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

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Boston University

CH 102 – General Chemistry 2

Midterm 1: 2/16/2016

Exam Guide

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Topics Included:

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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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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