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.
144
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Calculating the mean free path using the mean square displacement [closed]
I want to obtain the mean free path of a gas by using the mean square displacement, which I have calculated with the formula $$MSD= 2 \cdot D \cdot t$$ where $D$ is the diffusion coefficient of the ...
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1
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184
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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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Does KE(avg) stay the same for ideal gas if the PV value changes?
We know that Kinetic Energy is a function of Temperature for an ideal gas.
So KE (1 Mole of gas) = (3/2)RT = (3/2)PV.
So it's said that even if P or V change their change will counteract the other (...
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2
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171
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Why do we subtract the volume correction term in the van der Waals gas equation [duplicate]
The following equation is valid for ideal gasses
$$pV=nRT$$
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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1
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472
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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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1
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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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1
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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 ...
0
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1
answer
310
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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 ...
1
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1
answer
126
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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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1
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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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1
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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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1
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567
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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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2
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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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138
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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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3
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0
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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$$
where $N$ is the number density, equal to $...
0
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0
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Is the value for the Boltzmann Constant different in 2D?
So I'm simulating some hard sphere collisions and want to determine the Boltzmann constant in two dimension, using the equation
$$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}$$
where the ...
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0
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158
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What exactly is a photon gas?
I came upon this question in a JEE Advanced mock test online:
The number of photons of wavelength $\lambda$ required to achieve pressure $P$ in an empty cubical box of edge length $l$ is given by $\...
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3
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Comparing van der Waals constant for gases
How can I compare the van der Waals constant $a$ (the liquefication constant) for different compounds based on my knowledge of bonding in the compound? Let's pick the following sample set:
$$
\...
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0
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55
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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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2
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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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1
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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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2
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356
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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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2
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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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1
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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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1
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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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1
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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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1
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105
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Maxwell's distribution function for mixture of ideal gases
I came across a question demanding relations between the individual distribution functions $f_n$ for the $n$th gas, and the overall $f$ for the entire mixture.
I believe there is no simple way to ...
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1
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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 ...
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2
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Crossing at critical temperature of a gas
This is written in the book 'Treatise on Thermodynamics' by Max Plank-
the crossing of the critical temperature at any pressure other than the critical pressure differs in no way from the crossing of ...
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Calculating force and pressure of an ideal gas on a wall [duplicate]
The text below is from a discussion on ideal gases and the kinetic theory of gases:
After the collision the molecule must travel a distance $l$ to the
opposite wall, and then back across this same ...
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1
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Relative humidity at constant temperatures [closed]
It’s known that Relative humidity = (water pressure in a certain volume/ saturated water pressure in the same volume)* 100% “at the same temperature”
So my question is why does the amount of water ...
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Energy and impurities balance for adsorption with a fixed bed (with description)?
Do you have any suggestion where to look for a source of information about energy and impurities (component) balance for adsorption of mixture CO2/H2O in fixed bed?
I have looked into many articles /...
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Vapor Pressure and Boiling Point [duplicate]
I heard that the boiling point of a solution is the temperature where its vapor pressure at that temperature equals the atmospheric pressure at that temperature. Thus at higher altitudes, as the ...
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1
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If the gaseous molecules didn't have any kinetic energy would the surface of a filled balloon still be firm? [closed]
The most of the ideal gas law equation is based on the fact that the gaseous molecules are moving around and cause collisions and thus have some pressure. If these molecules were to not have any ...
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1
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423
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What is the relative rate of diffusion of ammonia to hydrogen chloride, both in gaseous states? [closed]
I encountered this problem during an assignment:
I answered it as C, but the assignment grader marked it as wrong and indicated that A is correct.
I asked another instructor about it and gave me a ...
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2
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The amount of heat energy required to raise the temperature of 1g of helium at NTP from T1 K to T2 K is?
The amount of heat energy required to raise the temperature of 1g of helium at NTP from $T_1 \pu{K}$ to $T_2 \pu{K}$ is?
My confusion is, that as the gas is at NTP, therefore, it is an isochoric ...
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2
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71
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Will NH3 gas decompose into N2 and H2 at 250 degrees celcius? [duplicate]
If I heat ammonia gas to 250 degrees celsius, will it decompose into its basic components - N2 and H2? What temperature is required for the reaction to occur?
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1
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106
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Is it possible to determine the composition of a gas mixture from the effusion of a gas through a pinhole?
Typically all the problems which I've seen regarding rate of diffusion involve relating the rate of one gas to the other and from there finding either speed of effusion or diffusion or getting the ...
3
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2
answers
692
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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 ...
0
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1
answer
2k
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Effect of pressure on viscosity of liquids and gases [closed]
My textbook says the following on viscosity and pressure:
increase in pressure decreases the viscosity of water but for other liquids it increases. Viscosity of gases does not change much
No ...
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