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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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How to derive the compressibility factor for a van der Waals gas?

So as far as I know, $$Z=\frac{p_\mathrm{r}V_\mathrm{r}}{nRT},$$ where $\mathrm{r}$ denotes the subscript for real. Solving it for a van der Waals gas gave me the following result, $$Z=1+\frac{p_\...
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2answers
62 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_\...
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1answer
120 views

How to calculate the average quadratic velocity of carbon dioxide from given data?

I am working on this question, and I am unsure of how to proceed. The question is: There is $31.7~\mathrm{g}$ of $\ce{CO2 (g)}$ in a container. The partial pressure of $\ce{CO2}$ is $2.62~\mathrm{...
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2answers
116 views

Volume of gas in containers

If gases occupy all the volume in a container then how can we define 'volume percent' as all different gases will have same volume?
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2answers
58 views

What happens to the pressure of gas when only one molecule of it is placed in a very large container?

We say that pressure due to gas is constant throughout the container. Pressure is created by molecules present in it. When there are many molecules I agree that they can apply the same pressure all ...
3
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1answer
43 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 ...
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1answer
48 views

Why 1 mole of H2 occupied the same volume occupied by 1 mole of O2?

I'm asking a question about the volume occupied by gasses in standard temperature and pressure. My textbook said that a mole of any gas occupies 22.4 L at standard temperature and pressure. But ...
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0answers
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Finding Pressure of M in a Charge Exchange

Ar (RE = 15.5 eV) is the reagent gas in a charge exchange experiment. If Ar+ reacts with anisole with a rate constant of 2.26x10-10cm3 molecules-1/s-1 and 65% of the Ar ions react in 25 milliseconds, ...
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2answers
114 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 ...
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2answers
93 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 ...
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1answer
286 views

How can one rationalize Avogadro's hypothesis using the equation of kinetic molecular theory?

How can one rationalize Avogadro's hypothesis using the equation of kinetic molecular theory? $$pV = \frac{1}{3} \cdot N \cdot m\overline{u^2} = \frac{2}{3} \cdot N \cdot \frac{1}{2}m\overline{u^2}$$ ...
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1answer
71 views

What is the radius of the atoms? [closed]

In a recipient there is an unknown monoatomic gas that occupies a volume of $\pu{230 cm3}$, at $\pu{300 K}$ and $\pu{1 atm}$. It is known that the atoms occupy a volume of $2\times10^{-4}$. Find the ...
2
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1answer
45 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 ...
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6answers
3k 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 ...
2
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0answers
43 views

Feasibility of application of Boyle's law in the case of varying number of moles [closed]

While reading up on ideal gases and the Boyle's law, I encountered a question in my textbook wherein a balloon was being filled with helium (assumed to be ideal) till it was just about to burst. The ...
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0answers
52 views

Comparing pressure and volumes of ideal and real gas

This question has been troubling me for quite a while now. Which has greater pressure: Real gas or an ideal gas under similar conditions? What about their volumes? I read this in many sources and ...
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1answer
43 views

Why are moles used in the ideal gas law and not simply mass?

The crux of my question is, why is just the amount of particles included in $PV=nRT$ and there is nothing to account for the mass of the individual molecules? Or is mass accounted for in temperature, ...
3
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3answers
583 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 ...
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0answers
59 views

How does degree of freedom work [closed]

I understand that the degree of freedom is the number of ways in which a molecule can acquire energy. I don't want you to explain the definition, but I want to see how it works. Please explain how is ...
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1answer
78 views

Does the translational part of internal energy mean the kinetic energy of the gas?

Internal energy of an ideal gas consists of energy due to translational, rotational , vibrational etc. This line from WP says: In thermodynamics, the internal energy of a system is the energy ...
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1answer
119 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 $\mathrm{XCEBY}$....
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1answer
113 views

Interpreting straight lines in a graph of isotherms of carbon dioxide

I am having difficulty in understanding pressure-volume graphs of $\ce{CO2}$ at different temperatures which describes liquefaction of $\ce{CO2}$. I know that at the critical temperature of $\pu{31.1^...
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3answers
314 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}...
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1answer
217 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 ...
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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 rate of effusion: My reasoning is thus: Pressure is the number of impacts of particles in a ...
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1answer
76 views

Dependency of rate of diffusion on mean free path and velocity of molecules? [duplicate]

What is the dependency of rate of diffusion ( Graham's law) on mean free path, molecular size , average velocity, collision frequency and pressure? I have searched everywhere on internet but just ...
2
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0answers
44 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 ...
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2answers
165 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 ...
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1answer
69 views

Is there a better model than the Kinetic Theory of Gases [closed]

I'm looking for a better relationship between the Kinetic energy of a gas and it's Temperature, and also how they vary with gravity (not altitude, just gravity!). So is there a model better than the ...
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1answer
148 views

van der Waals equation for deviation of gases from ideal behavior

$(P + an^2/V^2)(V - nb) = nRT$ I understand that the term $nb$ is subtracted from the volume term as the available volume for the gas molecules to move around decreases in the case of a real gas ...
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1answer
63 views

Does the probability function for a molecule to have energy in a certain mode depend on the minimum required quantum energy level of that mode?

I understand that the probability density for a particular velocity v+dv in one dimension for a molecule in a system is: $$f(v) = \sqrt{\frac{m}{2\pi k_B T}} \cdot e^{\frac{-mv^2}{2k_B T}}$$ I'm ...
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0answers
80 views

Effusion rate 1.4 times faster SO2(g)

How do I solve this- Which diatomic gas would effuse at a rate that is 1.4 times faster than the rate at which so2(g) effuses at any given temperature? This is high school chemistry. I did: (using ...
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1answer
790 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 ...
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1answer
783 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 ...
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1answer
174 views

Effect on rate of diffusion in addition of an inert gas

What will be the effect on the rate of diffusion on addition of an inert gas to the gaseous mixture? I think the rate of diffusion should increase as the addition of extra gas will increase the ...
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0answers
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Is the kinetic gas equation valid for non-cubical containers?

I have seen the derivation of the following equation for a cubical container with $N$ molecules. $$PV = \frac 13 mNu^2 $$ How is this equation valid even for spherical container or any other non ...
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1answer
400 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 ...
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2answers
1k 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 ...
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2answers
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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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1answer
50 views

How to determine if pressure surpasses capacity with the van der Waals equation of state?

I have to decide whether a $\pu{20 L}$ container with $\pu{0.8 kg}$ ethane can withstand the pressure at $\pu{373.15 K}$. The following information is given: \begin{align} b &= \pu{6.448x10^-2 ...
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1answer
5k 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 $U$ = ...
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1answer
7k 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 ...
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1answer
41 views

Volume of gas in a system [closed]

With two closed vessels of equal volume that are connected to each other through a narrow tube, the temperature of one of the containers is increased. Why does the final volume of gas inside each ...
2
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1answer
345 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 ...
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0answers
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An elementary question worth asking [closed]

We all know that an atom starts moving faster when it's heated.But actually atom is not some new thing itself in the sense that it is just a bunch of electrons and protons. So, I think that same ...
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3answers
929 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.
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1answer
536 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 ...
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1answer
169 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 ...
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1answer
656 views

Maximum in Maxwell–Boltzmann distribution [closed]

I need to find the maximum of the Maxwell–Boltzmann distribution $$P(v) = \left(\frac{m}{2\pi kT}\right)^{3/2}4\pi v^2 \exp{\left(-\frac{mv^2}{2kT}\right)}$$ I know that occurs when $\mathrm dP(v)/\...
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3answers
3k 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?