ADAMSON UNIVERSITY
Chemical Engineering Department
A.Y. 2023-2024
Physical Chemistry I
Prelim Coverage | Homework 1
Name: Ginger Leigh V. De Leon
Date of Submission: February 9, 2024
Student Number: 202213868
Section: 51041 Tuesday 10:30-1:30
HONOR CODE
As a student who takes pride and upholds the ideals of this university, I,
Ginger Leigh V. De Leon
, do hereby certify on my honor that I will not engage to any form of
cheating and that I will neither give nor receive any form of assistance during the examination. I
understand that any acts of academic dishonesty will result to receiving a grade of zero for this
examination and will be subjected to further disciplinary actions.
Signature over printed name
Physical Chemistry 1 by Engr. Elen Cris O. Manangan | 1
I.
Conceptual
Kinetic Molecular Theory of Gases
Introduced by Daniel Bernoulli in 1783 that was later developed further by Rudolf Clausius (1857)
and James Clerk Maxwell (1857). The kinetic molecular theory (KMT) is a simple microscopic
model that effectively explains the states of matter, and is composed of tiny particles that are
always in motion.
The Kinetic Molecular Theory of Gases are based on five (5) basic postulates according to Fleming
(2000)
1. Gas particles obey Newton’s laws of motion and travel in straight lines unless they collide with
other particles or the walls of the container.
2. Gas particles are very small compared to the averages of the distances between them.
3. Molecular collisions are perfectly elastic so that kinetic energy is conserved.
4. Gas particles so not interact with other particles except through collisions. There are no attractive or
repulsive forces between particles.
5. The average kinetic energy of the particles in a sample of gas is proportional to the temperature.
The test of the Kinetic Molecular Theory and its postulates is its ability to explain and describe the
behavior of a gas (Lumen Learning, n.d.). Hence why various of gas laws are derived from the
assumptions which led to believe that these assumptions accurately representing the properties of gas
molecules.
Mean Free Path in Molecular Collision
The mean free path or average distance between collisions for a gas molecule may be estimated
from kinetic theory (Serway, 1990) It could be then taken as the length of the path divided by the
number of collisions.
Mean Free Path Formula:
!"
𝜆 = √$%&! '
Where:
𝜆 = Mean free path
𝜌 = pressure
𝐾 = Boltzmann’s constant 1.380649 x 10-23 J K-1
𝑇 = temperature
𝑑 = radius
Physical Chemistry 1 by Engr. Elen Cris O. Manangan | 2
Maxwell Distribution of Molecular Speed
The motion of molecules in a gas is random in magnitude and direction for individual molecules, but
a gas of many molecules has a predictable distribution of molecular speeds (University Physics
Volume 2, n.d.). This distribution of molecular speeds is known as the Maxwell-Boltzmann
distribution, proposed by James Clerk Maxwell and Ludwig Boltzmann. This distribution defines the
speed for a gas at a certain temperature.
Distribution Formula:
!"
#
!
#$
= ($%&')" 𝑒 "%& 𝑑𝑣
"
Where:
𝑑𝑁
= the fraction of molecules moving at velocity v to v + dv
𝑁
m = the mass of the molecule
𝐾 = Boltzmann’s constant 1.370649 x 10-23 m2 kg s-2 K-1
𝑇 = temperature
a. Most probable speed (Cmp): Is the maximum value on the distribution plot
$*"
𝐶() = ) +
b. Mean or average speed (Cavg): Is the sum of the speeds of all the molecules divided by the
number of the molecules
/*"
𝐶,-. = ) π+
c. Root-mean-square (RMS) speed (Crms): The square root of the average speed-squared
𝐶!"# = 3
3𝑅𝑇
𝑀
Where:
R = the gas constant
T = the absolute temperature and
M = the molar mass of the gas.
Physical Chemistry 1 by Engr. Elen Cris O. Manangan | 3
II.
Computational
Check your understanding:
1. The collision diameter of a molecular oxygen is 4.37𝑥10−10 𝑚. Calculate the mean free path,
λ, for oxygen at STP.
Given:
P = 101325 Pa d = 4.37x10-10m
T=0℃
𝜆=
K = 1.380649 x 10-23 m2 kg s-2 K-1
89.;/<=>? @ 9<A$; B ! "# C($E;.9FG)
I$%(>.;E@9<"#$ ()! (9<9;$F J,)
= 4.38x10-8 m/s
2. For nitrogen gas at STP, calculate the:
T = 273.15 K
R = 8.314 J/mol K
MM = 28.02 g/mol = 0.02802 kg/mol
a. Most probable speed, 𝑢𝑚𝑝
𝐶() = /
$(/.;9>
%
)($E;.9F !)
&'( *
<.<$/<$ K./(MN
= 402.61 m/s
b. Mean speed, 𝑢
̅
%
)($E;.9F!)
&'( *
+,
π(<.<$/<$&'()
/(/.;9>
𝐶,-. = /
= 454.30 m/s
c. RMS speed, 𝑢𝑟𝑚𝑠
𝐶!"# = 3
3(8.314𝑚𝑜𝑙𝐽 𝐾)(273.15𝐾)
𝑘𝑔
(0.02802𝑚𝑜𝑙
)
= 493.09 m/s
Physical Chemistry 1 by Engr. Elen Cris O. Manangan | 4
III.
References
The Kinetic Molecular Theory (n.d) Lumen Learning. Retrieved from
https://courses.lumenlearning.com/chemistryformajors/chapter/the-kinetic-molecular-theory/
The Kinetic Molecular Theory of Gases (2000) Patrick Fleming, LibreTexts. Retrieved from
https://chem.libretexts.org/Bookshelves/Physical_and_Theoretical_Chemistry_Textbook_Maps/Physical_Che
mistry_(Fleming)/02%3A_Gases/2.03%3A_The_Kinetic_Molecular_Theory_of_Gases#:~:text=In%201738%
2C%20Daniel%20Bernoulli%20(Bernoulli,the%20modern%20Kinetic%20Molecular%20theory.
Mean Free Path (1990) Raymond Serway, Physics for Scientists and Engineers with Modern Physics, 3rdEd,
Saunders College. Retrieved from http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/heatrf.html#serway
Distribution of Molecular Speeds (n.d.) University Physics Volume 2. Retrieved from
https://openstax.org/books/university-physics-volume-2/pages/2-4-distribution-of-molecular-speeds
Maxwell Boltzmann Distributions (n.d.) LibreTexts. Retrieved from
https://chem.libretexts.org/Bookshelves/Physical_and_Theoretical_Chemistry_Textbook_Maps/Supplemental
_Modules_(Physical_and_Theoretical_Chemistry)/Kinetics/03%3A_Rate_Laws/3.01%3A_Gas_Phase_Kineti
cs/3.1.02%3A_Maxwell-Boltzmann_Distributions
Physical Chemistry 1 by Engr. Elen Cris O. Manangan | 5