Questions tagged [kinetic-theory-of-gases]
Questions about the assumptions, equations, and properties of gases derived from kinetic theory. For questions pertaining to rates of reactions, please use the kinetics tag instead.
123
questions
30
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3answers
4k views
Why don't gases escape Earth's atmosphere?
Some gases are lighter than others and rise. Why don't they continue going up, leave the atmosphere, and then enter outer space?
18
votes
6answers
6k views
Does the Maxwell-Boltzmann distribution apply to gases only?
The Maxwell-Boltzmann distribution can be used to determine the fraction of particles with sufficient energy to react. I know that the curve applies to gaseous reactants and would like to know whether ...
12
votes
2answers
3k views
Does gravity affect the trajectory of gas particles?
We're studying the kinetic theory of gases in school, and one of the points that was brought up was that: "Gases consist of particles in constant, random motion." How is it possible for gas particles ...
11
votes
3answers
24k views
Reason for negative Joule Thomson coefficient of Helium and Hydrogen at NTP conditions
Recently, while reading my textbook I came to know that Helium, Hydrogen and Neon are the only gases which have negative Joule Thomson coefficient at NTP conditions, i.e heating effect is observed ...
11
votes
2answers
1k views
Why does gas particle velocity affect rate of effusion?
I understand why smaller particles have more velocity, but I don't understand what velocity has to do with the rate of effusion:
My reasoning is thus:
Pressure is the number of impacts of particles ...
9
votes
1answer
28k views
Derivation of mean speed from Maxwell–Boltzmann distribution
I found that if a velocity of a gas follows the Maxwell–Boltzmann distribution, the mean velocity is given by
$$\langle v \rangle = \sqrt{\frac{8RT}{\pi M}}$$
where $R$ is the gas constant, $T$ is ...
9
votes
3answers
206 views
Comparing van der Waals constant for gases
How can I compare the van der Waals constant $a$ (the liquefication constant) for different compounds based on my knowledge of bonding in the compound? Let's pick the following sample set:
$$
\...
9
votes
5answers
967 views
Why do we need to assume that gas is made up of large number of small particles in kinetic molecular theory of gases?
Among the five postulates or assumptions of kinetic molecular theory of gases (KMT), only the assumption that a gas is made up of large number of small particles doesn't seem to make any sense to me. ...
8
votes
1answer
303 views
Uranium enrichment via effusion through a porous membrane
The following problem is from Principles of General Chemistry, Silberberg, 1st edition:
One way to utilize naturally occurring uranium ($0.72\%$ $\ce{^235U}$ and $99.27\%$ $\ce{^238U}$) as a ...
8
votes
1answer
198 views
When temperature is decreased, why do reactions occur at all?
I admit that my knowledge of collision theory may be lacking, but, as I understand it, when particles collide, a reaction will not occur without overcoming the activation energy.
That being said, as ...
7
votes
1answer
11k views
Why do we need the rms, mean, and most probable velocities?
In the kinetic theory of gases, we have rms (root mean square), mean, and mp (most probable) velocities. I understand the concept well. But my question is why do we have three different kinds of ...
7
votes
1answer
824 views
Contribution of vibrational degrees of freedom in linear triatomic molecule
The ratio $\displaystyle\frac{C_p}{C_v}$ for linear triatomic molecules including vibration contribution is given by ____.
Attempt:
We are aware that $C_v = \frac{fR}{2}$ and $C_p = C_v+ R$
Hence, $\...
6
votes
2answers
650 views
According to KMT, is the velocity of an ideal gas always sqrt(3RT/M)?
It is a common textbook question to treat the root mean square velocities of an ideal gas as given by the following equation:
$$v_\text{rms}=\sqrt{\frac{3RT}{M}}$$
I was wondering about the validity ...
6
votes
1answer
794 views
Is oxygen above the critical point always supercritical fluid? Would it still appear to roughly follow the ideal gas law?
In this answer I've asserted (without a "Chemist's license") that as long as oxygen is above it's critical point in both temperature (154.5 K) and pressure (50.4 bar) it's going to be a supercritical ...
6
votes
2answers
862 views
Is this a violation of Equipartition theorem?
My book has a question asking to calculate average kinetic energy of the molecules in 8g of methane.
By the Equipartition theorem, I calculated that energy:
1. per molecule per degree of freedom = $(...
6
votes
1answer
34k views
Calculating Compressibility factor from the Van der Waals' Gas equation
So this problem has been bugging me for a long time. According to Wikipedia the compressibility factor $Z$ is defined as the ratio of the volume occupied by a real gas divided by the volume occupied ...
6
votes
5answers
854 views
Is the average kinetic energy of evaporating water molecules (at room temperature) equivalent to the average kinetic energy of boiling water?
Purpose:
On new year's eve, after a splendid red and an assortment of sumptuous repasts, I made a bold remark which, on further consideration, may turn out to be incorrect. Unless! Unless I can ...
5
votes
3answers
3k views
Kinetic energy of molecules in liquid state?
My book (book link) has this question:
The kinetic energy of molecules at constant temperature in gaseous state is:
more than those in the liquid state
less than those in the liquid ...
5
votes
2answers
22k views
Is Internal Energy = (3/2)nRT for a ideal monoatomic gas?
Internal Energy is a state variable and its value at a particular state cannot be measured; only the change in internal energy can be measured. So how come we write that
$$U=\frac32nRT$$
where
$U$ = ...
5
votes
2answers
6k views
Latent Heat and Kinetic Energy
The kinetic theory says that temperature is the measure of the average kinetic energy. That would mean then: The temperature rises with the rise in kinetic energy. We know that when matter changes ...
5
votes
2answers
530 views
Finite probability from discrete distribution and zero probability from continuous distribution in Maxwell-Boltzmann statistics
I have difficulty understanding a certain concept with the derivation of the Maxwell-Boltzmann distribution $f(v)$ function from Boltzmann statistics. The derivation starts with the Boltzmann ...
4
votes
1answer
1k views
Why do gases need to be cooled to liquefy/solidify?
My book states:
Gases do not liquify on compression only, although molecules come close to each other and Weak forces operate at a maximum.
Why is it that we cannot just keep on compressing gas ...
4
votes
1answer
306 views
Estimation of pressure and kinetic energy density of stellar interior using kinetic theory of gases
In Physical Chemistry we are working a problem that is confusing. We started by calculating the pressure half way to the centre of the sun assuming that the interior consisted of ionized hydrogen ...
4
votes
1answer
289 views
How is the Maxwell-Boltzmann curve obtained?
Is it purely qualitative and determined by experiment?
Or is there some function which defines the familiar graph?
(Image source: Wikipedia)
4
votes
2answers
3k views
How to interpret the Maxwell-Boltzmann distribution to find the activation energy?
I understand activation energy to be the relative difference in energy between that of the activated complex/transition state (at some temperature) and the average energy of the reactants like shown ...
4
votes
1answer
90 views
Rigorous reason behind internal energy change being zero while mixing
A container is divided in two parts: one part contains oxygen gas $(n_1$ moles, at temperature $T_1)$ and the other part contains helium gas $(n_2$ moles, at temperature $T_2).$ The partition ...
3
votes
2answers
8k views
Derivation of mean kinetic energy
I read from a book that average kinetic energy is equal to $3kT/2$ where $k$ is Boltzmann's constant and $T$ is the kelvin temperature. I don't know how the formula was derived. Any help to gain ...
3
votes
3answers
740 views
Equalization of pressure in heat exchanger
I was solving numericals on Kinetic Theory of Gases when I came across this question
Two closed vessel of equal volume contain air at 105 kPa, 300 K and are connected through narrow tube. If one of ...
3
votes
1answer
87 views
Question regarding $Z$ (Compressibility factor)
Oh! This problem has been bugging me for a long time. According to Wikipedia, the Compressibility factor $Z$ is defined as the ratio of the volume occupied by a real gas to the volume occupied by an ...
3
votes
2answers
610 views
Compressibility factor (Z) of a real gas [closed]
I was wondering whether the compressibility factor of a real gas (given by $Z = V_{\mathrm{real}}/V_{\mathrm{ideal}}$) is supposed to be measured while keeping pressure constant?
I was attempting to ...
3
votes
1answer
113 views
The distance that CO2 molecules travel in the air before they collide with each other
Well the title covers most.
But further at 410 ppm, 1 atm and 23 °C.
I believe they call it the mean free path of CO2-CO2 collisions. So not just the mean free path of CO2 in air colliding with every ...
3
votes
1answer
626 views
Temperature in the Maxwell-Boltzmann Distribution
I am attempting to generate the probability for the specific speed of a molecule using the Maxwell-Boltzmann distribution, but I cannot decide on which temperature I should use in the equation.
For ...
3
votes
0answers
130 views
What exactly is a photon gas?
I came upon this question in a JEE Advanced mock test online:
The number of photons of wavelength $\lambda$ required to achieve pressure $P$ in an empty cubical box of edge length $l$ is given by $\...
3
votes
0answers
44 views
What gas would be suited best to form a density gradient in a long tube? [closed]
I want to set up an aero-optics experiment using a sealed ~5 m length of pipe with a gas inside. The gas must form a density gradient, and must be transparent enough to view a target at the other end ...
2
votes
3answers
1k views
What are the units for m in the average kinetic energy formula?
For the equation $E_k=\frac{1}{2}mu^2$ what does the $m$ variable represent?
I would say mass but the textbook does not say explicitly that it is anything.
2
votes
3answers
2k views
What is the term used as correction for attractive forces in the Van der Waals Equation?
I have seen a question in my textbook which is little bit confusing,
The term that corrects for attractive forces present in real gas in van der Waal equation is
(i) ${nb}$
(ii) $\frac{an^2}{V^2}$
(...
2
votes
2answers
2k views
The respective speed of five molecules are 2, 1.5, 1.6, 1.6 and 1.2 km/s. The most probable speed in km/s will be?
The respective speed of five molecules are 2, 1.5, 1.6, 1.6 and 1.2 km/s. The most probable speed in km/s will be?
1. 2
2. 1.58
3. 1.6
4. 1.31
I think the answer should be 1.6 km/h but the ...
2
votes
2answers
2k views
Compressibility Factor Of Gases
In the general equation of the compressibility factor $Z$, we define $Z$ as
$$Z=\frac{pV}{nRT}$$
Here, what is $p$? Is it $p_\text{real}$ or $p_\text{ideal}$?
Also, what is $V$? $V_\text{real}$ or $V_\...
2
votes
1answer
1k views
Speed distribution of lighter vs heavier gases
I cannot understand why the range of molecular speed is not always wider for a lighter gas as compared to a heavier gas .
If the same energy is supplied to both gases then wouldn't the molecular ...
2
votes
2answers
47k views
How to calculate the final temperature of a gas when it undergoes adiabatic expansion?
The question is as follows:
A sample of $\pu{4.0 moles}$ of a gas ($C_{v,m} = \pu{21 J mol-1 K-1}$) has an initial pressure of $\pu{304.4 kPa}$ and an initial volume of $\pu{20 dm3}$ at $\pu{270 K}$...
2
votes
1answer
221 views
What happens when a super-critical fluid is compressed?
Suppose that I have some substance with a critical temperature of 20°C. That means above that temperature, the substance exists neither as a gas nor a liquid, but instead as a super-critical fluid. ...
2
votes
1answer
651 views
Why is the rate inversely proportional to the square root of temperature in Grahams Law of Diffusion?
In my book it is given that:
The general form of the Grahams Law of Diffusion can be stated as follows when one or all of the parameters are varied:
$$\text{rate} \propto \frac{PA}{\sqrt{TM}},$$
...
2
votes
1answer
428 views
Identifying the gas given ratio of its specific heats
The ratio of the heat capacities $\frac{C_\mathrm p}{C_\mathrm v}$ for one mole of a gas is $1.67$. The gas is:
a) $\ce{He}$
b) $\ce{H2}$
c) $\ce{CO2}$
d) $\ce{CH4}$
I know how to answer ...
2
votes
1answer
481 views
Why do gases coexist as liquid and vapour?
I have having difficulty in understanding the liquefaction of gases.In the graph
of isotherms of $\ce{CO2}$ I cannot understand how can gas coexist as liquid and vapour under area of $\mathrm{XCEBY}$....
2
votes
1answer
6k views
What is the relation between absolute temperature, and rates of diffusion and effusion of a gas?
According to Graham's diffusion law, rate of diffusion is directly proportional to square root of temperature but rate of effusion is inversely proportional to square root of temperature.
Why is this ...
2
votes
1answer
2k views
Chemical reactions in plasma state
I am wondering about chemical reactions when the reactants are in a plasma state. Consider hydrogen and oxygen. Heated, these would react to form water.
If hydrogen and oxygen plasma were combined, ...
2
votes
1answer
814 views
What is the mole fraction of dihydrogen in a mixture, given the relative rates of effusion of its components?
A mixture of $\ce{H2}$ and $\ce{He}$ at $\pu{300 K}$ effuses from a small hole in a gas chamber. What is the mole fraction of $\ce{H_2}$ in the original mixture, if $3.0$ times as many $\ce{He}$ atoms ...
2
votes
2answers
465 views
How to get the first step of the derivation of the Maxwell-Boltzmann distribution
To derive the Maxwell-Boltzmann distribution the first step requires the knowledge that the equation will take the form $$f(v)=Ke^{-\epsilon/ kT}$$ where $\epsilon$ is the sum of the kinetic energies ...
2
votes
1answer
2k views
Ideal gas law derivation from kinetic theory
Consider the derivation of the ideal gas law from kinetic theory presented here: http://en.wikipedia.org/wiki/Kinetic_theory
I have some questions
This derivation assumes the container is a cube, ...
2
votes
1answer
52 views
Shape of the container and the number of possible energy states
A question came up when studying the formula for calculating the total number of possible energy states of a particle within a container.
Why is the number of possible energy states independent of ...