Docsity
Docsity

Prepare for your exams
Prepare for your exams

Study with the several resources on Docsity


Earn points to download
Earn points to download

Earn points by helping other students or get them with a premium plan


Guidelines and tips
Guidelines and tips

Kinetic Molecular Model of Gases: Assumptions, Pressure, and Velocity Distribution, Lecture notes of Physical Chemistry

this document is my lecture notes on the kinetic theory of gases

Typology: Lecture notes

2020/2021

Uploaded on 04/21/2021

sabila-aisyah
sabila-aisyah ๐Ÿ‡ฎ๐Ÿ‡ฉ

1 document

1 / 4

Toggle sidebar

This page cannot be seen from the preview

Don't miss anything!

bg1
๏€ก Kinetic Molecular Model of Gases
o Assumption
1) Gas molecules in ceaseless random motion (no phase change).
2) Molecular size is negligible (no repulsion).
3) Molecules do not interact (no attraction).
All gases at same P and T have the sam properties.
o Definition of Pressure
โ€œgas pressure is caused by collective collision of gas molecules with containerโ€™s wallโ€
Gas molecule has mass m and velocity v
๐น
1โˆ’ ๐‘š๐‘œ๐‘™๐‘’๐‘๐‘ข๐‘™๐‘’ = ๐น
๏Œค=๐‘‘๐‘ƒ
๏Œค
๐‘‘๐‘ก =๐‘ƒ
๏Œค(๐‘ก = 1)โˆ’๐‘ƒ
๏Œค(๐‘ก = 0)
1โˆ’0 = ๐‘š๐‘ฃ๎ชง๐‘ฅโˆ’(โˆ’๐‘š๐‘ฃ๎ชง๐‘ฅ)
= 2 ๐‘š๐‘ฃ๎ชง๐‘ฅ
Middle of container
Let V = volume of container and N = number of molecules at equilibrium
๐‘ 2
โ„travel left with + |๐‘ฃ๎ฌฆ| speed
๐‘ 2
โ„travel right with โˆ’ |๐‘ฃ๎ฌฆ| speed
Number of molecules that hit wall per second = number of molecules at distance |๐‘ฃ๐‘ฅ
๓ฐ‡
๓ฐ‡
๓ฐ‡
๓ฐ‡
๎ฌฆ
| for walls.
In volume V there are N molecules
In volume |๐‘ฃ๐‘ฅ
๓ฐ‡
๓ฐ‡
๓ฐ‡
๓ฐ‡
๎ฌฆ
|๐ด there are ๐‘|๐‘ฃ๐‘ฅ
๓ฐ‡
๓ฐ‡
๓ฐ‡
๓ฐ‡
|๐ด
๐‘‰ molecules
๐ด โ‰ก surface area of a wall
Force exerted on right wall per second
๐น = 1
2๐‘|๐‘ฃ๐‘ฅ
๓ฐ‡
๓ฐ‡
๓ฐ‡
๓ฐ‡
๎ฌฆ
|๐ด
๐‘‰(2๐‘š|๐‘ฃ๐‘ฅ
๓ฐ‡
๓ฐ‡
๓ฐ‡
๓ฐ‡
๎ฌฆ
|)
Only 1
2๐‘|๐‘ฃ๐‘ฅ|
๓ฐ‡
๓ฐ‡
๓ฐ‡
๓ฐ‡
๓ฐ‡
๓ฐ‡
๓ฐ‡
๎ฌฆ
๐ด
๐‘‰(2๐‘š|๐‘ฃ๐‘ฅ
๓ฐ‡
๓ฐ‡
๓ฐ‡
๓ฐ‡
๎ฌฆ
|) hit right wall (N/2 out of N travel right)
๐น = ๐‘š๐‘|๐‘ฃ๐‘ฅ
๓ฐ‡
๓ฐ‡
๓ฐ‡
๓ฐ‡
๎ฌฆ
|2๐ด
๐‘‰ ๐‘ƒ = ๐น
๐ด=๐‘๐‘š|๐‘ฃ๐‘ฅ
๓ฐ‡
๓ฐ‡
๓ฐ‡
๓ฐ‡
๎ฌฆ
|2
๐‘‰
pf3
pf4

Partial preview of the text

Download Kinetic Molecular Model of Gases: Assumptions, Pressure, and Velocity Distribution and more Lecture notes Physical Chemistry in PDF only on Docsity!

๏€ก Kinetic Molecular Model of Gases

o Assumption

  1. Gas molecules in ceaseless random motion (no phase change).

  2. Molecular size is negligible (no repulsion).

  3. Molecules do not interact (no attraction).

All gases at same P and T have the sam properties.

o Definition of Pressure

โ€œgas pressure is caused by collective collision of gas molecules with containerโ€™s wallโ€

Gas molecule has mass m and velocity v

๐น

1 โˆ’ ๐‘š๐‘œ๐‘™๐‘’๐‘๐‘ข๐‘™๐‘’

= ๐น

ฬ…

=

๐‘‘๐‘ƒ

ฬ…

๐‘‘๐‘ก

=

๐‘ƒ

ฬ…

(๐‘ก = 1 ) โˆ’ ๐‘ƒ

ฬ…

(๐‘ก = 0 )

1 โˆ’ 0

= ๐‘š๐‘ฃฬ…

๐‘ฅ

โˆ’

( โˆ’๐‘š๐‘ฃฬ…

๐‘ฅ

)

= 2 ๐‘š๐‘ฃฬ…

๐‘ฅ

Middle of container

Let V = volume of container and N = number of molecules at equilibrium

๐‘ 2

โ„ travel left with +

| ๐‘ฃโƒ—

| speed

๐‘ 2

โ„ travel right with โˆ’

| ๐‘ฃโƒ—

| speed

Number of molecules that hit wall per second = number of molecules at distance

| ๐‘ฃ

๐‘ฅ

โƒ—โƒ—โƒ—โƒ—โƒ—

| for walls.

In volume V there are N molecules

In volume |๐‘ฃ

๐‘ฅ

โƒ—โƒ—โƒ—โƒ—โƒ— |๐ด there are

๐‘|๐‘ฃ

๐‘ฅ

โƒ—โƒ—โƒ—โƒ—โƒ— |๐ด

๐‘‰

molecules

๐ด โ‰ก surface area of a wall

Force exerted on right wall per second

๐น =

1

2

๐‘|๐‘ฃ

๐‘ฅ

โƒ—โƒ—โƒ—โƒ—โƒ— |๐ด

๐‘‰

( 2 ๐‘š

| ๐‘ฃ

๐‘ฅ

โƒ—โƒ—โƒ—โƒ—โƒ—

|)

Only

1

2

๐‘|๐‘ฃ

๐‘ฅ

|

โƒ—โƒ—โƒ—โƒ—โƒ—โƒ—โƒ—โƒ—

๐ด

๐‘‰

( 2 ๐‘š|๐‘ฃ

๐‘ฅ

โƒ—โƒ—โƒ—โƒ—โƒ— |) hit right wall ( N/2 out of N travel right)

๐น =

๐‘š๐‘|๐‘ฃ

๐‘ฅ

โƒ—โƒ—โƒ—โƒ—โƒ— |

2

๐ด

๐‘‰

๐‘ƒ =

๐น

๐ด

=

๐‘๐‘š|๐‘ฃ

๐‘ฅ

โƒ—โƒ—โƒ—โƒ—โƒ— |

2

๐‘‰

Vector can be written as:

๐‘ฃโƒ— = ๐‘ฃ

๐‘ฅ

๐‘–ฬ‚ + ๐‘ฃ

๐‘ฆ

๐‘—ฬ‚ + ๐‘ฃ

๐‘ง

๐‘˜

ฬ‚

๐‘

2

=

| ๐‘ฃโƒ—

|

2

= ๐‘ฃ

๐‘ฅ

2

  • ๐‘ฃ

๐‘ฆ

2

  • ๐‘ฃ

๐‘ง

2

๐‘ = gas speed

Assume velocity in all 3 axes are equal

๐‘ฃ

๐‘ฅ

= ๐‘ฃ

๐‘ฆ

= ๐‘ฃ

๐‘ง

or ๐‘

2

= 3 ๐‘ฃ

๐‘ฅ

2

โˆด ๐‘ฃ

๐‘ฅ

2

=

1

3

๐‘ฃ

๐‘ฅ

2

๐‘ƒ =

1

3

๐‘๐‘š๐‘

2

๐‘‰

Or ๐‘ƒ๐‘‰ =

1

3

2

2

n = number of moles

M = molar mass

๏€ก KECEPATAN GAS

Every gas does not travel at the same speed

Maxwell distribution of gas velocity

Distribution of gas velocity can be presented by a mathematical function cal โ€œMaxwell

Distributionโ€.

3 / 2

2

โˆ’๐‘€๐‘

2

/ 2 ๐‘…๐‘‡

โˆž

0

3 / 2

3

โˆ’๐‘€๐‘

2

/ 2 ๐‘…๐‘‡

โˆž

0

3

โˆ’๐‘Ž๐‘ฅ

2

โˆž

0

2

2

from

2

๐‘ƒ๐‘‰ = ๐‘›๐‘…๐‘‡ ideal gas law

2

1 / 2

๐‘Ÿ๐‘š๐‘