S1.5.1 and S1.5.2 Ideal gases and deviation from ideal gas behaviour

Summary

This video explores the deviation of real gases from ideal gas behavior. Ideal gases, as per kinetic molecular theory, have no volume, no intermolecular forces, and their kinetic energy is directly proportional to temperature. Real gases, however, exhibit deviations, especially at low temperatures and high pressures, due to finite volume and intermolecular forces. The video illustrates these concepts with graphs and examples, highlighting how gases like hydrogen and nitrogen show less deviation than those with stronger intermolecular forces, such as carbon dioxide and methane. It concludes with a comparison between ideal and real gases, noting that real gases follow the Van der Waals equation rather than the simple ideal gas law.

Takeaways

• 🌟 Ideal gases are hypothetical and follow the gas laws and kinetic molecular theory, with no intermolecular forces and negligible volume.
• 🌡 Real gases deviate from ideal behavior due to finite volume and intermolecular forces, especially at low temperatures and high pressures.
• 📊 At standard conditions, real gases' molar volumes are similar to the ideal gas value of 22.414 cubic decimeters per mole, indicating near-ideal behavior.
• 📉 The deviation of real gases from ideal behavior increases at low temperatures and high pressures, as shown by the graph comparing pv/rt ratios.
• ⚖️ The ideal gas law, pv = nrt, is rearranged to solve for moles, n, and is always equal to one for ideal gases, but not for real gases.
• 🔍 At moderately high pressures, real gases show deviation from ideal behavior due to intermolecular forces reducing the effective pressure.
• 🔍 At very high pressures, the deviation is due to the molecular volume becoming significant compared to the container volume, increasing the pv/rt ratio.
• 🚀 At higher temperatures, gases behave more ideally as particles have enough kinetic energy to overcome intermolecular forces.
• 🌌 Different gases show varying degrees of deviation from ideal behavior, influenced by the strength of their intermolecular forces.
• 🏷 Gases with weaker intermolecular forces, like hydrogen, show less deviation from ideal gas behavior compared to those with stronger forces, like carbon dioxide and methane.
• 🔄 Real gases are described by the van der Waals equation, which accounts for molecular volume and intermolecular forces, unlike the ideal gas law.

Q & A

What is an ideal gas according to the kinetic molecular theory?

An ideal gas is a hypothetical gas that obeys the gas laws and kinetic molecular theory, characterized by particles in constant random straight-line motion, elastic collisions, negligible volume compared to the container, no intermolecular forces, and average kinetic energy directly proportional to the absolute temperature in Kelvin.

How does a real gas differ from an ideal gas?

A real gas deviates from ideal gas behavior by having a finite, measurable volume, intermolecular forces acting between particles, and exhibiting deviations from ideal behavior especially at low temperatures and high pressures.

What is the molar volume of an ideal gas at standard temperature and pressure (STP)?

The molar volume of an ideal gas at STP is 22.414 cubic decimeters per mole.

Under what conditions do real gases behave almost ideally?

Real gases behave almost ideally under conditions of relatively high temperatures and low pressures.

What does the product of PV over RT represent in the context of ideal gases?

For an ideal gas, the product of PV over RT is always equal to one, which is derived from the ideal gas equation rearranged to solve for the amount in moles (n).

How does the deviation of real gases from ideal behavior manifest at different temperatures and pressures?

Real gases deviate the most from ideal behavior at low temperatures and high pressures. At moderately high pressures, the product PV/RT is less than one due to intermolecular forces, and at very high pressures, it is greater than one due to the effects of molecular volume.

What causes the deviation from ideal gas behavior at moderately high pressures?

At moderately high pressures, the deviation from ideal gas behavior is mainly because of the effects of intermolecular forces, which reduce the force of collisions with the container wall, resulting in a lower pressure and thus a PV/RT value less than one.

What is the reason for the deviation from ideal behavior at very high pressures?

At very high pressures, the deviation from ideal behavior is mainly because of the effects of molecular volume. As the external pressure increases, the volume occupied by the gas particles becomes significant, reducing the available volume for the gas particles and thus increasing the PV/RT value above one.

How does temperature affect the deviation of a real gas from ideal gas behavior?

At lower temperatures, the particles in a real gas have lower average kinetic energy and are less able to overcome intermolecular forces, showing greater deviation from ideal behavior. As temperature increases, real gases behave more ideally due to the particles having sufficient kinetic energy to overcome these forces.

Why do gases with stronger intermolecular forces show more deviation from ideal gas behavior at moderately high pressures?

Gases with stronger intermolecular forces, such as carbon dioxide and methane, show more deviation from ideal behavior at moderately high pressures because these forces have a more significant impact on the gas particles' motion and collision with the container walls.

What is the fundamental difference between the behavior of ideal gases and real gases in terms of intermolecular forces and volume?

Ideal gases are assumed to have no intermolecular forces and their volume is considered negligible. In contrast, real gases have intermolecular forces acting between particles and occupy a finite, measurable volume.

What equation describes the behavior of real gases, as opposed to the ideal gas law?

Real gases obey the van der Waals equation, which accounts for the effects of molecular volume and intermolecular forces, unlike the ideal gas law (PV=nRT) which assumes ideal behavior.

Outlines

00:00

🔬 Ideal Gas Behavior and Deviation

This paragraph introduces the concept of ideal and real gases. An ideal gas is a theoretical construct that perfectly follows the gas laws and kinetic molecular theory. It is characterized by particles in constant, random, straight-line motion with elastic collisions, negligible volume, and no intermolecular forces. The average kinetic energy of its particles is directly proportional to the absolute temperature in Kelvin. Real gases, however, deviate from these ideal conditions, especially at low temperatures and high pressures. The molar volumes of real gases are compared to that of an ideal gas, and it is observed that they behave almost ideally at high temperatures and low pressures but significantly deviate under conditions of high pressure and low temperature. The ideal gas equation is rearranged to solve for the amount in moles, and it is shown that for real gases, the product of PV over RT does not equal one, indicating deviation from ideal behavior.

05:02

🌡️ Effects of Temperature on Gas Deviation

The second paragraph delves into the impact of temperature on the deviation of real gases from ideal behavior. At lower temperatures, the particles of a real gas have reduced kinetic energy, making them more susceptible to intermolecular forces, which leads to greater deviation from ideal gas behavior. Conversely, at higher temperatures, such as 1000 Kelvin, particles possess sufficient kinetic energy to overcome these forces, resulting in behavior closer to that of an ideal gas. The paragraph includes a graph illustrating the deviation from ideal behavior for different gases—hydrogen, nitrogen, methane, and carbon dioxide—at various temperatures and pressures. It is noted that gases with stronger intermolecular forces, such as carbon dioxide and methane, show greater deviation from ideal behavior compared to hydrogen and nitrogen, which have weaker forces due to lower molar mass. The summary concludes by contrasting ideal and real gases, highlighting that while ideal gases obey the simple equation PV=nRT, real gases follow the more complex Van der Waals equation, which will be explored in a subsequent video.

Keywords

💡Ideal Gas

An ideal gas is a theoretical construct that perfectly adheres to the gas laws and kinetic molecular theory. It is defined by properties such as particles in constant motion, elastic collisions, negligible volume, absence of intermolecular forces, and a direct relationship between average kinetic energy and absolute temperature. The concept is central to the video's theme, illustrating the behavior of gases under ideal conditions and contrasting it with real gases. For example, the script mentions that 'an ideal gas is a hypothetical gas, that obeys the gas laws and the kinetic molecular theory'.

💡Deviation

Deviation in the context of the video refers to the departure of real gases from the behavior predicted by the ideal gas model. This concept is crucial as it highlights the limitations of the ideal gas law and the need for more complex models like the van der Waals equation to describe real gases accurately. The script explains that 'real gases deviate from ideal gas behavior' and shows how this deviation is more pronounced at low temperatures and high pressures.

💡Kinetic Molecular Theory

Kinetic molecular theory is the foundation for understanding the behavior of gases, including ideal gases. It posits that gas particles are in constant, random motion, and that collisions are elastic, among other postulates. The theory is integral to the video's narrative, providing a framework for discussing ideal gas properties and their deviations in real gases. The script states that 'the kinetic molecular theory states the following', listing the properties that define an ideal gas.

💡Molar Volume

Molar volume is the volume occupied by one mole of a substance, and it is a key parameter in the study of gases. In the video, molar volumes are used to compare the behavior of real gases with that of an ideal gas, which has a fixed molar volume of 22.414 cubic decimeters per mole at standard temperature and pressure (STP). The script uses molar volumes to demonstrate how real gases behave almost ideally under certain conditions but deviate at others.

💡Intermolecular Forces

Intermolecular forces are the forces of attraction or repulsion that act between molecules. In the context of the video, these forces are absent in ideal gases but present in real gases, affecting their behavior significantly. The script explains that 'real gases have intermolecular forces that act between the particles', and it discusses how these forces influence the deviation of real gases from ideal behavior, especially at moderately high pressures.

💡Molecular Volume

Molecular volume refers to the space occupied by the molecules of a substance. In the video, it is highlighted that real gases have a finite, measurable volume, unlike ideal gases, which are assumed to have negligible volume. The script uses the concept of molecular volume to explain why real gases deviate from ideal behavior at very high pressures, where the volume occupied by gas particles becomes significant compared to the container volume.

💡Pressure

Pressure is a key variable in the study of gases and is central to the video's exploration of gas behavior. It is discussed in relation to both ideal and real gases, with the script showing how the product of pressure and volume (PV) over temperature (RT) differs for real gases compared to the ideal gas law. The video explains that real gases deviate from ideal behavior at high pressures, particularly when intermolecular forces and molecular volume become significant factors.

💡Temperature

Temperature, measured in Kelvin, is a critical factor in the behavior of gases. The video discusses how temperature affects the kinetic energy of gas particles and their ability to overcome intermolecular forces. It is used to illustrate that real gases behave more ideally at higher temperatures and deviate more at lower temperatures. The script mentions that 'at lower temperatures the particles in a real gas have lower average kinetic energy', affecting their deviation from ideal gas behavior.

💡Van der Waals Equation

The van der Waals equation is a more accurate model for real gases than the ideal gas law, as it accounts for the finite size of gas molecules and the intermolecular forces between them. The video concludes with a mention of the van der Waals equation, indicating that it will be explored in more detail in a subsequent video. The script states that 'real gases obey the van der Waals equation', contrasting it with the ideal gas law that ideal gases obey.

💡London Dispersion Forces

London dispersion forces are a type of intermolecular force that arises from temporary dipoles in molecules, even nonpolar ones. The video uses the concept to explain why certain gases, like hydrogen, show less deviation from ideal behavior due to their low molar mass and consequently weaker London dispersion forces. The script points out that 'hydrogen... shows less deviation... because of its low molar mass, which results in weak London dispersion forces between its molecules'.

Highlights

An ideal gas is a hypothetical gas that obeys the gas laws and kinetic molecular theory.

The kinetic molecular theory states five key properties of an ideal gas, including constant random motion, elastic collisions, negligible volume, no intermolecular forces, and direct proportionality of average kinetic energy to absolute temperature.

Real gases deviate from ideal gas behavior due to finite volume and intermolecular forces.

Real gases exhibit nearly ideal behavior at high temperatures and low pressures but deviate at low temperatures and high pressures.

The molar volume of real gases is similar to that of an ideal gas under certain conditions, indicating near-ideal behavior.

The product of PV/RT for an ideal gas is always equal to one, whereas for real gases, it deviates from this value.

Deviation from ideal gas behavior in real gases is greatest at 200 Kelvin and high pressures.

At moderately high pressures, the deviation from ideal behavior is due to the effects of intermolecular forces.

Intermolecular attractions reduce the force of collisions with the container wall, leading to lower pressure and PV/RT less than one.

At very high pressures, the deviation from ideal behavior is due to the effects of molecular volume.

The volume occupied by gas particles becomes significant at very high pressures, affecting the PV/RT ratio.

As temperature increases, real gases behave more ideally due to higher average kinetic energy overcoming intermolecular forces.

Gases with stronger intermolecular forces, such as carbon dioxide and methane, show greater deviation from ideal behavior at moderately high pressures.

Hydrogen shows the least deviation from ideal behavior due to its low molar mass and weak London dispersion forces.

Gases with weak intermolecular forces show less deviation from ideal gas behavior compared to those with stronger forces.

Ideal gases are assumed to have negligible volume and no intermolecular forces, obeying the ideal gas law PV=nRT.

Real gases, on the other hand, follow the Van der Waals equation, which accounts for molecular volume and intermolecular forces.

Transcripts

this is msj chem in this video i'll be

looking at

deviation from ideal gas behavior an

ideal gas is a hypothetical gas

that obeys the gas laws and the kinetic

molecular theory

the kinetic molecular theory states the

following

particles of an ideal gas are in

constant random

straight line motion collisions between

particles of an ideal gas are elastic

which means that total kinetic energy is

conserved

the volume occupied by the particles of

an ideal gas

is negligible relative to the volume of

the container

there are no intermolecular forces

acting between particles of an ideal gas

and finally the average kinetic energy

of the particles of an ideal gas

is directly proportional to the absolute

temperature in kelvin

a real gas is a gas that deviates from

ideal gas behavior

for example real gases have a finite

measurable volume they also have

intermolecular forces that act between

the particles

real gases exhibit nearly ideal behavior

at relatively high temperatures and low

pressures

they deviate the most from ideal

behavior at low temperatures and high

pressures

in this table we have the molar volumes

for a range of real gases

as well as an ideal gas for an ideal gas

we have a value of 22.414 cubic

decimeters per mole

if we look at the molar volumes for the

real gases under these conditions

we can see that they are similar this

tells us that real gases

behave almost ideally under these

conditions

however as mentioned in the previous

slide real gases deviate from ideal

behavior

at low temperatures and high pressures

which we'll look at next

for one mole of an ideal gas the product

of pv

over rt is always equal to one

here we have the ideal gas equation

that's been rearranged

to solve for n which is amount in moles

if we substitute in the values for the

pressure and temperature at

stp we get a value of one mole

as we'll see in the next slide for real

gases the product of

pv over rt is not equal to one

in this graph on the y-axis we have the

product of pv

over rt on the x-axis we have

pressure from the graph we can see that

for an ideal gas

the product of pv over rt is equal to 1

at all pressures the three curves on the

graph

show the deviation of nitrogen from

ideal behavior

at three different temperatures the

greatest deviation from ideal behavior

occurs at 200 kelvin this tells us that

real gases

deviate the most from ideal gas behavior

under two conditions

high pressures and low temperatures

on the graph we can see that at

moderately high pressures

the product of pv over rt is less than

one

and at very high pressures the product

of pv

over rt is greater than one so as we saw

in the previous slide

at moderately high pressures the values

of pv

over rt are less than one which is

mainly because of the effects of

intermolecular forces

in this diagram we can see that at lower

external pressures

the particles are too far apart for

intermolecular forces to act

as the external pressure increases the

particles are forced

closer together on the right we can see

the effect of this increased pressure on

the intermolecular forces of a gas

intermolecular attractions between the

gas particles

reduce the force of the collisions with

the container wall

which results in a lower pressure

because the pressure of the gas becomes

less than expected

the product of pv over rt is less than

one

so to summarize at moderately high

pressures the deviation from

ideal gas behavior is mainly because of

the effects of intermolecular forces

next we look at the cause of the

deviation from ideal behavior at very

high pressures

as we saw previously at very high

pressures the values of pv

over rt are greater than one this is

mainly because of the effects of

molecular volume

from the diagram we can see that at

lower external pressures

the volume occupied by the gas particles

is negligible

compared to the volume of the container

at very high external pressures the

volume occupied by the gas particles

becomes significant

the v in pv over rt is the volume of the

container

however the volume available for the gas

particles

is less than the container volume

therefore the product of pv

over rt is greater than one so to

summarize at very high pressures the

deviation from ideal behavior

is mainly because of the effects of

molecular volume

so far in this video we've considered

the effects of intermolecular forces

and pressure on the deviation of a real

gas from ideal gas

behavior next we'll consider the

temperature

at lower temperatures the particles in a

real gas have lower average kinetic

energy

and the particles of a real gas at

higher temperatures have higher average

kinetic energy

because the particles of a gas at lower

temperatures are moving more slowly

they are less able to overcome the

effects of the intermolecular forces

at higher temperatures for example 1000

kelvin

the particles of the gas have sufficient

kinetic energy

to overcome the effects of the

intermolecular forces

so as we can see as temperature

increases real gases behave more ideally

and at lower temperatures they show the

greatest deviation from ideal gas

behavior on this graph we can see the

deviation from ideal behavior for four

different gases

they are hydrogen nitrogen methane and

carbon dioxide

from the graph we can see that each gas

differs in its deviation from ideal

behavior

at moderately high pressures we can see

that carbon dioxide and methane

show significant deviation from ideal

behavior

whereas hydrogen and nitrogen show less

deviation

previously we saw that the deviation at

moderately high pressures

was because of the effect of

intermolecular forces

both carbon dioxide and methane have

stronger intermolecular forces between

their molecules

than nitrogen and hydrogen therefore

they show the greatest deviation

at moderately high pressures the gas

that shows the least deviation

from ideal behavior is hydrogen this is

because of its low molar mass

which results in weak london dispersion

forces between its molecules

so to summarize gases with weak

intermolecular forces

will show less deviation from ideal gas

behavior

and gases with stronger intermolecular

forces will show more deviation

from ideal gas behavior we'll end the

video with a comparison of ideal gases

and real gases as we've seen ideal gases

behave

ideally at all temperatures and

pressures

real gases on the other hand deviate the

most from ideal behavior at low

temperatures

and high pressures the volume occupied

by an ideal gas

is assumed to be negligible however real

gases have a finite

measurable volume ideal gases have no

intermolecular forces acting between the

particles

real gases do have intermolecular forces

acting between their particles

and finally ideal gases obey the ideal

gas law

which is pv equals nrt

real gases obey the van der waals

equation

which we'll look at in more detail in

the next video