# CAS CH 102 Study Guide - Midterm Guide: Boiling-Point Elevation, Ideal Gas Law, Colligative Properties

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Professor Boston University
CH 102 General Chemistry 2
Midterm 1: 2/16/2016
Exam Guide
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1. Gas Properties
a. Ideal Gas Law
b. Kinetic Molecular Theory
c. Molecular Speeds and Distribution
d. Real Gases/Van der Waals
2. Solution Properties
a. Phase Diagrams
b. Enthalpy of Solution
3. Colligative Properties
a. Vapor Pressure Lowering, Boiling Point Elevation
b. Freezing Point Depression
c. Osmotic Pressure
4. Reaction and Equilibrium
a. Reaction Quotient, Predicting Direction of Change
b. (To be continued throughout the upcoming week)
5. Review Questions
1. Gas Properties
A. Ideal Gas Equation
a. Ideal Gas Law: PV = nRT
i. T (temperature) = Kelvin
ii. R = fundamental constant = 8.314 J/(K*mol) = 0.082 L*atm/(K*mol)
iii. P = pressure, V = volume → labels should match with R constant
b. The ideal gas law makes two assumptions:
i. Gas particles take up no volume
ii. Gas particles exert no attraction on each other
iii. These two assumptions are addressed in the real gas law equation (Part 1d)
c. Understand how to apply the relationship between these variables. Review questions
available in the “Review Questions” portion.
B. Kinetic Molecular Theory
a. Using the ideal gas law, a derivation for molecular speed can be made:
i. PV = NM(uavg)2 = nM(uavg)2
ii. Note: uavg = urms (rms = root mean square)
iii. However, this derivation assumes that particles move in straight lines. To adjust
for this untrue assumption, reduce it by three (moves in 3D, not one dimension)
iv. Final: PV = ⅓ nM(uavg)2
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Already have an account? Log in b. Now, there are equations for Pressure * Volume on two different levels:
i. Microscopic level: ⅓ nM(uavg)2
ii. Macroscopic level: nRT
iii. Using both of these, the average molecular speed (uavg) can be determined:
iv. uavg = √(3RT/M)
C. Molecular Speeds and Distributions
a. uavg = √(3RT/M)
b. This equation is only an average. Each particle has its own speed, resulting in a
distribution of different speeds. This is due to the collisions of gas particles with each
other -- collisions of gas particles with walls do not affect the distribution of speeds
because momentum is conserved/elastic collision, in which momentum (and therefore
speed) is conserved.
i. The collisions of gas particles with walls may not affect the distribution of
speeds, but it DOES determine the pressure of a gas
1. Pressure = force of gas / area of container hit
c. What this equation means:
i. Average speed is higher at higher temperatures
ii. Average speed is higher at small molecular masses
d. Understand the bell-shaped distribution of molecular speeds:
i. The average speed is slightly to the right of the peak.
ii. The left tail of each distribution begins at 0 m/s.
iii. As the average speed of a molecule increases, the bell-shape becomes wider
and the peak becomes lower.
D. Real Gases/Van der Waals
a. The ideal gas equation makes two assumptions: (1) There are no attractions between
molecules (2) Molecules have no volume. However, this is untrue. The Van der Waals
equation makes up for these discrepancies.
b. Attraction: ɑ = constant accounting for intermolecular attractions
i. Ideal pressure = Pideal
1. Pideal = nRT/V
ii. Real pressure = Pobserved
1. Pobserved = nRT/V - ɑ (n/V)2
iii. Meaning, actual pressure < ideal pressure. The presence of IMF makes
molecules attracted to each other = more collisions with other molecules and
less collisions with walls = less pressure.
c. Volume: b = value accounting for volume of gas particles (L/mol)
i. Ideal volume = Vcontainer
ii. Real volume = Vreal = Vcontainer - bn
iii. Meaning, real volume < ideal volume. Gas particles may be tiny compared to the
volume of their container, but they still take up space.
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