Gas Behavior formulas from models § 17.1–17.2

Ideal Gas Model molecules: non-interacting point masses collide elastically with surfaces Temperature T is related to kinetic energy K K tr = 1/2 kT per mode of motion k =  10 –23 J/K (Boltzmann constant)

What determines the pressure of a sample of a gas? Increasing the volume: A. Has no effect B. Increases the pressure C. Decreases the pressure CPS Question

What determines the pressure of a sample of a gas? Increasing the number of molecules: A. Has no effect B. Increases the pressure C. Decreases the pressure CPS Question

What determines the pressure of a sample of a gas? Increasing the temperature: A. Has no effect B. Increases the pressure C. Decreases the pressure CPS Question

Ideal Gas EOS What is the pressure? LxLx LyLy LzLz

Ideal Gas EOS p = F/A F =  p/  t  p = impulse on wall per collision = 2mv x  t = average time between collisions of one molecule with the wall = 2L x /v x If there are N molecules,  t = 2L x /Nv x A = area of wall = L y L z 1/2 mv x 2 = 1/2 kT

Ideal Gas EOS p = F/A p = Nmv x 2 LxLyLzLxLyLz = NkT/V = nRT/V 2mv x Nv x 2Lx2Lx LyLzLyLz =

Ideal Gas Model shows expansion with increasing T at constant p shows p increase with increasing T at constant V shows p = 0 at T = 0 K

RMS Speed 1/2 mv 2 = 3/2 kT v 2 = 3kT/m M = molar mass 3kT/m v = 3RT/M=

Ideal Gas Model Does not address interaction behavior condensation mean-free path sound transmission slow diffusion

van der Waals EOS Molecules have volume Molecules attract (dimerize) p = an 2 V 2V 2 nRT V – nb –

Mean Free Path r = molecular radius = V 4  2 r 2 N = kT 4  2 r 2 p

CPS Question At constant temperature, how are pressure and volume of an ideal gas related? A.They are directly proportional. B.They are negatively correlated. C.They are inversely proportional. D.They are unrelated.

p-V plots Ideal gas Source: Y&F, Figure 18.6 Real Substance Source: Y&F, Figure 18.7

Boyle’s Law Ideal gas at constant pressure P 1 V 1 = P 2 V 2 Pressure and volume inversely related

V-T plots Gas Source: Y&F, Figure 17.5b P1P1 V P2P2 P3P3

Charles’s Law Ideal gas at constant pressure V 2 /T 2 = V 1 /T 1 Volume and temperature directly related

p-T plots Gas Source: Y&F, Figure 17.5b

Elastic Moduli reversible deformation § 17.3

Young’s Modulus Fractional elongation under tension or shortening under compression L0L0 L 0 +  L Y = Young’s Modulus; Units: Pa Area perpendicular to force = Y F A LL L0L0 stress strain

Shear Modulus Deformation under shear stress L0L0 S = Shear Modulus Area parallel to force = S F A xx L0L0 xx

Bulk Modulus Volume change B = Bulk Modulus; Units: Pa  P = B VV V0V0 V 0 +  V V0V0

Phases of Matter Behavior and diagrams § 17.4

Liquids Atoms constantly moving Molecules stay close to each other –do not separate –do not pass through each other –slide around

Think Question In liquids, molecules are close together. In gases, molecules are far apart. Are the molecules’ potential energies higher when they are together in the liquid or when they are separated in the gas?

Think Question If the molecules of a gas, without any outside force acting on them, move toward each other and condense to form a liquid, will their kinetic energies increase or decrease? (Hint: in an isolated system, total energy is conserved.)

Solid Water (Ice) Source: M. Chaplin, Water Structure and Behavior.

Solids Strong connections between atoms –rigidity and elasticity Atoms vibrate about fixed positions

Phase Changes Potential energies: Solid < Liquid < Gas During a phase change, potential energy, not kinetic energy (temperature) changes. Heating or cooling a changing phase does not change its temperature!

Variables and Diagrams State Variables: p, V, n, T Hard to visualize in 2-D Useful plots: p-V, p-T

p-V-T Surface Ideal Gas Source: Y&F, Figure 18.27

p-V-T Surface Real Substance Source: Y&F, Figure 18.26

p-T plot Phase Diagram Source: Y&F, Figure 18.24

Water’s Phase Diagram Source: P.W. Atkins, Physical Chemistry, 2 ed., 1978, p.193.

The Book is Wrong About Salting cooking water –It doesn’t raise boiling temperature much Pressure melting of ice –not at attainable pressures