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F09_230_L05_pre[1]

# F09_230_L05_pre[1] - CHEM 230 F09 Lecture 5 Chapter 4 Click...

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Click to edit Master subtitle style CHEM 230 F09 Lecture 5 Chapter 4: Speed and Non-Ideality Session ID: 230

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Topics Kinetic Model of Gases Root-mean-square speed of a gas Maxwell Distribution of Speeds Real Gases Assumptions for an ideal gas Real gases differ from a ideal gases van der Waals coefficients
Kinetic Molecular Theory (KMT) Macroscopic = bulk -pressure -volume -temperature Microscopic = particle -energy -size -interactions Connect macroscopic with microscopic How does the macroscopic relationships arise from the motions of individual gas particles?

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Pressure is proportional to frequency of collisions of particles with wall of container If particles travel 5 cm/s (vx) than any particle w/i 5 cm ( x ) of wall will hit the wall over the course of a second ( t) x x = vx t Velocity, time, length
Velocity, Time, Length, Area If particles travel 5 cm/s (vx) than any particle w/i the volume = A* x where x = 5 cm could hit the wall over the course of 1 second ( t) x Particles in V col = Avx t could hit the wall in t

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Total number of particles = N Total volume = V Vcol = A*vx t NincolV = N * A*v x t V
1/2 particles in Vcol are moving toward the wall and 1/2 are moving away NincolV = N * A*v x t V Actual Ncol = N * A*v x t 2V

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momentum = mass * velocity momentum = |momentumf - momentumi| = |-mvx - mvx| = 2mvx A single particle hitting the wall has a change in momentum
Total momentum change the system is = Ncol*2mvx = N * A*v x t * 2mvx 2V momentum = N A v x2 t m V Newton’s second law: F = momentum t F = NAv x2 tm = NAv x2m tV V Simplify Sub in momentum

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Pressure = Force/area P = NAv x2m = Nv x2m VA V vx
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F09_230_L05_pre[1] - CHEM 230 F09 Lecture 5 Chapter 4 Click...

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