GASES AND COLLISION THEORY

GASES

Every material expands when heated. Why?

Heat energy added is absorbed by the particles of materials [solid, liquid or gas].

This absorbed heat energy goes to increase the vibrations particles of matter.

Increased vibrations of the particles of a substance = increase temperature of the substance

Increase in vibrations of the particles = surrounding particles pushed farther away so particles for more space to vibrate = increased amount of space (volume) occupied by each particle of the substance = EXPANSION of materials.

Gas and liquids take the shape of the container they fill.

Total collision between gas particles and the walls of their container = total pressure of gas in the container.

Amount of Gas in a specific volume of space can be measured by the pressure they exert on the walls of their container.

Pressure= force/area

Force = Newtons (N)=kgm/s²

Pressure SI units = Pascal (Pa) = N/m²

Standard atmospheric pressure = 1 atm= 760mmHg = 760 torr

1atm= 101325 Pa = 1.01325 kPa

GAS LAWS

LUSSAC’s LAW

More heat = higher temperature = more vibrations of gas particles = higher gas pressure

This shows temperature (T) of a gas is directly proportional to the gas pressure (P). 

T α  P 

or

P = KT   , where K is a constant.

P/T = K constant

P₁/T₁= P₂/T₂

CHARLES Law

More heat = higher temperature = more vibrations of gas particles = larger volume of space occupied by gas particles

T α V      or    

 V = K T,     

V/T = constant K

where K is a proportionality constant.

   V₁/T₁=V₂/T₂

Boyle’s Law

Squeezing OR reducing the volume of container = increased vibrations between particles and container walls = increased pressure of gas particles.

Pressure of gas is inversely proportional to the volume of gas.

P α 1/V   

or   

P = K (1/V)  ,    where K is a constant

V = K x 1/P

PV = constant K

P₁V₁=P₂V₂

AVOGADRO LAW

Volume and moles      ;  1 mole of gas = 22.41L at STP

IDEAL GAS

1. Behave as particle spheres. Gas particles are particles like tennis balls.
2.  No attraction or repulsion between particles
3. Particles bounce of walls of container without losing energy.
4. No chemical reaction occurs between particles or wall of container.
5. gas volume is negligible compared to container.

V = K T

P = K T

Therefore, PV = K T,

PV/T = K = constant     ,  P₁V₁ /T₁ = P₂V₂/T₂

K is Boltzmann’s constant

For 1 mole of a gas K=R/N    , 

N = Avogadro’s number = 6.23 x 10 ^-23 particles.

where R = UNIVERSAL gas constant 8.314 J mol^-1 K^-1

K= n R , where n = number of moles of a gas

PV/T = n R     or     PV = n RT   …..ideal gas equation.

P₁V₁ /T₁ = P₂V₂/T₂

QUESTIONS 

R = 0.082057Latm/Kmol     at STP=1atm and 273.15K

1. Calculate the pressure of 5 moles of gas in a volume of 5.43L at 69.5^o

Suggestion: Use ideal gas equation, PV=nRT

2. Calculate volume(L) of 1000g of CO₂ gas at STP.

Suggestion: Use Avogadro’s Law OR Ideal gas equation

3. An unknown gas at 9L, 0.5atm and 89^oC changes to a final volume of 5L at a temperature of 50^o What is final Volume of the gas.

Suggestion: Use Boyle’s Law and Charles Law combination.

HENRY’S LAW:

Solubility of a gas, or the concentration of solution from dissolved gas particles in solvent is proportional to the gas pressure at the surface of the solution at any specific temperature.

M=kP, where M is the concentration of solution from dissolved gas particles.

P=gas pressure at surface of solution.

k is a temperature dependent constant.

PARTIAL PRESSURES OF MIXTURES

Mixtures = Different things added together.

Mole of each item in mixture/Total moles = Mole Fraction

For mixture of items , A ,B ,C and D.

Na = moles of A

Xa = Mole fraction of A = Na /[Na + Nb + Nc + Nd]

Partial pressure is the pressure exerted by an individual gas in the presence of other gases.

Depends on its mole fraction.

If Air is a mixtures of gases A, B, C and D,

Pa = Pressure exerted by A = partial pressure of A

Pa = X_aP_a^o   , where P_a^o is pressure of gas A in pure form when no other gas is present.

Total pressure of air = P = Pa + Pb + Pc + Pd

 VOLATILE SOLUTES + VOLATILE SOLVENT

TOTAL PRESSURE = sum of partial pressures of all solutes and solvent particles in vapor phase above the solution.

A solution of made up of substance 1, 2 and 3 volatile substances.

P_t = P₁ + P₂ + P₃ ……..etc.

P_t = total pressure

P₁, P₂, and P₃ are partial pressures of 1, 2 and 3 above the solution.

For a two-component system; a volatile liquid solute A [e.g. acetone] and a volatile liquid solvent B

[e.g. benzene].

Pt = Psolute + Psolv

     = P_B + P_A = X_BP_B^o + X_AP_A^o

_where X_{B   and}  X_A  , where are mole fractions of A and B in solution

P_B and  P_A  are partial pressures of gaseous A and B above the solution at that temperature.

P_B^o and  P_A^o  are vapor pressure of pure A and B at that temperature.

X_{A =} n_A /(n_A+n_B)   = 1 – X_B

Pt = Psolute + Psolv

= P_B + P_A

= X_BP_B^o + (1-X_B)P_A^o

= X_BP_B^o + P_A^o – X_B P_A^o

= P_A^o   + X_BP_B^o   – X_B P_A^o

   Pt – P_A^o   = X_BP_B^o   – X_B P_A^o   

                          = X_B ( P_B^o   –  P_A^o ) 

 

 

PARTICLE MOTION AND DISTRIBUTION

RMS speed of particles

Colliding particles leads to change of speed (higher or slower than before collision), change of direction and energy. Heating molecules increases their speed due to absorption of energy this increases the collision frequency. Heavy particles or molecules have lower speed compared to lighter molecules.      E.g. CO₂ is slower than H₂ molecules.

The average speed of particles varies over a broad range when gas is heated compared to when not heated.

c = (3RT/M)^1/2

High temperatures or Lower molecular weight

Lower temperatures or High molecular weight

Collision theory:

Molecules must have the right energy and phase angle to collide and form a chemical bond.

e.g. Diels alder reaction of diene and dienophile; both must be in right orientation for bond to form after collision.

Activation energy (Ea) : energy needed to overcome activation barrier and form a chemical bond between two atoms.

Pre- exponential factor (A*):

This is a constant that includes collision frequency and the phase angle of colliding molecules.

A* = Ke^[Ea/RT]    , Where K is rate constant at temperature T

K = A*/e^[Ea/RT] = A*e^{-[ Ea/RT]}

InK =InA* + -Ea/RT

InK =InA* – Ea/RT

Reactions with high Ea have very low rate constant and occur very slowly. They take long time to occur or require some energy (e.g. heat energy) or catalysis to occur readily.

Ea = ΔH^o + nRT.