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# Category Archives: gas laws

### Reasoning

(from Modern Chemistry, Davis, HRW)

### As shown below, the coefficients in a chemical reaction involving gases indicate the relative numbers of molecules, the relative numbers of moles, and the relative volumes. ## As an equation

### or ## Important! This is not a law of physics!

### Rather, this is a generally useful rule, which is only valid when gas temperature and pressure is low enough for the atoms to usually be far apart from each other.  As we begin to deal with more extreme cases, this rule doesn’t hold up.

At what point does Avogadro’s law not apply?

## Example problems

### V1 / n1 = V2 / n2

2.00 L / 0.500 mol = 2.70 L / x

x = 0.675 mol

### 0.675 mol – 0.500 mol = 0.175 mol

0.175 mol x 4.00 g/mol = 0.7 grams of He added

### We can perform a calculation using Avogadro’s Law:

V1 / n1 = V2 / n2

Let’s assign V1 to be 1 L and V2 will be our unknown.

Let us assign 1 mole for the amount of neon gas and assign it to be n1.

The mass of argon now added is exactly equal to the neon, but argon has a higher gram-atomic weight (molar mass) than neon. Therefore less than 1 mole of Ar will be added. Let us use 1.5 mol for the total moles in the balloon (which will be n2) after the Ar is added. (I picked 1.5 because neon weighs about 20 g/mol and argon weighs about 40 g/mol.)

1 / 1 = x / 1.5

x = 1.5

### V1 / n1 = V2 / n2

 5.120 L 18.10 L –––––––– = –––––– 8.500 mol x

x = 30.05 mol <— total moles, not the moles added

30.05 – 8.500 = 21.55 mol (to four sig figs)

## Charles’s Law

### This relationship can be written as: ### This relationship can be written as: ### Important! This is not a law of physics! Rather, this is a generally useful rule, which is only valid when gas temperature and pressure is low enough for the atoms to usually be far apart from each other.  As we begin to deal with more extreme cases, this rule doesn’t hold up.

Let’s see this in action! https://www.grc.nasa.gov/WWW/K-12/airplane/aglussac.html

## Origin

### Named after Jacques Alexandre César Charles (1746 – 1823)  a French inventor, scientist, mathematician, and balloonist. Just so we’re all clear on this, he was kind of a mad scientist. And I say that with the utmost approval! Contemporary illustration of the first flight by Prof. Jacques Charles with Nicolas-Louis Robert, December 1, 1783. Viewed from the Place de la Concorde to the Tuileries Palace (destroyed in 1871)

.Apps

Charles’s law app

## Learning standards

Massachusetts Science and Technology/Engineering Curriculum Framework

8.MS-PS1-4. Develop a model that describes and predicts changes in particle motion, relative spatial arrangement, temperature, and state of a pure substance when thermal energy is added or removed.

Next Generation Science Standards

MS-PS1-4. Develop a model that predicts and describes changes in particle motion, temperature, and state of a pure substance when thermal energy is added or removed.

College Board Standards

Objective C.1.5 States of Matter

C-PE.1.5.2 Explain why gases expand to fill a container of any size, while liquids flow and spread out to fill the bottom of a container and solids hold their own shape. Justification includes a discussion of particle motion and the attractions between the particles.

C-PE.1.5.3 Investigate the behavior of gases. Investigation is performed in terms of volume (V ), pressure (P ), temperature (T ) and amount of gas (n) by using the ideal gas law both conceptually and mathematically.

Common Core Math

Analyze proportional relationships and use them to solve real-world and mathematical problems.

Ratios & Proportional Relationships

Ratios & Proportional Relationships

CCSS.MATH.CONTENT.7.RP.A.2

Recognize and represent proportional relationships between quantities.

CCSS.MATH.CONTENT.7.RP.A.2.A

Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin.

CCSS.MATH.CONTENT.7.RP.A.2.B

Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.

## Boyle’s law (gas laws)

A general relationship between pressure and volume: Boyle’s Law

As the pressure on a gas increases, the volume of the gas decreases because the gas particles are forced closer together.

Conversely, as the pressure on a gas decreases, the gas volume increases because the gas particles can now move farther apart.

Example: Weather balloons get larger as they rise through the atmosphere to regions of lower pressure because the volume of the gas has increased; that is, the atmospheric gas exerts less pressure on the surface of the balloon, so the interior gas expands until the internal and external pressures are equal.

from Libretexts, Chemistry, 5.3: The Simple Gas Laws: Boyle’s Law, Charles’s Law and Avogadro’s Law, CC BY-NC-SA 3.0.

This means that, at constant temperature, the pressure (P) of a gas is inversely proportional to the volume (V).

PV = c

Important! This is not a law of physics! Rather, this is a generally useful rule, which is only valid when gas temperature and pressure is low enough for the atoms to usually be far apart from each other.  As we begin to deal with more extreme cases, this rule doesn’t hold up.

Let’s see the relationship in action, here: Early scientists explored the relationships among the pressure of a gas (P) and its temperature (T), volume (V), and amount (n) by holding two of the four variables constant (amount and temperature, for example), varying a third (such as pressure), and measuring the effect of the change on the fourth (in this case, volume).

The history of their discoveries provides several excellent examples of the scientific method.

The Irish chemist Robert Boyle (1627–1691) carried out some of the earliest experiments that determined the quantitative relationship between the pressure and the volume of a gas. Boyle used a J-shaped tube partially filled with mercury.

In these experiments, a small amount of a gas or air is trapped above the mercury column, and its volume is measured at atmospheric pressure and constant temperature. More mercury is then poured into the open arm to increase the pressure on the gas sample.

The pressure on the gas is atmospheric pressure plus the difference in the heights of the mercury columns, and the resulting volume is measured. This process is repeated until either there is no more room in the open arm or the volume of the gas is too small to be measured accurately. Details: Boyle’s Experiment Using a J-Shaped Tube to Determine the Relationship between Gas Pressure and Volume.

(a) Initially the gas is at a pressure of 1 atm = 760 mmHg (the mercury is at the same height in both the arm containing the sample and the arm open to the atmosphere); its volume is V.

(b) If enough mercury is added to the right side to give a difference in height of 760 mmHg between the two arms, the pressure of the gas is 760 mmHg (atmospheric pressure) + 760 mmHg = 1520 mmHg and the volume is V/2.

(c) If an additional 760 mmHg is added to the column on the right, the total pressure on the gas increases to 2280 mmHg, and the volume of the gas decreases to V/3

(This section from from Libretexts, Chemistry, 5.3: The Simple Gas Laws: Boyle’s Law, Charles’s Law and Avogadro’s Law, CC BY-NC-SA 3.0)

## Learning standards

Massachusetts Science and Technology/Engineering Curriculum Framework

8.MS-PS1-4. Develop a model that describes and predicts changes in particle motion, relative spatial arrangement, temperature, and state of a pure substance when thermal energy is added or removed.

Next Generation Science Standards

MS-PS1-4. Develop a model that predicts and describes changes in particle motion, temperature, and state of a pure substance when thermal energy is added or removed.

College Board Standards

Objective C.1.5 States of Matter

C-PE.1.5.2 Explain why gases expand to fill a container of any size, while liquids flow and spread out to fill the bottom of a container and solids hold their own shape. Justification includes a discussion of particle motion and the attractions between the particles.

C-PE.1.5.3 Investigate the behavior of gases. Investigation is performed in terms of volume (V ), pressure (P ), temperature (T ) and amount of gas (n) by using the ideal gas law both conceptually and mathematically.

Common Core Math

Analyze proportional relationships and use them to solve real-world and mathematical problems.

Ratios & Proportional Relationships

Ratios & Proportional Relationships

CCSS.MATH.CONTENT.7.RP.A.2

Recognize and represent proportional relationships between quantities.

CCSS.MATH.CONTENT.7.RP.A.2.A

Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin.

CCSS.MATH.CONTENT.7.RP.A.2.B

Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.

## Vapor cones and mach cones

A vapor cone, also known as shock collar or shock egg, is a visible cloud of condensed water which can sometimes form around an object moving at high speed through moist air, for example an aircraft flying at transonic speeds. When the localized air pressure around the object drops, so does the air temperature. If the temperature drops below the saturation temperature a cloud forms. In the case of aircraft, the cloud is caused by supersonic expansion fans decreasing the air pressure, density and temperature below the dew point. Then pressure, density and temperature suddenly increase across the stern shock wave associated with a return to subsonic flow behind the aircraft. Since the local Mach number is not uniform over the aircraft, parts of the aircraft may be supersonic while others remain subsonic — a flight regime called transonic flight.

A vapor cone is caused by the formation of so-called ‘Prandtl–Meyer’ expansion fans, which temporarily decrease the air pressure, density and temperature below the air’s dew point. It is not the same thing as the Mach Cone (which is an invisible pressure front), but the two often occur in tandem, allowing us to pretend that we have just seen the sound barrier broken. In this incredible clip of a Boeing F/A-18 Hornet flying at a height of 25 feet, you can see both the Vapor Cone and evidence of the Mach Cone on the surface of the water…

http://physicsfootnotes.com/vapor-cone-versus-mach-cone/

## Triple point

### Amazing: See a flask of liquid cyclohexane brought to the brink of its triple-point: suddenly it can boil and freeze at the same time. A volumetric flask containing liquid cyclohexane is depressurized to a very low pressure by a turbo-molecular vacuum pump. The rapid drop in pressure results in a rapid drop in temperature, causing the substance to temporarily freeze, but the system is unstable, flirting with the triple point (a point of pressure and temperature at which a substance is simultaneously solid, liquid, and gas). The result is a fluctuation between all three states of matter, in a spectacular display of chemistry and physics in action.

http://physicsfootnotes.com/triple-point/