Chapter 6: Unit 4. Gas Laws

Gas Laws

Volume, temperature, pressure and number of moles are interrelated in gaseous system.

https://phet.colorado.edu/en/simulation/legacy/gas-properties

Click on the above simulation and observe the properties of Gas.

• Now introduce 50 molecules into the chamber using the handle pump. Slowly decrease the volume of the container using the man symbol. Notice that the pressure monitoring system is giving higher and higher values. This is called Boyle’s law.

Boyle’s law: Volume of a fixed amount of gas is inversely proportional to the pressure applied to the gas if the Temp is kept constant.

Boyle’s law has wide application in various fields like scuba diving, human breathing technique. When a person breathe in, the diaphragm contracts and volume of the lungs get bigger and pressure is low inside the body than outside pressure. Since outside pressure is high, air goes inside the body. When we breathe out, the diaphragm relaxes, volume decreases, high pressure  gas comes out of the body.

Mathematically we can write,

at constant T

P1= initial pressure, P2= final pressure, T1= initial temp in Kelvin, T2= final temp in Kelvin

If we plot different Pressure vs. Volume for a gaseous system at a constant temperature, the curve will be parabolic in nature.

Example: A 4.0 L container of Helium gas has a pressure of 15.0 atm. What pressure does the gas exert if the volume is increased to 8.0 L?

Ans: since the volume is doubled, pressure must be half of the initial pressure.

New pressure= 15.0/2= 7.50 atm

• Now introduce heat to the activity: Increase the temp from 400K to 1500K by adding heat keeping the pressure at 1:00atm. On the right top corner of the screen, keep pressure as constant parameter. You will notice that volume of the chamber is increasing. This is called Charles’s law.

Charles’s law: Volume of a fixed amount of gas is directly proportional to the kelvin temp if the pressure is kept constant.

This concept is applied in hot air balloon, where the volume of the gas is expanded by applying heat and once it becomes less dense than air, it can float in air.

Mathematically we can write:

at constant P

V1= initial pressure, V2= final pressure, T1= initial temp in Kelvin, T2= final temp in Kelvin

We can understand the absolute zero temperature from Charles’s law. For a sample of gas, when temperature is decreases, volume of the gas molecules decrease. According to the kinetic Molecular theory, the energy of the gas molecules is directly proportional to the kelvin temp. So gas molecules will move slowly as the temperature decreases. Therefore, hypothetically if the absolute temperature of a gaseous system reaches zero i.e. -273⁰C, all the gas molecules motion will be ceased and the volume of the gas molecule would be zero. In reality, experiments done at lower temp that show the volume decreases steadily but so far, zero volume hasn’t reached.

https://youtube.com/watch?v=JHXxPnmyDbk%3Ffeature%3Doembed

Example: A volume of 1.00L of gas at 37⁰C is expelled from the lungs to cold outside at temperature -5⁰C. What is the volume of the air at that temperature?

Ans: V2 is unknown.

1.00/(37+ 273) = V2/( -5+ 273) , 1/310=V2/268 or V2= 0.865 L

• Avogadro’s law: Increase the number of molecules from 50 to 100 in the simulation system keeping the pressure and Temperature constant. You may notice that volume of the container is increasing. This is Avogadro’s law.

Avogadro’s law: Volume of a of gas is directly proportional to the number of moles of gas if the pressure and Temp are kept constant.

V1= initial volume v2= final volume, n1= initial moles n2= final moles

Example:  The lungs of an average male holds 0.25 mol of air in a volume of 5.5 L. How many mole sof air do the lungs of an average female hold if the volume is 4.5 L?

Ans: n2 is unknown.

5.5/0.25= 4.5/n2, 22= 4.5/n2 or n2= 0.205 mol or 0.20 mols

• Gay Lusaac’s law or Amonton’s law: With volume remaining constant, the pressure of a gas molecule is directly proportional to its absolute temperature. According to KMT theory, when temperature increases, the gas molecules possess high kinetic energy. They collide with other molecules and with the walls of the container with high speed and try to expand. If the volume is kept constant, they collide each other more frequently and gas pressure increases.

P1= initial pressure, P2= final pressure, T1= initial temp, T2= final temp

Gay Lusaac’s law can also be observed the above diagram, where application of heat to a gaseous system increases the pressure of the gas.

Example: The tire on a bicycle in a cool garage is stored at 20⁰C and 80. Psi. What is the pressure inside the tire after riding the bike at 43⁰C?

Ans: P2 is unknown, 80/(20+273)= P2/(43+ 273)

0.273= P2/316  or P2= 0.273*316= 86.3 psi or 86 psi.

The following activity has been taken from AACT ( American association of chemical teachers)

https://teachchemistry.org/periodical/issues/november-2015/gas-laws

In this investigation you will examine three gas laws including Boyle’s Law, Charles’ Law and Gay-Lussac’s Law. You will explore how manipulating the variables of volume (L), pressure (atm) and temperature (K) can affect a sample of gas. The formula for each of the gas laws are:

	Boyle’s Law		Charles’s law		Gay Lussaac’s Law
	P1V1= P2V2		V1/T1= V2/T2		P1/T1= P2/T2

Prelab Questions

1. Solve for “x” in the following algebraic equations and report your final answer with the correct number of significant digits:

1. (1.34)(5.46) = (1.76)(x)

4. 38 =    x_      

332          267

2. 25 =   4.85_      

295             x

2. Briefly describe, in your own words the meaning of each of the following variables, and common units of measurement associated with each:

1. Volume

1. Pressure

1. Temperature

Procedure

Visit  http://www.teachchemistry.org/gaslaws. Make sure that you select the “Boyle’s Law” tab to begin; it will be shown in white. You should see the picture below on your screen.

Boyle’s Law

1. Which one of the three variables: Pressure, Volume or Temperature cannot be changed in Boyle’s Law? This variable is considered a constant.

1. Using the volume control arrows, reduce the volume of the gas to 1.70L.
2. In the space below record your observations regarding the behavior of the particles in the gas sample as the volume is reduced. Make certain to discuss collisions in your comments.

1. Calculate the new pressure value for the gas, showing all of your work.
2. Check your final answer for part b by clicking the calculate button next to P₂.

a. Observations when Volume is reduced:	b. Calculation
	P1V1 = P2V2

3. Press the reset button at the top right of the screen.

Using the pressure control arrows, reduce the pressure of the gas to 0.700atm.

1. In the space below record your observations regarding the behavior of the particles in the gas sample as the pressure is reduced.
2. In the space below calculate the new volume value for the gas.
3. Check your final answer for part b by clicking the calculate button next to V₂.

a. Observations when Pressure is reduced:	b. Calculation
	P1V1 = P2V2

4. Press the reset button at the top right of the screen.
   1. Using the pressure control arrows, increase the pressure value to 1.50 atm, and fill in the corresponding V₂ value in the data table below.
   2. Press the Add Data Using the pressure control arrows, increase the pressure to 2.00atm and fill in the corresponding V₃ value in the data table below.
   3. Repeat step b for pressure values of 2.50atm and 2.90atm.

P1 = 1.00atm	P2 = 1.50atm	P3 = 2.00atm	P4 = 2.50atm	P5 = 2.90atm
V1 =	V2 =	V3 =	V4 =	V5 =

1. Based on the data collected in the table above, what trend can be observed for volume of a gas when the pressure of the gas is increased?

Important Terms

Direct relationship: A relationship between two variables, where a change in one variable results in the same change in the other variable. For example, if one variable is increased, then the other variable will also increase.

Indirect relationship: A relationship between two variables, where a change in one variable results in the opposite change in the other variable. For example, if one variable is increased, then the other variable will decrease.

1. Considering the terms described above, do the variables of pressure and volume have a direct or an indirect relationship in Boyle’s Law? Justify your answer with data.

1. Considering what you now know about Boyle’s law, make a prediction based on the following situation: What would happen to the pressure of a gas inside a sealed bottle, if the bottle was squeezed tightly, reducing the volume of the gas by half? Explain your thoughts.

Charles’ Law

Change the simulation to “Charles’ Law” by clicking the tab at the top of the screen it will be shown in white. You should see the picture below on your screen.

1. Which one of the three variables: Pressure, Volume or Temperature cannot be changed in Charles’ Law? This variable is considered a constant.

1. a. Using the Temperature controls, increase the temperature of the gas. What changes do you observe in the behavior of the particles of the gas while the temperature is increased?

1. Continue to increase the temperature value until T₂ = 443K. Using the equation for Charles’ law, calculate the volume of the gas at this increased temperature. Check your final answer for part b by clicking the calculate button next to V₂:

V₁ = V₂

T₁    T₂

1. Based on the final value calculated in part b) is Charles’ law considered a direct or an indirect relationship between the variables? Explain your choice with reasoning.

3. Press the reset button at the top right of the screen.

Using the volume control arrows, reduce the volume of the gas to 1.86L.

1. In the space below record your observations regarding the behavior of the particles in the gas sample as the volume is reduced.
2. In the space below calculate the new temperature value for the gas.
3. Check your final answer for part b by clicking the calculate button next to T₂.

a. Observations when Volume is reduced:	b. Calculation
	V1 = V2T1     T2

1. Convert the final value for T₂ into Celsius units.

4. Press the reset button at the top right of the screen.

• Using the pressure control arrows, increase the temperature value to a measurement of your choosing. Then press Add Data. This will fix a data point on the graph for T₂.
• Increase the temperature three additional times; select Add Data for each data point: T_3, T_4, and T

1. Plot these points on the graph below, estimating the five data points created:

Volume (L)

Temperature (K)

1. Based on the data points collected on the graph, make a statement about the trend that can be observed between the volume and temperature of a gas.

5. Considering what you now know about Charles’ law, make a prediction based on the following situation: What would happen to the volume of a gas inside a sealed bottle, if the bottle was heated to double its original temperature? Explain your thoughts.

Gay-Lussac’s Law

Change the simulation to “Gay-Lussac’s Law” by clicking the tab at the top of the screen it will be shown in white. You should see the picture below on your screen.

2. The equation for Gay-Lussac’s law is                    does it look most similar to the equation for Boyle’s Law or the equation for Charles’ law?

1. What variable is held constant in Gay Lussac’s law?

1. Based on your answer to part a) what prediction can you make about the relationship between the variables of Pressure and Temperature of a gas?

3. Using the pressure control arrows, increase the pressure value to 1.50atm, and

fill in the corresponding T₂ value in the data table below.

2. Press the Add Data Using the pressure control arrows, increase the pressure to 2.00atm and fill in the corresponding T₃ value in the data table below.
3. Repeat step b for pressure values of 2.50atm and 2.90atm.

P1 = 1.00atm	P2 = 1.50atm	P3 = 2.00atm	P4 = 2.50atm	P5 = 2.90atm
T1 =	T2 =	T3 =	T4 =	T5 =

1. Based on the data collected in the table above, what trend can be observed for temperature of a gas when the pressure of the gas is increased? Is this considered a direct or an indirect relationship between the variables?

4. Press the reset button at the top right of the screen.

Using the temperature control arrows, reduce the temperature of the gas to 158K.

1. In the space below record your observations regarding the behavior of the particles in the gas sample as the temperature is reduced. Make certain to discuss collisions in your comments.
2. In the space below calculate the new pressure value for the gas.
3. Check your final answer for part b by clicking the calculate button next to P₂.

a. Observations when Volume is reduced:	b. Calculation
	P1 = P2T1     T2

5. Considering what you now know about Gay-Lussac’s law, make a prediction based on the following situation: What would happen to the pressure of a gas inside a sealed bottle, if the bottle was cooled to half of its original temperature? Explain your thoughts.

Checking Comprehension

Please create a list of the variable given in each problem and show all your work required to complete the calculation.

1. Calculate the temperature of a gas when it is expanded to 5.25L. The gas originally occupies 3.45L of space at 282K.

2. The temperature of a gas is increased from 125⁰C to 182⁰C inside of a rigid container. The original pressure of the gas was 1.22atm, what will the pressure of the gas be after the temperature change?

3. The volume of gas in a container was originally 3.24L, while at standard pressure, 1.00atm. What will the volume be if the pressure is increased to 1.20atm?

The Gas Laws

Gas Law

Boyle’s Law

P1V1=P2V2

Charles’s Law

V1 T1

=

V2 T2

Combined Gas Law

P1 V1 T1

=

P2 V2 T2

Dalton’s Law

P to 1=P1+P2+P3+…….

SYNOPSIS

At constant temperature volume of a gas is inverse by proportional to the pressure applied to it.

Product of pressure and volume of a fixed amount of gas is directly proportional to the kelvin temp

Connect pressure, volume, temp and molar amount of a gas under one set of conditions. If three of the four variables are known, fourth one can be calculated.

total pressure exerted by a mixture of gases is equal to the sum of the partial pr. of individual gases.

CONSTANT

Temp, moles

Pressure, moles

Number of moles

R= .0821 L-atm/motk

VARIABLES

Pressure, volume

Volumes, temp

Pressure , temp, volume

Pressure, volume, moles , temp