmosphere really put the squeeze on us?

Gases Units of Pressure Pascals  1 Pa = 1 N/m 2 Bar  1 bar = 10 5 Pa = 100 kPa Demonstrating Atmospheric Pressure!

Gases Units of Pressure mm Hg or torr  These units are literally the difference in the heights measured in mm ( h ) of two connected columns of mercury. Atmosphere  1.00 atm = 760 torr

Gases Manometer Used to measure the difference in pressure between atmospheric pressure and that of a gas in a vessel.

Gases Standard Pressure Normal atmospheric pressure at sea level. It is equal to  1.00 atm  760 torr (760 mm Hg)  kPa

Gases Molecular Motion

Gases P, V, n, T

Gases Boyle’s Law The volume of a fixed quantity of gas at constant temperature is inversely proportional to the pressure.

Gases Boyle’s Law

Gases Boyle’s Law

Gases Boyle’s Law

Gases P and V are inversely related. A plot of V versus P results in a curve. Since V = k (1/P) This means a plot of V versus 1/P will be a straight line. PV = k

Gases The Effect of Temperature on Gas Volume

Gases Expansion of a Gas with Temperature

Gases

Charles’ Law The volume of a fixed amount of gas at constant pressure is directly proportional to its absolute temperature. A plot of V versus T will be a straight line. i.e., VTVT = k

Gases

Avogadro’s Law The volume of a gas at constant temperature and pressure is directly proportional to the number of moles of the gas. Mathematically, this means V = kn

Gases

Pressure-Temperature Relationship (number of molecules and volume constant) Gay-Lussac

Gases Pressure-Temperature Relationship (number of molecules and volume constant) The Kelvin temperature scale is an energy scale; absolute zero is the “zero” of kinetic energy. No molecular motion exists at -273 °C (0 K).

Gases Dalton’s Law of Partial Pressures P total = P 1 + P 2 + P 3 +..…+ P n

Gases Dalton’s Law of Partial Pressures The total pressure of a mixture of gases equals the sum of the pressures that each would exert if it were present alone. In other words, P total = P 1 + P 2 + P 3 + …

Gases The total pressure exerted by a mixture of gases is 0.38 atm. If the mixture is made up of mol Ar and mol He, what is the partial pressure exerted by each gas? Example: Dalton’s Law of Partial Pressures

Gases

Partial Pressures When one collects a gas over water, there is water vapor mixed in with the gas. To find only the pressure of the desired gas, one must subtract the vapor pressure of water from the total pressure.

Gases Ideal-Gas Equation V  1/P (Boyle’s law) V  T (Charles’s law) V  n (Avogadro’s law) So far we’ve seen that Combining these, we get V V  nT P

Gases

Ideal-Gas Equation The constant of proportionality is known as R, the gas constant.

Gases Ideal-Gas Equation The relationship then becomes nT P V V  nT P V = R or PV = nRT

Gases Densities of Gases If we divide both sides of the ideal-gas equation by V and by RT, we get nVnV P RT =

Gases We know that  moles  molecular mass = mass Densities of Gases So multiplying both sides by the molecular mass (  ) gives n   = m P  RT mVmV =

Gases Densities of Gases Mass  volume = density So, Note: One only needs to know the molecular mass, the pressure, and the temperature to calculate the density of a gas. P  RT mVmV = d =

Gases Molecular Mass We can manipulate the density equation to enable us to find the molecular mass of a gas: Becomes P  RT d = dRT P  =

Gases Temperature and Molecular Speeds Molecular KE = ½ mv 2

Gases Molecular Speed vs. Temperature

Gases Temperature: a measure of the average kinetic energy of a collection of molecules; the average kinetic energy of a collection of molecules is directly related to the Kelvin temperature. Temperature defined…

Gases Kinetic-Molecular Theory This is a model that enhances our understanding of what happens to gas particles as conditions change.

Gases A gas consists of a large number of molecules that are in continuous, random motion. Main Tenets of Kinetic-Molecular Theory

Gases The combined volume of all the molecules of a gas is negligible relative to the total volume in which the gas is contained. Attractive and repulsive forces between gas molecules are negligible. Main Tenets of Kinetic-Molecular Theory

Gases

Main Tenets of Kinetic-Molecular Theory Energy can be transferred between molecules during collisions, but the average kinetic energy of the molecules does not change with time, as long as the temperature of the gas remains constant.

Gases Molecular Speed Distributions

Gases Molecular Speed Distribution

Gases The average kinetic energy of the molecules is proportional to the absolute temperature. Main Tenets of Kinetic-Molecular Theory

Gases Gaseous Effusion Animated Effusion: the escape of gas molecules through a small aperture under pressure.

Gases If bromine molecules move at 215 m/s, on the average, how long should it take for them to travel, say, a foot (0.30 m)? Between one and two thousandths of a second! Diffusion: the random movement of atoms, molecules, or ions from high concentration to low concentration.

Gases Do gases always behave ideally? Do they always obey the gas laws?

Gases

Have you ever had the COOP fill your propane tank? Why do they refer to the fuel as LP?

Gases Compressing a gas sufficiently will cause it to liquify!

Gases Accurate pressure-volume measurements for grams of ammonia gas at 25 ˚C. Pressure (atm) Volume (L) P x V (atm. L) (condensation begins) (no gas left,liquid only) (only liquid present) (only liquid present) Ammonia does not obey PV = nRT at high pressures!

Gases Real Gases In the real world, the behavior of gases only conforms to the ideal-gas equation at relatively high temperature and low pressure.

Gases An “ideal” gas is a hypothetical gas and obeys PV = nRT. An ideal gas consists of molecules that: Real gases consist of molecules that attract each other and take up space. 1.do not exert electrical attractions on one another, and 2.do not occupy space. Reality Check

Gases Deviations from Ideal Behavior The assumptions made in the kinetic-molecular model break down at high pressure and/or low temperature.

Gases Corrections for Nonideal Behavior The ideal-gas equation can be adjusted to take these deviations from ideal behavior into account. The corrected ideal-gas equation is known as the van der Waals equation.

Gases The van der Waals Equation ) (V − nb) = nRT n2aV2n2aV2 (P +

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