Unit 10 Notes-2 Avogadro's & Ideal Gas Laws HChem
Unit 11: Avogadro’s and Ideal Gas Laws
Overview
Focus: Avogadro’s Law and Ideal Gas Laws, crucial concepts in understanding gas behavior in chemistry.
Page 1
Introduction to Chapter 13 of Honors Chemistry focusing on gas laws including Avogadro's Law and the Ideal Gas Law.
Page 2: Avogadro’s Law
Definition: States that equal volumes of gases, at the same temperature (T) and pressure (P), contain equal numbers of particles (moles).
Volume Dependence:
The volume occupied by gas is dependent on the number of particles, not their size due to the significant spacing between particles at low pressure.
Mathematical expression: V/n = k (where k is a constant).
For changes: V1/n1 = V2/n2.
Page 3: Molar Volume of a Gas
Molar Volume: Standard molar volume = 22.4 L at STP (Standard Temperature and Pressure: 1 atm and 273 K).
Key Point: At STP, 1 mole of any gas occupies 22.4 L.
Conversion Factor: 22.4 L can be used for calculations involving gases at STP.
Example Problem: Calculation of volume occupied by 90.0 g of H2 at STP.
Calculation: 90.0g x (1 mol / 2.02g) x 22.4 L/mol = 998 L @ STP.
Page 4: Kinetic Molecular Theory (KMT)
Purpose: Describes behavior of ideal gases.
Key Assumptions:
Composed of large numbers of small particles, distant compared to their size.
Collisions between particles are elastic (no energy loss).
Continuous, rapid, random motion of particles.
No forces of attraction or repulsion exist between particles.
Average kinetic energy is dependent on temperature.
Page 5: Ideal vs. Real Gases
Ideal Gases:
Have no volume, all collisions elastic, no attraction/repulsion.
Real Gases:
Have volume, energy is lost during collisions, particles interact.
Conditions Affecting Ideal Behavior:
Ideal behaviors mostly observed in noble gases; deviations seen at low temperatures and high pressures.
Page 6: Conditions of Deviation from Ideal Behavior
Real gases deviate from ideal behavior under:
High Pressure: Particles are close together, occupying significant volume.
Low Temperature: Particles slow down, attractive forces become significant.
Page 7: The Ideal Gas Law
Equation: PV = nRT, combining various gas laws (Boyle's, Charles's, Gay-Lussac's, Avogadro’s).
Describes the behavior of an ideal gas through its pressure (P), volume (V), temperature (T), and number of moles (n).
Rearranged forms: P1V1 = P2V2 (k constant).
Page 8: Ideal Gas Law Variables
Measured Quantities:
Pressure (P), Volume (V in liters), Number of moles (n), Temperature (T in Kelvin).
Ideal Gas Constant (R): Different values depending on pressure units:
0.08206 L·atm/(mol·K)
8.3145 L·kPa/(mol·K)
62.4 L·torr/(mol·K)
Page 9: Calculating the Ideal Gas Constant (R)
Derivation of R from the ideal gas equation at STP:
R = (PV)/(nT) = (1 atm x 22.4 L) / (1 mol x 273 K) = 0.0821 L·atm/(mol·K).
Emphasis on using the appropriate value of R depending on pressure units used.
Page 10: Ideal Gas Law Example
Problem: Find moles of ammonia in a 3.0 L vessel at 300 K and pressure of 1.50 atm.
Using Ideal Gas Law, rearranged to solve for n:
n = PV / (RT) = (1.50 atm x 3.0 L) / (0.0821 L·atm/(mol·K) x 300 K) = 0.18 moles (2 significant figures).
Page 11: Finding Molar Mass from Ideal Gas Law
Understanding Molar Mass: M = m / n.
Rearranged Ideal Gas Law: M = (mRT) / (PV).
Example: Find molar mass from given data:
M = (1.05 g)(0.0821 L·atm/(mol·K)(310 K)) / (0.840 atm)(2.35 L) = 13.5 g/mol.
Page 12: Finding Gas Density from Ideal Gas Law
Density Relationship: D = m/V.
Substituting into the ideal gas equation gives M = DRT/P.
Example Calculation: Density of argon gas at given pressure and temperature:
D = (39.95 g/mol)(551 mmHg) / (62.4 L·torr/(mol·K)(298 K)) = 1.18 g/L.
In class notes:
1 mole of any gas - 22.4 L at STP.
Idea gases fits all assumptions of kinetic molecular theory
Gases consist of large numbers of small particles that are very apart to their individual sizes
all collisions are elastic (no energy transferred)
particles are continuous, rapid, random motion
no frces of attraction or repulsion
the average kinetic energy depends on the temp.
Ideal vs Real
Idea - Particles have no vliume, elastic collitions, no forces of attraction or repulsion
real - Gases are matter, matter has volume, energy will be transferred sfered, when they get close they interact.
**When do real gases differ from ideal gases
1) high pressure (particles will be close and volume occupied by the gas particles become a significant part of volume
Low temp (low KE slows and attraction between molecules pull them together.
PV = n RT, where P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant, and T is the temperature in Kelvin.
R = 0.0821 Latm/molK
R - 8.314 LkPa/MolK
R = 62.4 LTorr/molK
Molar mass = mass of gas*R*T/PV
Density = MolarMass*P/RT