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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Dependence of Collision frequency on Temperature
If the formula of collision frequency (as given in Atkins) is
then it should decrease with increasing temperature if we keep the pressure same. But logically, high temperature means more speed, more ...
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Demon Kinematics: Estimating Moles converted/kWh in a (gas phase) Flow System
I have a magic demon that watches passing air and changes some of the molecules of type A to B. (It's actually a reaction, obviously, but what it specifically is probably doesn't matter for present ...
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Testing Combustion Kinetic Mechanisms
The chemical modeling of combustion depends on kinetic mechanisms, that is, intricate networks of chemical reactions that describe the transformation of reactants into products. For a mechanism of $...
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Maxwell Boltzmann Curve two peaks
In the image, the second peak appears lower and more plateau-like. What is the chemical reasoning behind this phenomenon? While I understand the relationship between temperature and peak height (with ...
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Is rate of effusion directly proportional to pressure [duplicate]
From Graham's law of effusion we know that rate of effusion is inversely proportional to square root of density of gas but if two gases are being effused at different pressures then is rate directly ...
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Bubbling air through hydrochloric acid to generate HCl gas
I am trying to build a system to generate dry HCl gas. I was wondering if you bubble air through diluted HCl will it produce a gas with mostly water vapor or HCL vapor, can we vary the proportions of ...
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When a gas is expanded, why doesn't the number of moles of a gas increase despite it's volume increasing? [closed]
This question might be elementary, but it is genuine. I realise that some users might downvote the question for being so basic, but I urge them to be a little merciful, and help out a confused high ...
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Can a heated gas leave a container through downwards direction?
If I have a flask full of heated gas, with an opening at the BOTTOM of the flask and connected pipe facing downwards, can the heated gas can leave the flask through that opening?
And for an alternate ...
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In collision theory why we multiply collision frequency by N/2?
In kinetic theory of gases we know that the average number of collisions, $N_\mathrm{col}$, is given by
$$N_\mathrm{col} = \sqrt{2\pi\sigma^2 \overline{v}_\mathrm{rel}}\ N $$
where $N$ is the number ...
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Kinetic energy change in reaction
If we consider a reaction occurring at constant pressure and temperature , we know that enthalpy represent the net heat released or absorbed by the system and internal energy accounts for both heat ...
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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 ...
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RMS Speed of Gases as Standard Deviation
In kinetic molecular theory, the average velocity of gas particle is zero since the molecule move in different directions, and the overall effect is zero. Howeever, you can calculate different speeds.
...
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Validly of the equation, du= nCv dt, for an adiabatic process [duplicate]
In an adiabatic process, there is no heat exchange, hence, $Q=0$.
The equation $\mathrm dU=nC_V\,\mathrm dT$ is valid for every type of process given the gas is ideal, where $C_V$ is heat at constant ...
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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 ...
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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 ...
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Why is the isenthalpic condition required in the Joule–Thomson effect?
I have been struggling to understand how the molecules behave during the Joule–Thomson effect. I would love to get some help on this concept. Here is what I got so far.
Under adiabatic and isenthalpic ...
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Average molecular distance between hydrogen gas [closed]
The whole question goes like this:
Calculate the de Broglie wavelength of hydrogen molecule at 300K (Take the translational energy to be 1.5kT) Compare this to the average intermolecular spacing for ...
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What is the average collision duration?
So I've been trying to figure this out: What is the average collision duration of a gas in terms of macroscopic variables?
What I have figured out. Whenever two molecules collide they must reach a ...
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What ideal gas behavior is observed by a real gas that observes Boyle's law (at Boyle's temperature)?
Boyle's temperature is a constant for a particular gas. At this temperature the real gas behaves ideally.
So, does the real gas only follow Boyle's law at this temperature, or are all the gas laws ...
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Why is real volume not smaller than ideal volume in the van der Waals gas equation correction terms? [duplicate]
The following equation is valid for ideal gases
$$pV=nRT$$
Please mind the following notation, any parameter that is related to an ideal gas would be denoted with a subscript $i$ and anything related ...
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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 ...
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Question on Thermodynamics from a recently conducted Examination
This is a question from the recently conducted JEE Main exam (in India). I had solved it myself, but found the answer to be incorrect. Here's the question.
Here is how I solved it:
$\Delta H = \pu{41....
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Isolation is a Consequence of Definition [closed]
Let's consider a ballon, such that it has an adiabatic wall, and there is no exchange of heat with the surroundings. Now, let the balloon wall be completely impermeable to the movement of matter ...
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Cubic nature of van der Waals' gas equation
$V_m^3-\dfrac{RT+bP}{P}V_m^2+\dfrac{a}{P}V_m-\dfrac{ab}{P}=0$
So, At $T<T_c$ the above equation has three real roots say $V_1,V_2,V_3$, my doubt is what does this mean physically because for some ...
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According to Maxwell-Boltzmann distribution, what is probability distribution function proportional to?
If, according to the Maxwell-Boltzmann distribution
$${f(v)}\propto\exp\left(-\frac{\varepsilon}{kT}\right),\tag{1}$$
which is the equation from which the whole final equation is derived, then why is ...
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Why is the value of $A$, in the expression for Boltzmann's distribution of speeds, not directly calculated?
I've read the proof for the expression for Boltzmann's distribution of speeds on this site. There, $f(v)$ is first factorized into $f(v_x)$, $f(v_y)$ and $f(v_z)$ and $A$ into $A_x$, $A_y$ and $A_z$. ...
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If Graham's law doesn't apply to the ammonia and hydrogen chloride diffusion in a glass tube demonstration, is there a law that does?
A comment below What exactly are "white fumes" and why does holding a bottle of ammonia (conc) next to a bottle of HCl (conc) make them? links to The
Royal Society Of Chemistry video ...
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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 $$J_{z}=-\frac{1}{2}v_{mean}\lambda(\frac{d\mathcal{N}}{...
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Relation between concentration and activation energy
Will increasing the concentration of the reactants in a chemical reaction increase the proportion of molecules with an energy greater than the activation energy $E_\mathrm{a}$?
It seems to me that the ...
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What is heat bath here?
At the beginning $\pu{1 mol}$ of air is compressed to $\pu{3 atm}$ at a of temperature $\pu{523 K}$. After a random process, the pressure of the air equates to $\pu{1 bar}$ at a temperature of $\pu{...
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Density gradient vs. entropy of mixing
I was wondering how real gases would behave when they are released into a closed container with fixed volume.
For example, suppose we use chlorine and nitrogen gas. Obviously, chlorine has a higher ...
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Degrees of freedom of a molecule of N atoms [closed]
Apparently a molecule of N atoms has 3N degrees of freedom. How?
Shouldn't it be dependent on the structure of the molecule? How exactly do we derive this?
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Is air made 100% from atoms?
I know air is made up of roughly 78% nitrogen, 20% oxygen, etc.. but I would like to know what percentage of air is just space and has no atoms at all.
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Confusion regarding continuity of state
I was reading about Andrew's isotherms and about the continuity of state.
What confused me was the continuous conversion of gaseous state to liquid state.
Now my textbook says that by keeping volume ...
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Formula for collision frequency and mean free path
We were studying collision frequency and mean free path today, and in it, we got the equations of collision frequency as:
$$Z=\sqrt 2 \pi \sigma^2v_{rms}N$$
where $N$ is the number density, equal to $...
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Is the value for the Boltzmann Constant different in 2D?
So I'm simulating some hard sphere collisions and want to determine the Boltzmann constant in two dimension, using the equation
$$PA=Nk_BT$$
where $A=\pi R^2_{container}$, $P=(averageImpulse/time)/(2\...
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Virial expansion of real gas equation and volume work
Hi I am currently working on a thermodynamics problem, and it asks me to first find the volume work done on a gas that behaves like the simplified Dieterici equation (see below) predicts on isothermal ...
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Is this a valid interpretation of the Mean relative speed between two (Maxwell-Boltzmann) species?
In textbooks, the collision frequency $Z_{ab}$ is always given as something like:
$$Z_{ab} = n_an_b\sigma_{ab} \Bigg(\frac{8 k T}{\pi \mu}\Bigg)^{1/2}= n_an_b\sigma_{ab} \bar{C}_{rel}$$
where the ...
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What exactly is a photon gas?
I came upon this question in a JEE Advanced mock test online:
The number of photons of wavelength $\lambda$ required to achieve pressure $P$ in an empty cubical box of edge length $l$ is given by $\...
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Comparing van der Waals constant for gases
How can I compare the van der Waals constant $a$ (the liquefication constant) for different compounds based on my knowledge of bonding in the compound? Let's pick the following sample set:
$$
\...
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Which formula for kinetic energy of 1 mol of a gas is universally applicable? [duplicate]
I have read 2 formulas for kinetic energy of 1 mol of gas - 3/2 RT and 1/2fRT . But if I equate them then f comes out to be 3 . But f is different of mono, di, polyatomic gases . Where am I wrong in ...
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Graham's Law of Effusion when Looking at Samples with Equal Mass?
So, I had a question on a chemistry test about two gas samples, one of O2 and one of N2, that had equal masses. We were given the time of effusion for the sample of N2 and then asked to calculate the ...
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Change in Enthalpy in Free Expansion of Ideal and Real gas against Vacuum
By free expansion, I am referring to gas allowed to expand freely against vacuum in a Joule Expansion.
If gas is ideal then change in Internal Energy '∆U' and change in Enthalpy '∆H' is zero.
(By ∆H = ...
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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 ...
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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 ...
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Why are some liquids hotter than room temperature gases if liquid and solid molecules move more slowly than gases? [closed]
We learned in school that state change is a matter of molecules moving faster and faster. And we learned "heat em up, speed em up, spread em out". Why then can some liquids have higher ...
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Under what conditions does Real Gases show Ideal Behaviour? [closed]
MY textbook says : Real gases show Ideal Behavior under low pressure ,high temperature.
So I wanted to know what happens to real gases at high pressure ,low pressure
Do they also show ideal behavior ...
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Ideal gas equation derivation proportionality [duplicate]
While deriving the Ideal gas Equation using Boyle's, Charles', and Avogadro Laws,
how are each of the laws, which have different proportionality constants and different quantities as constant combined?...
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What gas law is involved when your ears "pop" when you are on a plane high in the air? [closed]
When you are up in the air, the air pressure decreases and the altitude increases. What gas law is involved in the situation wherein your ears "pop" because of the difference in pressure.
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Adiabatic expansion of gas
If a real gas is adiabatically expanded against constant pressure, then which of the following will definitely increase?
Compressibility factor (Z) or Entropy (S)
Correct answer: Entropy
My answer: ...
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