Chapter 4 The Gaseous State

NO2

AIR

Chemistry of Gases

SO3 .. corrosive gas

SO2…burning of sulfur in air

Pressure & Temperature

For 76cm of Hg, P = ρgh = 1.01325 x 105 kg m-1s-2

1 atm ≡ 1.01325 x 105 Pa

1662 Boyle “The Spring of the Air and its Effects”PV = C (fixed T & amount of gas)

~1760 CharleThe definition of the Temperature

All gases expand with increasing temperature by the same extent.t = c [(V/V0)-1] for all gases

1802 Gay-Lussac reproted c of 267 oClater refined to be c = 273.15

V = V0[1+(t/273.15oC)]

Kelvin T = 273.15 + t(Celsius)

Boyle’s Law

• The stirling engine, a heat engine invented by a Scottish minister, has been considered for use in automobile engines because of itsefficiency. In such an engine, a gas goes through a four-step cycle of (1) expansion at constant T, (2) cooling at constant V, (3) compression at constant T to its original volume, and (4) heating at constant V to its original temperature. Suppose the gas start at a pressure of 1.23 atm and the volume of the gas changes from 0.350 L to 1.31 L during its expansion at constant T. Calculated the pressure of the gas at the ene of this step in the cycle.

Charels’s Law

• A gas originally at a temperature of 26.5 °C is cooled at constant pressure. Its volume decreases from 5.40 L to 5.26 L. Determine its new temperature in degrees Celsius.

The Ideal Gas Law

PV = nRTR is a universal gas constant

R = 0.082058 L atm mol-1 K-1

=8.3145 J mol-1K-1

The Ideal Gas Law

• Iodine heptafluoride (IF7) can be made at elevated temperatures by the reaction

I2(g) + 7 F2(g) 2 IF7(g)Suppose 63.6 L of gaseous product is made by this

reaction at 300°C and a pressure of 0.459 atm. Calculated the volume this gas will occupy if heated to 400°C at a pressure of 0.980 atm.

The ideal gas law

• The pressure of a poisonous gas inside a sealed container is 1.47 atm at 20°C. If the brometic pressure is 0.96 atm, to what temperature (in degree Celsius) must the container and its contents be cooled so that the container can be opened with no risk of gas spurting out?

Mixtures of Gases

Partial pressurePA = nA [RT/V]

XA = nA/ntotPA = XAPtot

NOTE Ex. 4.6 (p.107)

The Kinetic Theory of GasesEmpirical ideal gas law can be explained by the kinetic theory of gases

Assumptions1. Pure gas consists of identical molecules separated by great distances2. Constantly moving in random directions with a speed distribution3. No forces between collisions – straight lines with constant velocities4. The collisions are elastic

Momentum change per collision

Δpx,mol = m(-vx)-mvx = -2 mvx = -Δpx,wall

Time between collisions to the original faceΔt = [2l/vx]The momentum transferred per second[Δpx,wall/ Δt] = (mvx

2)/l

For N molecules of mass m,F = (mvx1

2)/l + (mvx22)/l +….. = [Nm/l] vx

2

P = F/A = [Nm/Al]vx2

PV = Nmvx2

Since u2 = vx2 + vy

2 + vz2 = 3vx

2

PV = ⅓Nmu2, u2 is the mean-square speedFrom PV=nRT, ⅓Nmu2 = nRT, ⅓N0mu2 = RTKinetic energy per mole = ½N0mu2 = (3/2)RTOru2 = [3RT]/M, molar mass

Another look at T

Distribution of Molecular SpeedsRoot-mean square speed

Urms = (u2)½ = (3RT/M)½

Thermal equilibrium is a prerequisite for the definition ofTemperature

Effusion1846 Graham’s law of effusion

Frequency of Molecular Collisions – Mean Free path - Diffusion

Real Gases: Intermolecular Forces

Van der Waals Equation

[P+a(n2/V2)][V‐nb] = nRT

Intermolecular Forces

Lennard-Jones Potential

VLJ(R) =4ε[(σ/R)12 – (σ/R)6]