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Description

Pump gas molecules to a box and see what happens as you change the volume, add or remove heat, and more. Measure the temperature and pressure, and discover how the properties of the gas vary in relation to each other. Examine kinetic energy and speed histograms for light and heavy particles. Explore diffusion and determine how concentration, temperature, mass, and radius affect the rate of diffusion.

Sample Learning Goals

Determine how changing a variable among P, V, N, and T influences other gas properties.

Describe the relationship between particle-wall collisions and pressure.

Predict how changing temperature will affect the speed of molecules.

Predict the speed of molecules in thermal equilibrium based on the relative masses of molecules.

Identify when pressure-volume work is done on or by a gas.

Explain how two gases mix.

Design an experiment to find the factors which affect the rate of diffusion.

Overview of sim controls, model simplifications, and insights into student thinking ( PDF ).

Teacher-Submitted Activities

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Pump gas molecules to a box and see what happens as you change the volume, add or remove heat, and more. Measure the temperature and pressure, and discover how the properties of the gas vary in relation to each other. Examine kinetic energy and speed histograms for light and heavy particles.

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Copyright © 2019 BBC

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A balloon is blown up at night when the temperature is to a volume . Next afternoon, the temperature is .

If there is no change in air pressure, what is the new volume of the gas?

First convert the temperatures into kelvin.

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BBC Bitesize - National 5 Physics - Gas laws and the kinetic model - Revision 6

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A balloon is blown up at night when the temperature is to a volume . Next afternoon, the temperature is . If there is no change in air pressure, what is the new volume of the gas? First convert the temperatures into kelvin.

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Author: Florida State University
Copyright, Florida State University, 2019

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Gas Laws

The content that follows is the substance of lecture 18. In this lecture we cover the Gas Laws: Charles',Boyle's,Avagadro's and Gay Lussacs as well as the Ideal and Combined Gas Laws.

Laws of Gas Properties

There are 4 general laws that relate the 4 basic characteristic properties of gases to each other. Each law is titled by its discoverer. While it is important to understand the relationships covered by each law, knowing the originator is not as important and will be rendered redundant once the combined gas law is introduced. So concentrate on understanding the relationships rather than memorizing the names.

Charles' Law- gives the relationship between volume and temperature if pressure and amount of gas are held constant.

1) If the volume of a container is increased, the temperature increases.
2) If the volume of a container is decreased, the temperature decreases.

This means that the volume of a gas is directly proportional to its temperature.

Calculations using Charles' Law involve the change in either temperature (T ₂) or volume (V ₂) from a known starting amount of each (V ₁ and T ₁):

Boyle's Law - states that the volume of a given amount of gas held at constant temperature varies inversely with the applied pressure when the temperature and mass are constant.

The reduction in the volume of the gas means that the molecules are striking the walls more often increasing the pressure, and conversely if the volume increases the distance the molecules must travel to strike the walls increases and they hit the walls less often thus decreasing the pressure.

Like Charles' Law, Boyle's Law can be used to determine the current pressure or volume of a gas so long as the initial states and one of the changes is known:

Avagadro's Law- Gives the relationship between volume and amount of gas in moles when pressure and temperature are held constant.

If the amount of gas in a container is increased, the volume increases. If the amount of gas in a container is decreased, the volume decreases. This is assuming of course that the container has expandible walls.

The relationship is again directly proportional so the equation for calculations is

Gay Lussac's Law - states that the pressure of a given amount of gas held at constant volume is directly proportional to the Kelvin temperature.

If you heat a gas you give the molecules more energy so they move faster. This means more impacts on the walls of the container and an increase in the pressure. Conversely if you cool the molecules down they will slow and the pressure will be decreased.

To calculate a change in pressure or temperature using Gay Lussac's Law the equation looks like this:

To play around a bit with the relationships, try this simulation.

The Ideal Gas Law:

A combination of the laws presented above generates the Ideal Gas Law:

The addition of a proportionality constant called the Ideal or Universal Gas Constant (R) completes the equation.

As you can see there are a multitude of units possible for the constant. The only constant about the constant is that the temperature scale in all is KELVIN.

When using the Ideal Gas Law to calculate any property of a gas, you must match the units to the gas constant you choose to use and you always must place your temperature into Kelvin.

To use the equation, you simply need to be able to identify what is missing from the question and rearrange the equation to solve for it.

A typical question would be given as 6.2 liters of an ideal gas are contained at 3.0 atm and 37 °C. How many of this moles of the gas are present?

Because the units of the gas constant are given using atmospheres, moles, and Kelvin, it's important to make sure you convert values given in other temperature or pressure scales. For this problem, convert °C temperature to K using the equation:

T = °C + 273

T = 37 °C + 273
T = 310 K

Now, you can plug in the values. Solve for the number of moles

n = PV / RT

n = ( 3.0 atm x 6.2 L ) / ( 0.08206 L atm /mol K x 310 K)
n = 0.75 mol

Here are some practice problems using the Ideal Gas Law: Practice

The Combined Gas Law

I said above that memorizing all of the equations for each of the individual gas laws would become irrelevant after the introduction of the laws that followed. The law I was referring to is the Combined Gas Law:

The combined gas law allows you to derive any of the relationships needed by combining all of the changeable peices in the ideal gas law: namely pressure, temperature and volume. R and the number of moles do not appear in the equation as they are generally constant and therefore cancel since they appear in equal amounts on both sides of the equation.

As you can see above, the equation can be solved for any of the parameters in it. But more importantly, you can eliminate from the equation anything that will remain constant.

For Example, If a question said that a system at 1atm and a volume of 2 liters, underwent a change to 3.5 liters, calculate the new pressure, you could simply eliminate temperature from the equation and yield:
P₂ = P₁V₁/V₂ = (1atm)(2L)/3.5L) = 0.6 atm
Since the question never mentions a temperature we can assume it remains a constant and will therefore cancel in the calculation. You should also think about the answer you get in terms of what you know about the gases and how they act. We increased the volume so the pressure should go down. Checking our answer, this appears to be correct since the pressure went from 1atm to 0.6atm.

So the only equation you really need to know is the combined gas law in order to calculate changes in a gas' properties.

Here are some practice problems with solutions: Practice

Here are some problems for the other gas laws that you can derive from the combined gas law: Practice and KEY

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The content that follows is the substance of lecture 18. In this lecture we cover the Gas Laws: Charles',Boyle's,Avagadro's and Gay Lussacs as well as the Ideal and Combined Gas Laws. There are 4 general laws that relate the 4 basic characteristic properties of gases to each other.

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Author: Tyler DeWitt
Copyright © Tyler DeWitt 2011

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Author: Purdue University
Copyright © Purdue University 2004

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On 5 June 1783, Joseph and Etienne Montgolfier used a fire to inflate a spherical balloon about 30 feet in diameter that traveled about a mile and one-half before it came back to earth. News of this remarkable achievement spread throughout France, and Jacques-Alexandre-Cesar Charles immediately tried to duplicate this performance.

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Author: Jessie A Key
Public Domain

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Learning Objectives

1. Review other simple gas laws.

2. Learn and apply the combined gas law.

You may notice in Boyle's law and Charles's law that we actually refer to four physical properties of a gas: pressure ( P), volume ( V), temperature ( T), and amount (in moles, n). We do this because these are the only four independent physical properties of a gas. There are other physical properties, but they are all related to one (or more) of these four properties.

Boyle's law is written in terms of two of these properties, with the other two being held constant. Charles's law is written in terms of two different properties, with the other two being held constant. It may not be surprising to learn that there are other gas laws that relate other pairs of properties-as long as the other two are held constant. Here we will mention a few.

Gay-Lussac's law relates pressure with absolute temperature. In terms of two sets of data, Gay-Lussac's law is

Note that it has a structure very similar to that of Charles's law, only with different variables-pressure instead of volume. Avogadro's law introduces the last variable for amount. The original statement of Avogadro's law states that equal volumes of different gases at the same temperature and pressure contain the same number of particles of gas. Because the number of particles is related to the number of moles (1 mol = 6.022 × 10 ²³ particles), Avogadro's law essentially states that equal volumes of different gases at the same temperature and pressure contain the same amount (moles, particles) of gas. Put mathematically into a gas law, Avogadro's law is

(First announced in 1811, it was Avogadro's proposal that volume is related to the number of particles that eventually led to naming the number of things in a mole as Avogadro's number.) Avogadro's law is useful because for the first time we are seeing amount, in terms of the number of moles, as a variable in a gas law.

Example 7

A 2.45 L volume of gas contains 4.5 × 10 ²¹ gas particles. How many gas particles are there in 3.87 L if the gas is at constant pressure and temperature?

Solution

We can set up Avogadro's law as follows:

We algebraically rearrange to solve for n ₂:

The L units cancel, so we solve for n ₂:

n ₂ = 7.1 × 10 ²¹ particles
Test Yourself
A 12.8 L volume of gas contains 3.00 × 10 ²⁰ gas particles. At constant temperature and pressure, what volume do 8.22 × 10 ¹⁸ gas particles fill?
Answer
0.351 L

The variable n in Avogadro's law can also stand for the number of moles of gas in addition to the number of particles.

One thing we notice about all the gas laws is that, collectively, volume and pressure are always in the numerator, and temperature is always in the denominator. This suggests that we can propose a gas law that combines pressure, volume, and temperature. This gas law is known as the combined gas law , and its mathematical form is

This allows us to follow changes in all three major properties of a gas. Again, the usual warnings apply about how to solve for an unknown algebraically (isolate it on one side of the equation in the numerator), units (they must be the same for the two similar variables of each type), and units of temperature (must be in kelvins).

Example 8

A sample of gas at an initial volume of 8.33 L, an initial pressure of 1.82 atm, and an initial temperature of 286 K simultaneously changes its temperature to 355 K and its volume to 5.72 L. What is the final pressure of the gas?

Solution

We can use the combined gas law directly; all the units are consistent with each other, and the temperatures are given in Kelvin. Substituting,

We rearrange this to isolate the P ₂ variable all by itself. When we do so, certain units cancel:

Multiplying and dividing all the numbers, we get

P ₂ = 3.29 atm

Ultimately, the pressure increased, which would have been difficult to predict because two properties of the gas were changing.
Test Yourself
If P ₁ = 662 torr, V ₁ = 46.7 mL, T ₁ = 266 K, P ₂ = 409 torr, and T ₂ = 371 K, what is V ₂?
Answer
105 mL

As with other gas laws, if you need to determine the value of a variable in the denominator of the combined gas law, you can either cross-multiply all the terms or just take the reciprocal of the combined gas law. Remember, the variable you are solving for must be in the numerator and all by itself on one side of the equation.

Key Takeaways

There are other gas laws that relate any two physical properties of a gas.

The combined gas law relates pressure, volume, and temperature of a gas.

Exercises

1. Use Gay-Lussac's law to determine the final pressure of a gas whose initial pressure is 602 torr, initial temperature is 356 K, and final temperature is 277 K. Assume volume and amount are held constant.

2. Use Gay-Lussac's law to determine the final temperature of a gas whose initial pressure is 1.88 atm, initial temperature is 76.3 K, and final pressure is 6.29 atm. Assume volume and amount are held constant.

3. If 3.45 × 10 ²² atoms of Ar have a volume of 1.55 L at a certain temperature and pressure, what volume do 6.00 × 10 ²³ atoms of Ar have at the same temperature and pressure?

4. If 5.55 × 10 ²² atoms of He occupy a volume of 2.06 L at 0°C at 1.00 atm pressure, what volume do 2.08 × 10 ²³ atoms of He occupy under the same conditions?

5. Use Avogadro's law to determine the final volume of a gas whose initial volume is 6.72 L, initial amount is 3.88 mol, and final amount is 6.10 mol. Assume pressure and temperature are held constant.

6. Use Avogadro's law to determine the final amount of a gas whose initial volume is 885 mL, initial amount is 0.552 mol, and final volume is 1,477 mL. Assume pressure and temperature are held constant.

7. Use the combined gas law to complete this table. Assume that the amount remains constant in all cases.

V ₁ =

P ₁ =

T ₁ =

V ₂ =

P ₂ =

T ₂ =

8. Use the combined gas law to complete this table. Assume that the amount remains constant in all cases.

V ₁ =

P ₁ =

T ₁ =

V ₂ =

P ₂ =

T ₂ =

9. A gas starts at the conditions 78.9 mL, 3.008 atm, and 56°C. Its conditions change to 35.6 mL and 2.55 atm. What is its final temperature?

10. The initial conditions of a sample of gas are 319 K, 3.087 L, and 591 torr. What is its final pressure if volume is changed to 2.222 L and temperature is changed to 299 K?

11. A gas starts with initial pressure of 7.11 atm, initial temperature of 66°C, and initial volume of 90.7 mL. If its conditions change to 33°C and 14.33 atm, what is its final volume?

12. A sample of gas doubles its pressure and doubles its absolute temperature. By what amount does the volume change?

Answers 1.
The pressure of a gas is proportional to its absolute temperature.
3.
468 torr
5.
27.0 L
7.
10.6 L
9.

V ₁ =

P ₁ =

T ₁ =

V ₂ =

P ₂ =

T ₂ =

56.9 mL

334 torr

266 K

33.1 mL

722 torr

334 K

0.976 L

2.33 atm

443 K

1.223 L

1.49 atm

355 K

3.66 L

889 torr

23°C

2.19 L

739 torr

147 K, or −126°C

11.
126 K, or −147°C
13.
40.6 mL

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Introductory Chemistry- 1st Canadian Edition

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Review other simple gas laws. Learn and apply the combined gas law. You may notice in Boyle's law and Charles's law that we actually refer to four physical properties of a gas: pressure ( P), volume ( V), temperature ( T), and amount (in moles, n).

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The Ideal Gas Law: Crash Course Chemistry #12

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The Ideal Gas Law: Crash Course Chemistry #12

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Author: Crash Course

Copyright © 2013 CrashCourse

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The Ideal Gas Law: Crash Course Chemistry #12

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Author: Tom Benson
Public Domain

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Beginner's Guide to Propulsion: Boyle's Law - Activity

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After reading the Web page Boyle's Law and using the Animated Gas Lab, complete the activity to answer questions using Boyle's Law.

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Author: LibreTexts
CC BY-NC-SA 3

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Page ID

14511

1. Empirical Derivation

2. Microscopic version

3. Isotherms
Calculation of Work

4. Constant Pressure

1. Isobaric Process

2. Monatomic Gas

3. Specific Heat

5. Problem Solving
Example

6. Avogador's Number

1. Role in Science

2. Measuring NA

7. Absolute Temperature
The Kelvin scale

8. Key Points

9. Key Terms

The ideal gas law is the equation of state of a hypothetical ideal gas (an illustration is offered in ). In an ideal gas, there is no molecule-molecule interaction, and only elastic collisions are allowed. It is a good approximation to the behavior of many gases under many conditions, although it has several limitations. It was first stated by Émile Clapeyron in 1834 as a combination of Boyle's law and Charles' law.

Atoms and Modules in a Gas: Atoms and molecules in a gas are typically widely separated, as shown. Because the forces between them are quite weak at these distances, they are often described by the ideal gas law.

Empirical Derivation

Boyle's law states that pressure P and volume V of a given mass of confined gas are inversely proportional:

\[\mathrm{P∝\dfrac{1}{V},}\]

while Charles' law states that volume of a gas is proportional to the absolute temperature T of the gas at constant pressure

\[\mathrm{V∝T.}\]

By combining the two laws, we get

\[\mathrm{\dfrac{PV}{T}=C,}\]

where C is a constant which is directly proportional to the amount of gas, n (representing the number of moles).

The proportionality factor is the universal gas constant, R, i.e. \(\mathrm{C = nR}\).

Hence the ideal gas law

\[\mathrm{PV=nRT}\]

Equivalently, it can be written as \(\mathrm{PV=NkT}\),

where k is Boltzmann's constant and N is the number of molecules.

(Since N = nN A, you can see that \(\mathrm{R=N_{Ak}}\), where N A is Avogadro's number. )

Note that the empirical derivation does not consider microscopic details. However, the equation can be derived from first principles in the classical thermodynamics (which goes beyond the scope of this Atom ).

Microscopic version

We have seen in the Atom on "Origin of Pressure" that

\[\mathrm{P=\dfrac{Nm\bar{v^2}}{3V},}\]

where P is the pressure, N is the number of molecules, m is the mass of the molecule, v is the speed of molecules, and V is the volume of the gas. Therefore, we derive a microscopic version of the ideal gas law

\[\mathrm{PV=\dfrac{1}{3}Nm\bar{v^2}}\]

Isotherms

An isothermal process is a change of a system in which the temperature remains constant: \(\mathrm{ΔT = 0}\).

An isothermal process is a change of a system in which the temperature remains constant: ΔT = 0. Typically this occurs when a system is in contact with an outside thermal reservoir (heat bath), and the change occurs slowly enough to allow the system to adjust continually to the temperature of the reservoir through heat exchange. In contrast, an adiabatic process occurs when a system exchanges no heat with its surroundings (Q = 0). In other words, in an isothermal process, the value ΔT = 0 but Q ≠ 0, while in an adiabatic process, ΔT ≠ 0 but Q = 0.

For an ideal gas, the product PV (P: pressure, V: volume) is a constant if the gas is kept at isothermal conditions (Boyle's law). According to the ideal gas law, the value of the constant is NkT, where N is the number of molecules of gas and k is Boltzmann's constant.

This means that \(\mathrm{p=\frac{NkT}{V}=\frac{Constant}{V}}\) holds.

The family of curves generated by this equation is shown in the graph presented in. Each curve is called an isotherm. Such graphs are termed indicator diagrams-first used by James Watt and others to monitor the efficiency of engines. The temperature corresponding to each curve in the figure increases from the lower left to the upper right.

Isotherms of an Ideal Gas: Several isotherms of an ideal gas on a PV diagram.

\[\mathrm{W_{A \rightarrow B}=∫_{V_A}^{V_B}PdV.}\]

Constant Pressure

Isobaric processis a thermodynamic process in which the pressure stays constant (at constant pressure, work done by a gas is \(\mathrm{PΔV}\)).

Under a certain constraint (e.g., pressure), gases can expand or contract; depending on the type of constraint, the final state of the gas may change. For example, an ideal gas that expands while its temperature is kept constant (called isothermal process) will exist in a different state than a gas that expands while pressure stays constant (called isobaric process). This Atom addresses isobaric process and correlated terms. We will discuss isothermal process in a subsequent Atom.

\[\mathrm{W=PAd}\]

\[\mathrm{W=PΔV}\]

\[\mathrm{W=NkΔT}\]

\[\mathrm{Q=ΔU+W}\]

\(\mathrm{Q=ncPΔT}\)

Problem Solving

With the ideal gas law we can figure pressure, volume or temperature, and the number of moles of gases under ideal thermodynamic conditions.

The Ideal Gas Law is the equation of state of a hypothetical ideal gas. It is a good approximation to the behavior of many gases under many conditions, although it has several limitations. It is most accurate for monatomic gases at high temperatures and low pressures.

The ideal gas law has the form:

\[\mathrm{PV=nRT,}\]

where R is the universal gas constant, and with it we can find values of the pressure P, volume V, temperature T, or number of moles n under a certain ideal thermodynamic condition. Typically, you are given enough parameters to calculate the unknown. Variations of the ideal gas equation may help solving the problem easily. Here are some general tips.

The ideal gas law can also come in the form:

\[\mathrm{PV=NkT,}\]

where N is the number of particles in the gas and k is the Boltzmann constant.

To solve the ideal gas equation:

1. Write down all the information that you know about the gas.

2. If necessary, convert the known values to SI units.

3. Choose a relevant gas law equation that will allow you to calculate the unknown variable.

4. Substitute the known values into the equation. Calculate the unknown variable.

Remember that the general gas equation only applies if the molar quantity of the gas is fixed. For example, if a gas is mixed with another gas, you may have to apply the equation separately for individual gases.

Solution:

Avogador's Number

The number of molecules in a mole is called Avogadro's number (N A)-defined as 6.02x 10 ²³ mol⁻¹.

When measuring the amount of substance, it is sometimes easier to work with a unit other than the number of molecules. A mole (abbreviated mol) is a base unit in the International System of Units (SI). It is defined as any substance containing as many atoms or molecules as there are in exactly 12 grams (0.012 kg) of carbon-12. The actual number of atoms or molecules in one mole is called Avogadro's constant (NA), in recognition of Italian scientist Amedeo Avogadro.

Amadeo Avogadro: Amedeo Avogadro (1776-1856). He established the relationship between the masses of the same volume of different gases (at the same temperature and pressure) corresponds to the relationship between their respective molecular weights.

Avogadro's number (N) refers to the number of molecules in one gram-molecule of oxygen. This indicates an amount of substance as opposed to an independent dimension of measurement. In 1811 Amedeo Avogadro first proposed that the volume of a gas (at a given pressure and temperature) is proportional to the number of atoms or molecules, regardless of the nature of the gas (i.e., this number is universal and independent of the type of gas). In 1926, Jean Perrin won the Nobel Prize in Physics, largely for his work in determining the Avogadro constant (by several different methods). The value of Avogadro's constant, N A , has been found to equal 6.02×10 ²³mol −1.

\[\mathrm{R=kN_A=8.314472(15) J \; mol^{−1}K^{−1};}\]

\[\mathrm{F=N_Ae=96485.3383(83) C \; mol^{−1}.}\]

Absolute Temperature

Absolute temperature is the most commoly used thermodyanmic temperature unit and is the standard unit of temperature.

Thermodynamic temperature is the absolute measure of temperature. It is one of the principal parameters of thermodynamics and kinetic theory of gases. Thermodynamic temperature is an "absolute" scale because it is the measure of the fundamental property underlying temperature: its null or zero point ("absolute zero") is the temperature at which the particle constituents of matter have minimal motion and cannot become any colder. That is, they have minimal motion, retaining only quantum mechanical motion, as diagramed in.

Graph of Pressure Versus Temperature: Graph of pressure versus temperature for various gases kept at a constant volume. Note that all of the graphs extrapolate to zero pressure at the same temperature

At its simplest, "temperature" arises from the kinetic energy of the random motions of matter's particle constituents such as molecules or atoms, as seen in. Therefore, it is reasonable to choose absolute zero, where all classical motion ceases, as the reference point (T=0) of our temperature system. By using the absolute temperature scale (Kelvin system), which is the most commonly used thermodynamic temperature, we have shown that the average translational kinetic energy (KE) of a particle in a gas has a simple relationship to the temperature:

Translational Motion of Helium: Real gases do not always behave according to the ideal model under certain conditions, such as high pressure. Here, the size of helium atoms relative to their spacing is shown to scale under 1950 atmospheres of pressure.

\[\mathrm{\bar{KE}=\dfrac{3}{2}kT.}\]

Note that this equation would not look this elegant if the Fahrenheit scale were used instead.

Key Points

Ideal gas law was derived empirically by combining Boyle's law and Charles' law.

Although the empirical derivation of the equation does not consider microscopic details, the ideal gas law can be derived from first principles in the classical thermodynamics.

Pressure and volume of a gas can be related to the average velocity of molecues: \(\mathrm{PV=\frac{1}{3}Nm\bar{v^2}.}\)

Isothermal processes typically occur when a system is in contact with an outside thermal reservoir ( heat bath), and the change occurs slowly enough to allow the system to adjust continually to the temperature of the reservoir through heat exchange.

For an ideal gas, from the ideal gas law \(\mathrm{PV = NkT, PV}\) remains constant through an isothermal process. A curve in a P-V diagram generated by the equation \(\mathrm{PV = const}\) is called an isotherm.

For an isothermal, reversible process, the work done by the gas is equal to the area under the relevant pressure -volume isotherm. It is given as \(\mathrm{W_A \rightarrow B=NkT \ln \frac{⁡V_B}{V_A}}\).

Gases can expand or contract under a certain constraint. Depending on the constraint, the final state of the gas may change.

The heat transferred to the system does work but also changes the internal energy of the system. In an isobaric process for a monatomic gas, heat and the temperature change satisfy the following equation: \(\mathrm{Q=\frac{5}{2}NkΔT}\).

For a monatomic ideal gas, specific heat at constant pressure is \(\mathrm{\frac{5}{2}R}\).

Write down all the information that you know about the gas and convert the known values to SI units if necessary.

Choose a relevant gas law equation that will allow you to calculate the unknown variable, and substitute the known values into the equation. Then calculate the unknown variable.

The general gas equation only applies if the molar quantity of the gas is fixed.

Avogadro hypothesized that equal volumes of gas, at the same pressure and temperature, contain equal numbers of molecules, regardless of the type of gas.

Avogadro's constant is a scaling factor between macroscopic and microscopic (atomic scale) observations of nature. It provides the relation between other physical constants and properties.

Albert Einstein proposed that Avogadro's number could be determined based on the quantities observable in Brownian motion. NA was measured for the first time by Jean Baptiste Perrin in 1908.

Temperature arises from the kinetic energy of the random motions of matter 's particle constituents such as molecules or atoms. Therefore, it is reasonable to choose absolute zero, where all classical motion ceases, as the reference point.

By international agreement, the unit kelvin and its scale are defined by two points: absolute zero and the triple point of the standardized water.

At absolute zero, the particle constituents of matter have minimal motion and cannot become any colder. They retain minimal, quantum mechanical motion.

Key Terms

mole: In the International System of Units, the base unit of amount of substance; the amount of substance of a system which contains as many elementary entities as there are atoms in 12 g of carbon-12. Symbol: mol.

ideal gas: A hypothetical gas whose molecules exhibit no interaction and undergo elastic collision with each other and with the walls of the container.

Avogadro's number: the number of constituent particles (usually atoms or molecules) in one mole of a given substance. It has dimensions of reciprocal mol and its value is equal to 6.02214129·1023 mol-1

adiabatic: Occurring without gain or loss of heat.

internal energy: The sum of all energy present in the system, including kinetic and potential energy; equivalently, the energy needed to create a system, excluding the energy necessary to displace its surroundings.

the first law of thermodynamics: A version of the law of energy conservation: the change in the internal energy of a closed system is equal to the amount of heat supplied to the system, minus the amount of work done by the system on its surroundings.

specific heat: The ratio of the amount of heat needed to raise the temperature of a unit mass of substance by a unit degree to the amount of heat needed to raise that of the same mass of water by the same amount.

SI units: International System of Units (abbreviated SI from French: Le Système international d'unités). It is the modern form of the metric system.

gas constant: A universal constant, R, that appears in the ideal gas law, (PV = nRT), derived from two fundamental constants, the Boltzman constant and Avogadro's number, (R = NAk).

Faraday constant: The magnitude of electric charge per mole of electrons.

Brownian motion: Random motion of particles suspended in a fluid, arising from those particles being struck by individual molecules of the fluid.

absolute zero: The coldest possible temperature: zero on the Kelvin scale and approximately -273.15°C and -459.67°F. The total absence of heat; the temperature at which motion of all molecules would cease.

International System of Units: (SI): The standard set of basic units of measurement used in scientific literature worldwide.

Vienna Standard Mean Ocean Water: A standard defining a standardized isotopic composition of water.

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Page ID 14511 Empirical Derivation Microscopic version Isotherms Calculation of Work Constant Pressure Isobaric Process Monatomic Gas Specific Heat Problem Solving Example Avogador's Number Role in Science Measuring NA Absolute Temperature The Kelvin scale Key Points Key Terms The ideal gas law is the equation of state of a hypothetical ideal gas (an illustration is offered in ).

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Steven is a 30-something, futurist, father, and self-taught science nut.

What Is Boyle's Law and Equation?

In 1662, Robert Boyle discovered the volume and pressure of gasses are inversely proportionate when held at a constant temperature. Put simply, when volume rises, pressure drops, and vice versa.

The mathematic equation is equally as simple.

PV = k

In this equation, (P) represents pressure, (V) represents volume, and (k) is a constant.

This has become a basic principle in chemistry, now called "Boyle's law," and is included as a special case in the more general ideal gas law.

How Did Boyle Come up With His Law?

Using a vacuum pump invented by Otto von Guericke in 1654, Boyle carried out experiments investigating the properties of air and the vacuum.

During his experiments, he stumbled upon the greatest achievement of his life. By using a J-shaped glass tube that had air at the tip of the curve, Boyle altered the weight of the air using mercury and, as he did so, he saw that the space of air at the tip of the curve became smaller. He discovered that when you increase pressure on a gas, the gas's volume predictably shrinks.

Why Is Boyle's Law Important?

Boyle's law is important because it tells us about the behavior of gasses. It explains, with certainty, that the pressure and volume of gas are inversely proportional to one another. So, if you push on gas, its volume becomes smaller and the pressure becomes higher.

Examples of Boyle's Law in Life

You have probably been well-acquainted with Boyle's law for most of your life without realizing it. We experience examples of this law on a regular basis. The first example is a rather common one, assuming you have filled a tire with air before.

Generally, you fill a tire with somewhere between 30 to 35 PSI (pounds per square inch) of compressed air. This is a measurement of pressure. As you put more and more air into the tire, you are forcing all the gas molecules to get packed together, reducing their volume and increasing the pressure pushing on the walls of the tire. As long as the air temperature remains the same, you are experiencing a real life example of this law.

Other examples include:

Real-World Applications of Boyle's Law

1. Spray paint

2. The syringe

3. The soda can

4. The bends

Read on for descriptions of the examples listed above.

1. Spray Paint

While there are a couple different types of aerosol cans, some being a little more elaborate than other, they all rely on the same basic principle: Boyle's law.

Before you spray a can of paint, you are supposed to shake it up for a while as a ball bearing rattles around inside. There are two substances inside the can: one is your product (paint for example), and the other is a gas that can be pressurized so much that it retains a liquid state, even when it is heated past its boiling point.

This liquefied gas has a boiling point far below room temperature. Because the can is sealed, the gas is prevented from boiling and turning into a gas. That is, until you push down the nozzle.

The moment the nozzle of a spray paint can goes down, the seal is broken and the propellant instantly boils, expands into a gas, and pushes down on the paint. Under the high pressure, the paint is forced out of the nozzle as it attempts to reach an area with lower pressure.

2. The Syringe

This mechanism is far more simple than a can of spray paint. Syringes of all types utilize Boyle's law on a very basic level.

When you pull the plunger out on a syringe, it causes the volume within the chamber to increase. As we know, this causes the pressure to do the opposite, which then creates a vacuum. When a syringe is empty, the vacuum within the chamber sucks fluid in through the needle.

3. The Soda Can or Bottle

Typically when we open a bottle of soda, we slowly turn the cap to allow the air to escape before we completely remove the lid. We do this because we've learned over time that twisting it open too fast causes it to fizz up and spill all over. This happens because the liquid is pumped full of carbon dioxide, causing it to bubble up as the CO 2 makes its escape.

When a soda bottle is filled, it is also pressurized. Much like the aerosol can mentioned earlier, when you slowly open the cap, the gas is able to increase its volume and the pressure decreases.

Normally you can let the gas out of a can or bottle release cleanly, but if the bottle is shaken up and the gas is mixed into the liquid, then you may have a mess on your hands. This is because the gas trying to escape is mixed into the fluid, so, when it does escape, it brings the foamy fluid out with it. Pressure in the bottle goes down, volume of the gas goes up, and you have yourself a mess to clean up.

4. The Bends

Any properly trained scuba diver knows when they are ascending from deep waters, a slow ascension is critical. Our bodies are built for and accustomed to living in the normal pressure of our lower atmosphere. As a diver goes deeper underwater, that pressure begins to increase. Water is heavy, after all. With the increasing pressure causing a decrease in volume, nitrogen gasses begin to be absorbed by the diver's blood.

When the diver begins his ascent and the pressure is lessened, these gas molecules begin to expand back to their normal volume. With a slow ascent, or through the use of a depressurization chamber, those gasses can work their way back out of the bloodstream slowly and normally. But if the diver ascends too quickly, the blood in their vains becomes a foamy mess. The same thing that happens to a foamy soda is what happens to a diver's bloodstream during the bends. On top of that, any built up nitrogen between the diver's joints will also expand, causing the diver to bend over (hence its name) in severe pain. In the worst cases, this sudden depressurization of the body can kill a person instantly.

The Cartesian Diver: Build Your Own Example of Boyle's Law

By now you either have a basic understanding of Boyle's law and how it can be applied to the real world, or you're suddenly afraid to go swimming.

Either way, this last example of Boyle's law in action is something you can build yourself! First, you need a small list of supplies:
Supplies

One transparent 2-liter bottle

One small glass dropper

Water

Once you've managed to gather these supplies, follow the steps below.
How To Build a Cartesian Diver

1. Add water until the 2-liter bottle is full.

2. Take your eyedropper, the "diver," and fill it with just enough water so that the top of the dropper is just buoyant enough to float on top of the water.

3. Apply the lid to the 2-liter bottle. It must be airtight!

4. Squeeze the bottle.

5. Observe.

If you have successfully followed the instructions, your Cartesian diver should dive to the bottom as you squeeze the bottle. That's Boyle's law in action!

When you squeeze inward, you are reducing the volume of the bottle. As we know, this reduction in volume increases the pressure.

This increase in pressure pushes against the water, forcing more water up into the eyedropper. This additional water decreases the diver's buoyancy, causing it to "dive" to the bottom. Stop squeezing the bottle, and your diver will ascend back to the water's surface.

DIY Cartesian Diver (Video)

What Is the Ideal Gas Law?

Since it is hard to exactly describe a real gas, scientists created the concept of an ideal gas. The ideal gas law refers to a hypothetical gas that follows the rules listed below:

1. Ideal gas molecules do not attract or repel each other. The only interaction between ideal gas molecules would be an elastic collision with each other or with the walls of the container.

2. Ideal gas molecules themselves take up no volume. While the gas takes up volume, the ideal gas molecules are considered point particles that have no volume.

There are no gasses that are exactly ideal, but there are many that are close. This is why the ideal gas law is extremely useful when used as an approximation for many situations. The ideal gas law is obtained by combining Boyle's law, Charle's law, and Gay-Lussac's Law, three of the major gas laws.

What Is Charle's Law?

Charle's law, or the law of volumes, was discovered in 1787 by Jaques Charles and states that for a give mass of an ideal gas at constant pressure, the volume is directly proportional to it's absolute temperature. This means that as the temperature of a gas increases, so does its volume.

V / T = k

The equation of Charle's law is written above, with (V) representing volume, (T) representing temperature, and (k) representing a constant.

What Is Gay-Lussac's Law?

Gay Lussac's law, or the pressure law, was discovered by Joseph Louis Gay-Lussac in 1809 and states that, for a given mass and constant volume of an ideal gas, the pressure exerted on the sides of its container is directly proportional to its absolute temperature. This means that pressure indicates temperature.

P / T = k

The equation of Guy Lussac's law is written above, with (P) representing pressure, (T) representing temperature, and (k) representing a constant.

How Does Boyle's Law Relate to Breathing?

When it comes to the effects of Boyle's law on the body, the gas law specifically applies to the lungs.

When a person breathes in, their lung volume increases and the pressure within decreases. Since air always moves from areas of high pressure to areas of low pressure, air is drawn into the lungs.

The opposite happens when a person exhales. Since the lung volume decreases, the pressure within increases, forcing the air out of the lungs to the lower pressure air outside of the body.

What Are the Two Stages of the Breathing Process?

The breathing process, sometimes called respiration, can be simply broken down into two stages: inhalation and exhalation.
Inhalation
During inhalation, also called inspiration, the diaphragm contracts and pulls downward and the muscles between the ribs contract and pull upward, increasing the volume of the lung cavity and decreasing the pressure within. As a result, air rushes in to fill the lungs.
Exhalation
During exhalation, also called expiration, the diaphragm relaxes and the volume of the lung cavity decreases while the pressure within increases. As a result, air is forced out.

How Do You Know When to Breathe?

Breathing is controlled by a respiratory control center at the base of your brain. This center sends signals down your spine that ensure your breathing muscles in your lungs contract and relax regularly.

Your breathing can change depending on how active you are, as well as on the condition of the air around you. Other factors that may affect your breathing include your emotions or deliberate actions such as holding your breath.

A Final Word

I did leave a certain application of Boyle's law out of this list that is used far more than any of the above examples. This system is directly powered by the rules of Boyle's law, and is a device you use every day, everywhere you go.

What is it? Comment your answer below!

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Steven is a 30-something, futurist, father, and self-taught science nut. In 1662, Robert Boyle discovered the volume and pressure of gasses are inversely proportionate when held at a constant temperature. Put simply, when volume rises, pressure drops, and vice versa. The mathematic equation is equally as simple.