Gas law
Chapter 3: Foundations of Gas Law
Page 1
Introduction to the principles governing gas laws.
Page 2: Gases
Composition of air: 78% Nitrogen (N2), 21% Oxygen (O2), and 1% other gases (including CO2).
Interest in gas composition increased in the 1990s due to environmental pollution.
Gases defined under normal atmospheric conditions: 25°C and 1 atm.
Gas: A substance usually in gaseous state at ordinary temperatures and pressures.
Vapor: Gaseous form of a liquid or solid at normal temperatures and pressures.
Page 3: Substances Found as Gases at 1 atm and 25°C
Elements:
H2, N2, O2, O3, F2, Cl2, He, Ne, Ar, Kr, Xe, Rn
Compounds:
HF, HCl, HBr, HI, CO, CO2, NH3, NO, NO2, N2O, SO2, H2S, HCN.
Page 4: General Characteristics of Gases
Expansibility: Gases have limitless expansibility filling the entire vessel.
Compressibility: Easily compressed by applying pressure in a container with a movable piston.
Diffusibility: Ability to diffuse rapidly to form a homogeneous mixture.
Pressure: Exerts pressure in all directions against the walls of the container.
Effect of Heat: Heating a gas in a vessel increases its pressure; volume increases when heated in a piston-fitted vessel.
Page 5: Pressure of a Gas
Gases exert pressure due to constant motion and collisions.
Pressure = force per unit area; SI unit is Pascal (Pa).
Page 6: Atmospheric Pressure
Air density is higher near Earth's surface and decreases with altitude.
About 50% of the atmosphere is within 6.4 km of the surface.
Atmospheric pressure: Pressure exerted by Earth's atmosphere.
Page 7: Atmospheric Pressure Value
Actual atmospheric pressure varies by location, temperature, and weather conditions.
Standard atmospheric pressure (1 atm) = pressure supporting a mercury column of 760 mm at 0°C at sea level.
Page 8: Measuring Gas Pressures
Barometer: Measures atmospheric pressure.
Manometer: Measures gas pressure other than atmospheric pressure.
Page 9: Parameters of Gas
A gas sample is described by:
Volume (V)
Pressure (P)
Temperature (T)
Number of moles (n)
Page 10: The Gas Laws
From 17th to 19th century, scientists established relationships among pressure, temperature, and volume of a gas.
These relationships are referred to as gas laws.
Page 11: Boyle’s Law
Discovered by Robert Boyle in 1660.
States that at constant temperature, volume is inversely proportional to pressure (PV = k).
If pressure doubles, volume halves.
Page 12: Mathematical Expression of Boyle’s Law
V ∝ 1/P (at constant T, n), or V = k(1/P) where k is a proportionality constant.
PV = k.
Useful for determining gas volume at different pressures.
Page 13: Graph of Boyle’s Law
Graphs show the relationship between pressure and volume, illustrating that doubling the pressure halves the volume (P vs. V and P vs. 1/V).
Page 14: Charles’s and Gay-Lussac’s Law
Charles’ Law (1787): at constant pressure, volume is directly proportional to absolute temperature.
Increasing absolute temperature leads to increasing volume.
Page 15: Mathematical Expression of Charles’ Law
V ∝ T (at constant P, n), expressed as V = kT.
Page 16: Gay-Lussac’s Law
At constant volume and amount of gas, the pressure of a gas is proportional to its temperature.
Page 17: Graph of Charles's Law
At constant pressure, volume directly relates to absolute temperature.
Page 18: Avogadro’s Law
At constant temperature and pressure, gas volume is directly proportional to the number of moles present.
Page 19: Equal Volumes of Gases
Equal volumes of gases at the same temperature and pressure contain equal number of molecules (Avogadro’s Principle).
Page 20: Molar Gas Volume at STP
At STP (273 K, 1 atm), 1 mole of gas = 22.4 liters.
Page 21: The Combined Gas Law
Combines Boyle’s Law and Charles’ Law into a single relationship: Volume is directly proportional to temperature and inversely proportional to pressure (PV/T = k).
Page 22: Example Problem Using Combined Gas Law
Initial conditions: V1 = 25.8 L, P1 = 690 torr, T1 = 290 K.
Final conditions: P2 = 1.85 atm, T2 = 345 K, find V2 = 15.1 L.
Page 23: Universal (Ideal) Gas Law
Volume of gas is directly proportional to moles and temperature, inversely proportional to pressure.
Ideal Gas Law: PV = nRT, where R is the gas constant.
Page 24: Applying Ideal Gas Equation
The equation holds true for real gases at low pressures.
For 1 mole (n=1), it simplifies to PV = RT.
Page 25: Behavior of Ideal Gases
Under 0°C (273.15 K) and 1 atm, 1 mole of gas occupies 22.414 L, referred to as STP.
Page 26: Modified Ideal Gas Equation
Adjusts based on initial and final conditions (with constants).
Page 27: Example Problem for Bubble Rising in Lake
Initial and final conditions are set to calculate the final volume.
Page 28: Calculation of Volume from Pressure and Temperature Changes
Calculate V2; results indicate changes in mL.
Page 29: Density and Molar Mass of Gases
Using the ideal gas equation to explore density or molar mass of gases.
Page 30: Example on Calculating Molar Mass
Given density, temperature, and pressure to find molar mass.
Page 31: Dalton’s Law of Partial Pressures
Partial pressure = individual pressure of each gas in a mixture. Total pressure is the sum of partial pressures.
Page 32: Ideal Gas Equation for Gas Mixtures
Establishes equations for two gas components in a mixture.
Page 33: Total Pressure in a Gas Mixture
Total pressure results from collisions of different gas molecules in a container.
Page 34: Total Pressure Formula
PT = P1 + P2 + P3 + ...
Page 35: Mole Fraction
Mole fraction (XA): ratio of moles of each component to total moles in a mixture.
Page 36: Understanding Mole Fractions
Mole fractions of components always sum to 1.
Page 37: Example Problem for Gas Mixture
Given moles of gases, calculate partial pressures based on total pressure.
Page 38: Detailed Example Calculation
Calculate partial pressures for a mixture of neon, argon, and xenon gases based on given moles and total pressure.
Page 39: Kinetic Molecular Theory of Gases
Explains gas behavior in terms of molecular motion and energy.
Page 40: Understanding Gas Behavior
Conceptual description of gases helps in grasping the mathematics of gas laws.
Page 41: Assumptions of Kinetic Molecular Theory
Gases consist of small discrete particles.
Large distances between gas molecules.
Constant random motion and elastic collisions.
Pressure arises from molecule collisions with container walls.
Collisions among molecules are perfectly elastic.
Average kinetic energy is proportional to temperature in Kelvin.
Page 42: Kinetic Energy in Gases
Kinetic energy (KE) relates to temperature and molecular mass.
Page 43: Ideal vs Real Gases
Real gases show deviations from the ideal behavior defined in Kinetic Molecular Theory.
Page 44: Compressibility and Gas Laws
Boyle’s Law relates gas pressure to molecular collision rates.
Page 45: Relationship of Charles’s and Dalton’s Laws with Kinetic Theory
Molecular behavior influences pressure, temperature, and density relationships.
Page 46: Application of Avogadro's Law
Explains the relationship of gas density with number of moles at a fixed temperature and pressure.
Page 47: Root-Mean-Square Speed of Gas Molecules
Definition and importance in estimating molecular speed.
Page 48: Example Calculation for Molecular Speeds
Calculate root-mean-square speeds of helium and nitrogen gases at 25°C.
Page 49: Procedures for Calculating Molecular Speed
Detailed steps and calculations for determining rms speed for gases.
Page 50: Graham’s Law of Diffusion
Observes molecular movement leading to gas mixing.
Page 51: Inverse Proportionality of Diffusion Rates
Graham's Law: rates of diffusion inversely proportional to the square roots of molecular masses.
Page 52: Effusion Explained
Diffusion vs effusion in gas behavior through a barrier.
Page 53: Example of Gas Effusion Calculation
Use given times to calculate the molar mass of an unknown gas.
Page 54: Deviation from Ideal Behavior
Reasons for deviations based on Kinetic Molecular Theory assumptions.
Page 55: PV Behavior of Real Gases
Graph analysis of real gases indicating deviation from ideal behavior.
Page 56: Volume Correction in Real Gases
Relationships between molecular volume and free volume during compression.
Page 57: Pressure Correction in Gases
Adjustments in observed pressure due to intermolecular attractions.
Page 58: Detailed Equations for Pressure Corrections
Coefficients linked to molecular attractions defining pressure impacts.
Page 59: van der Waals Equation
Applies to real gases with correction terms for pressure and volume.
Page 60: van der Waals Constants Table
Values for constants a and b for various common gases.
Page 61: Significance of van der Waals Constants
Explanation of what a and b reveal about gas molecules.
Page 62: Compressibility Factor Z
Measures deviations from ideal behavior and its calculation.
Page 63: Graphical Representation of Compressibility Factor
Display the difference in behavior between ideal and real gases.
Page 64: Example Calculation using Ideal and van der Waals Equations
Pressure determination of CO2 using both equations for accuracy analysis.
Page 65: Final Calculations from van der Waals Equation
Detailed calculation process to derive CO2 pressure adjustments.