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.

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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?
S. GOLIZADEH's user avatar
18 votes
6 answers
8k 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 ...
Jaywalker's user avatar
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14 votes
2 answers
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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 ...
SirXYZ's user avatar
  • 365
13 votes
2 answers
5k 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 ...
Andi Gu's user avatar
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11 votes
1 answer
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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 ...
Daniel B.'s user avatar
  • 263
9 votes
1 answer
33k 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 ...
Stan Shunpike's user avatar
9 votes
3 answers
1k 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: $$ \...
Swadhin's user avatar
  • 307
9 votes
5 answers
1k 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. ...
Parth Patel's user avatar
8 votes
3 answers
4k 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 ...
Gaurang Tandon's user avatar
8 votes
1 answer
700 views

Confusion in Van der Waals Equation

I understand that the behavior of ideal gases deviates largely from that of real gases in terms of pressure exerted by the gas molecules on the container in which it is present, space available for ...
anotherhyooman's user avatar
8 votes
1 answer
346 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 ...
abjske's user avatar
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8 votes
5 answers
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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 ...
Jeff's user avatar
  • 83
8 votes
1 answer
1k 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, $\...
Archer's user avatar
  • 5,433
7 votes
2 answers
39k 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 ...
Serotonin's user avatar
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7 votes
1 answer
12k 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 ...
Hijaz Aslam's user avatar
7 votes
1 answer
234 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 ...
nmagerko's user avatar
  • 203
6 votes
2 answers
780 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 ...
Cyclopropane's user avatar
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6 votes
1 answer
1k 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 ...
uhoh's user avatar
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6 votes
2 answers
1k 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 = $(...
Gaurang Tandon's user avatar
6 votes
1 answer
200 views

Non-Arrhenius temperature dependence of bimolecular reaction rates at very high temperatures

Once I have read that in some cases bimolecular reactions can exhibit a maximum as a function of temperature due to the short lifetime of the activated complex at very high temperatures. At low ...
YoussefMabrouk's user avatar
6 votes
2 answers
7k 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 ...
user29898's user avatar
  • 111
5 votes
2 answers
36k views

Is internal energy equal to (3/2)nRT for an ideal monoatomic gas?

I came across a Khan Academy video providing the following relation for the internal energy of the system $U$: $$U=\frac32nRT,\label{eqn:1}\tag{1}$$ where $n$ is the amount of gas, $R$ is the ...
Rajdeep Dutta's user avatar
5 votes
2 answers
766 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 ...
Phy's user avatar
  • 637
4 votes
1 answer
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 ...
Shivay Vadhera's user avatar
4 votes
1 answer
1k 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: $$\text{rate} \propto \frac{PA}{\sqrt{TM}},$$ ...
user avatar
4 votes
1 answer
352 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 ...
hedenton's user avatar
4 votes
1 answer
327 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)
MrObjectOriented's user avatar
4 votes
2 answers
4k 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 ...
Yandle's user avatar
  • 901
4 votes
1 answer
210 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 ...
satan 29's user avatar
  • 379
4 votes
0 answers
71 views

Why does the factor of ⅔ come in when we calculate net flux due to diffusion for an ideal gas

As per Atkins' Physical Chemistry (11E) Pg:694. We arrive at a crude estimate for the net flux through an imaginary flux plane. We find it to be $$J_{z}=-\frac{1}{2}v_{mean}\lambda(\frac{d\mathcal{N}}{...
Uranium238's user avatar
3 votes
2 answers
2k views

Is air made 100% from atoms?

I know air is made up of roughly 78% nitrogen, 20% oxygen, etc.. but I would like to know what percentage of air is just space and has no atoms at all.
jon's user avatar
  • 163
3 votes
2 answers
9k 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 ...
LM2357's user avatar
  • 333
3 votes
2 answers
60k 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 $\pu{270 K}$...
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3 votes
3 answers
863 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 ...
user avatar
3 votes
1 answer
251 views

How was it possible to accurately measure the mass of gases in the 19th century?

I have seen periodic tables of Mendeleev (1834-1907) and Newland (1837-1898) in which masses of gases such as oxygen and nitrogen were shown. I don't think there were instruments to measure mass of ...
pranjal verma's user avatar
3 votes
2 answers
11k 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 ...
asquare's user avatar
  • 107
3 votes
1 answer
192 views

Is it Rigorous to Derive the Arrhenius Exponential Term from the Boltzmann Distribution?

The Boltzmann distribution is a probability density function which expresses the probability of finding a particle in an energy state $\epsilon$ while in thermal equilibrium given a specific ...
ScientiaNatura's user avatar
3 votes
1 answer
88 views

Can someone walk me through this gas mixture question?

Argon $(\ce{Ar})$ and helium $(\ce{He})$ are initially in separate compartments of a container at $\pu{25 °C}.$ The $\ce{Ar}$ in compartment A which has a volume $V_\ce{A}$ of $\pu{9.00 L}$ and a ...
NoCo's user avatar
  • 33
3 votes
1 answer
174 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 ...
Indrasen ghosh's user avatar
3 votes
2 answers
762 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 ...
Andrea Pettenello's user avatar
3 votes
1 answer
237 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 ...
TommyWhite's user avatar
3 votes
1 answer
796 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 ...
nmagerko's user avatar
  • 203
3 votes
0 answers
99 views

Probability distribution for the momentum of a particle undergoing a collision?

Background I haven't seen this mauver done before but let's say, I have a thermal gas and I have a molecule with momentum $\vec p$. It undergoes a collision and now has momentum $\vec P$. Now, due to ...
More Anonymous's user avatar
3 votes
0 answers
692 views

Formula for collision frequency and mean free path

We were studying collision frequency and mean free path today, and in it, we got the equations of collision frequency as: $$Z=\sqrt 2 \pi \sigma^2v_{rms}N$$ where $N$ is the number density, equal to $...
stonecraft bros's user avatar
3 votes
0 answers
194 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 $\...
Tatai's user avatar
  • 317
3 votes
0 answers
55 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 ...
Brosama bin Spartan's user avatar
3 votes
3 answers
1k views

Why is the speed of ideal gases mass dependent while the kinetic energy is not?

The rms speed of an ideal gas is $v_{\text{rms}}$ = $\sqrt{\frac{3RT}{M} }$ and the kinetic energy is $E_\text{k} = \frac32RT$. From this, it is concluded that the speed is mass dependent, while the ...
ILoveIL's user avatar
  • 39
2 votes
3 answers
2k 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.
Amuna's user avatar
  • 1,193
2 votes
3 answers
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) $\frac{an^2}{V^2}$ (...
pranjal verma's user avatar
2 votes
2 answers
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 ...
Khushvind Maurya's user avatar