Flashcards in THERMO2 Deck (33):

1

## Ideal Gas Equation

###
PV = nRT

P = pressure

V = volume

n = number of moles

R = molar gas constant

T = temperature

2

## Assumptions of Kinetic Gas Theory

###
1. Gas contains many molecules

2. Molecules are well separated

3. Direction of motion of molecules is random

4. Molecules exert no force on each other except during collisions

5. Collisions between molecules and with walls are elastic

3

## Ideal Gas Constant

### R = PV/nT = 8.31

4

## When do real gases behave as ideal gases?

### Real gases behave as ideal gases when molecules are well separated i.e. at high temperatures and low pressures

5

##
Units of Pressure

1 pascal

### 1Pa = 1 N/m^2

6

##
Units of Pressure

1 bar

### 1 bar = 10^5 Pa

7

##
Units of Pressure

1 atmosphere

### 1 atm = 1013millibar = 1.013x10^5 Pa

8

## Standard Temperature and Pressure (STP)

###
0C = 273.15K

1atm = 1.013x10^5 Pa

9

## How does kinetic gas theory explain pressure?

###
Collisions of molecules with the walls of the container

Change in momentum

10

## Pressure Equation

### P = (1/3) * Nm/V * (v^2)av

11

## Kinetic Energy per Molecule

### (1/2)mv^2 = (3/2)kT

12

## Dalton's Law of Partial Pressures

###
Ptotal = P1 + P2

Pt =RT/V (n1 + n2)

13

## Pressure in a Fluid

### P = ρhg

14

## Kinetic Energy per Mole

### (1/2)Mv^2 = (3/2)RT

15

## Number of Molecules and Moles Equation

###
N = n*Na

N = number of molecules

n = number of Moles

Na = advogadros constant

16

## Mass of Molecules and Moles Equation

###
M = m*Na

M = mass of a mole

m =mass of a molecule

Na = advogadros Constant

17

## Relationship between advogadros Constant, the molar Gas Constant and Boltzmann Constant

### R = k*Na

18

## Root Mean Square Speed Equation

### Vrms = √(Vav^2) = √(3kT/m)

19

##
Mean Free Path

Definition

### The average distance travelled by a Molecule between collisions

20

##
Mean Free Path

Equation

###
λ = 1/(√2*nv*π*d²)

λ = mean free path

nv = number density

d = diameter of a molecule

21

## What does mean free path depend on?

###
-size of molecules

-particle density of the gas

-doesn't depend on speed

-depends on geometric factors

22

##
Collision Time

Definition

### The average time between collisions

23

##
Collision Time

Equation

###
λ = Vav * τ

τ = collision Time

λ = mean free path

Vav = average velocity

24

## What does collision time depend on?

###
-mean free path

-speed of molecules

25

## NND

###
Nearest Neighbour Distance

NND = ∛(volume per molecule)

NND = ∛(1/nv) = ∛(V/N) = ∛(kT/P)

26

##
Maxwell Boltzmann Distribution

Description of Graph

###
-bell curve

-steeper on left hand side

-doesn't touch the y axis

-theoretically the Graph continues to x=∞

-speed on X axis

-fraction of molecules on y axis

27

##
Maxwell Boltzmann Distribution

Vmax

###
Vmax is the speed that the highest proportion of molecules have

I.e. The maxima of the Graph

To find it differentiate the Graph equation and set it equal to zero

Vmax = √(2RT/M)

28

##
Maxwell Boltzmann Distribution

Vrms

###
The square root of the average of the speeds squared

Calculated using an integral

Vrms = √(3kT/m) = √(3RT/M)

29

##
Maxwell Boltzmann Distribution

Vav

###
Average of the velocities of each molecule so accounts for direction

Calculated using an integral

Vav = √(8kT/πm) = √(8RT/πM)

30

## Relationship Between Vmax, Vrms and Vav

### Vmax < Vav < Vrms

31

##
Maxwell Boltzmann Distribution

Change With Temperature

###
For a fixed mass of gas, an increase in temperature results in:

-Vmax increases

-peak moves to the right

-height decreases

-area under graph remains constant as the number of molecules has not changed

32

##
Maxwell Boltzmann Distribution

Change With Molar Mass

###
Temperature remains constant but molar mass is increased results in:

-Vmax decreased

-height of graph increases

-area under graph remains constant as the number of molecules has not changed

33