🔵 CHE101. KINETIC THEORY

-

*KINETIC THEORY* 

Today's class shall be on Kinetic Theory of Gases

  The kinetic theory of gases is a historically significant, but simple, model of the thermodynamic behavior of gases, with which many principal concepts of thermodynamics were established.

 The kinetic theory of gases explains the macroscopic properties of gases, such as volume, pressure, and temperature, as well as transport properties such as viscosity, thermal conductivity and mass diffusivity. The model also accounts for related phenomena, such as *Brownian motion.*

 


 *The theory for ideal gases makes the following assumptions:*

1. The gas consists of very small particles known as molecules. This smallness of their size is such that the total volume of the individual gas molecules added up is negligible compared to the volume of the smallest open ball containing all the molecules. This is equivalent to stating that the average distance separating the gas particles is large compared to their size.

2. These particles have the same mass.

 3. The number of molecules is so large that statistical treatment can be applied.

 4. The rapidly moving particles constantly collide among themselves and with the walls of the container. All these collisions are perfectly elastic. This means the molecules are considered to be perfectly spherical in shape and elastic in nature.

 5. The average kinetic energy of gas molecules is directly proportional to absolute temperature only; this implies that all molecular motion ceases if the temperature is reduced to absolute zero.


*Kinetic Molecular Theory and Gas Laws*

 1. Kinetic Molecular Theory states that gas particles are in constant motion and exhibit perfectly elastic collisions.

2. Kinetic Molecular Theory can be used to explain both Charles’ and Boyle’s Laws.

3.  The average kinetic energy of a collection of gas particles is directly proportional to absolute temperature only.

  

 *Applying Kinetic Theory to Gas Laws*

 *Charles’ Law🔥* states that at constant pressure, the volume of a gas increases or decreases by the same factor as its temperature. This can be written as:

V₁/T₁ = V₂/T₂

 According to Kinetic Molecular Theory, an increase in temperature will increase the average kinetic energy of the molecules. As the particles move faster, they will likely hit the edge of the container more often. If the reaction is kept at constant pressure, they must stay farther apart, and an increase in volume will compensate for the increase in particle collision with the surface of the container.

 

 *Boyle’s Law🔥* states that at constant temperature, the absolute pressure and volume of a given mass of confined gas are inversely proportional. This relationship is shown by the following equation:-

V₁P₁= V₂P₂

 At a given temperature, the pressure of a container is determined by the number of times gas molecules strike the container walls. If the gas is compressed to a smaller volume, then the same number of molecules will strike against a smaller surface area; the number of collisions against the container will increase, and, by extension, the pressure will increase as well. Increasing the kinetic energy of the particles will increase the pressure of the gas.

 

*Kinetic energy* can be distributed only in discrete amounts known as quanta, so we can assume that any one time, each gaseous particle has a certain amount of quanta of kinetic energy. These quanta can be distributed among the three directions of motions in various ways, resulting in a velocity state for the molecule; therefore, the more kinetic energy, or quanta, a particle has, the more velocity states it has as well

 

 *Effect of temperature on root-mean-square speed distributions*

 As the temperature increases, so does the average kinetic energy (v), resulting in a wider distribution of possible velocities.

n = the fraction of molecules.

Larger molecular weights narrow the velocity distribution because all particles have the same kinetic energy at the same temperature.

 Therefore, by the equation 

KE=1/2mv²

 the fraction of particles with higher velocities will increase as the molecular weight decreases.

 

 *QUESTIONS*

1.  During a compression process involving am ideal gas at pressure P₁, when the volume, V₁ of the gas was halved, the temperature in Kelvin increases by half its initial value. The final pressure P₂ is given by ________

2. A given mass of a gas occupies a certain volume at 300K. At what temperature will its volume be doubled?

 3. A certain volume of a gas at 298K is heated such that its volume and pressure are now four times the original values. What is the new temperature? 

 4. The volume occupied by 30cm³ of a gas after its temperature has been raised from 27 to 127°C and its pressure from 760 to 380mmHg is _______


  *Solutions*

1. 

P₁ = P₁

V₁ = V₁

V₂= 1/2V₁

T₂= 3/2T₁

T₁ = T₁     

P₂ = ?


Formula is

P₂=  P₁V₁T₂/T₁V₂

= P₁V₁3/2T₁/ T₁1/2V₁

Therefore :-

 P₂  = 3P₁✅✅✅


2.

V₁= V₁

T₁= 300K

V₂= 2V₁

T₂= ?

Therefore

V₁/T₁ = V₂/T₂

T₂= 2V₁ x 300/ V₁

T₂= 2×300

    =600K ✅✅✅


3.

P₁= P₁T₁= 298K

V₁= V₁

P₂= 4P₁

V₂= 4V₁

Therefore:-

T2= V₂P₂T₁/ P₁ V₁

When you substitute all, you'll get

T2 = 4768.0K ✅✅✅


4.

P₁V₁/T₁ = P₂V₂/T₂

760 × 30/(27+273) = 380 × V₂/ (127+273)

V₂ = 80cm³ ✅✅✅

 

 This brings us to the end of today's class

  Have a lovely day ahead📚


By: *Ms. Olabiyi Peter* 


✍️ *FLASHPEE EDUCATIONAL TEAM*

Comments

Post a Comment

Popular posts from this blog

📝 GNS101

-
21ST CENTURY LITERACY SKILLS  There are 4 language skills:  1. Listening 2. Speaking 3.Reading 4. Writing.  *The four skills are related to each other by two parameters:*  (a). the mode of communication: oral or written   (b) the direction of communication: receiving or producing the  message   *PRODUCTIVE SKILLS*  The productive skills are  1. SPEAKING 2. WRITING Learners doing these need to produce language.  These skills are contrasted with the *receptive skills* of listening and reading.    *RECEPTIVE SKILLS*  The receptive skills are  1. LISTENING 2. READING Learners do not need to produce language to do these: they receive and understand it.  They can be contrasted with the productive of speaking and writing.  These skills are sometimes erroneously described as   *passive skills,* as if they require no activity.  Note that all skills require some activity.   1. *LITERACY*  ...
Read more

📓 GNS101 WORD FORMATION (Morpheme)

-
WORD FORMATION (Morpheme)  *Word formation* refers to the way in which new words are formed in the basis of other words or morpheme.  And a morpheme is meaningful linguistic unit consisting of a word that cannot be divided into smaller meaning parts  _There is a difference between a morpheme and a word_  ▪️ *A word* can stand alone and can be meaningful but *a morpheme* can not always stand alone ▪️ *A word* can have 2 or more morphemes   ```LET ME GIVE EXAMPLE```   *RECONSTRUCT*    This is a word that has two morphemes (RE/CONSTRUCT).   When we have a sentence, it consists of clause. ⚡Clause consists of phrase ⚡Phrases consists of words ⚡And words consist of morpheme ⚡Morpheme consists of syllables   *Define a phrase*    Group of words without finite verb. So we can break this to phrase They/ might be thinking/of words/ and their meaning   Each of these phrases consists of one or two words   So words can be broken to...
Read more

📝GNS101. GOAL SETTING

-
GOAL SETTING AND TIME MANAGEMENT  *What is Time?* *Time* is a *limited* , *non-renewable* resource.  ❗❗❗. Note:  those key words must be there *What is Management?*  *Management* is the skilful handling or use of resources such as people (human capital), money,  materials and time  *What is Time Management?* *Time management* is an essential skill in the modern world where several activities have to be crammed into each day.  *There are several time management tools you can use.*  They are cheap and easily available. 🔘 a. *TIMETABLE* :  this is a tabulated list of the times at which certain events or activities are required to occur.  🔘b. *ORGANIZER* : This is a small portable calendar and data book used for planning, or a handheld  computerized device with a simple database for managing appointments and other information.  🔘 c. *TIMEPIECE* : A timepiece is any instrument for recording or showing the time, especially one tha...
Read more