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RSPT 1060 MODULE C MODULE C Lesson #4 GAS LAWS

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OBJECTIVES At the end of this module, the student should be able to…At the end of this module, the student should be able to… Define terms associated with gas laws. Define Boyle’s Law. Describe the relationship between volume, pressure, mass and temperature. Describe how Boyle’s Law can be used to explain normal ventilation. Given appropriate information, use the mathematical formula for Boyle’s Law to solve for an unknown. Define Charles’s Law. Describe the relationship between volume, pressure, mass and temperature. State a clinical example of when Charles Law is applied in respiratory therapy. Given appropriate information, use the mathematical formula for Charles’s Law to solve for an unknown.

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OBJECTIVES At the end of this module, the student should be able to…At the end of this module, the student should be able to… Define Gay Lussac’s Law. Describe the relationship between volume, pressure, mass and temperature. Give a clinical example of when Gay-Lussac's Law is applied in respiratory therapy Given appropriate information, use the mathematical formula for Gay-Lussac's Law to solve for an unknown. State the combined gas law. Given appropriate information, use the mathematical formula for the Combined Gas Law to solve for an unknown. State the Universal (Ideal) Gas Law.

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SUPPORTIVE READINGS Egan: Gas Behavior Under Changing Conditions, pgs. 109 – 111Egan: Gas Behavior Under Changing Conditions, pgs. 109 – 111 Sibberson’s Math for RC:Sibberson’s Math for RC: Chapter 2 – Boyle’s Law, pgs. 17 – 19, Sample Problems Fourth Set.Chapter 2 – Boyle’s Law, pgs. 17 – 19, Sample Problems Fourth Set. Chapter 2 – Charles’s Law, pgs. 19 – 20, Sample Problems Fifth Set.Chapter 2 – Charles’s Law, pgs. 19 – 20, Sample Problems Fifth Set. Chapter 2 – Gay Lussac’s Law, pgs. 20 – 21, Sample Problems Sixth Set.Chapter 2 – Gay Lussac’s Law, pgs. 20 – 21, Sample Problems Sixth Set. Chapter 2 – Combined Gas Law, pgs. 22 – 26, Sample Problems Seventh & Eighth Set.Chapter 2 – Combined Gas Law, pgs. 22 – 26, Sample Problems Seventh & Eighth Set. Chapter 2 – Practice Exercises, pgs. 29 – 32, #21 – 60.Chapter 2 – Practice Exercises, pgs. 29 – 32, #21 – 60.

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Web Sites http://www.grc.nasa.gov/WWW/K- 12/airplane/boyle.htmlhttp://www.grc.nasa.gov/WWW/K- 12/airplane/boyle.htmlhttp://www.grc.nasa.gov/WWW/K- 12/airplane/boyle.htmlhttp://www.grc.nasa.gov/WWW/K- 12/airplane/boyle.html

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Gas Laws Laws describing the behavior of gases.Laws describing the behavior of gases. Supported by the Kinetic Molecular TheorySupported by the Kinetic Molecular Theory Six assumptionsSix assumptions Applies to most situations.Applies to most situations. Exceptions to these laws may occur when there is…Exceptions to these laws may occur when there is… Extremely high pressuresExtremely high pressures Extremely low temperaturesExtremely low temperatures

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Physical Properties Compared in the Gas Laws Mass – “amount of matter”Mass – “amount of matter” Pressure – “The force per unit of surface area” (pounds per square inch or psi). Results from molecular collisions.Pressure – “The force per unit of surface area” (pounds per square inch or psi). Results from molecular collisions. Temperature – measurement of the degree of molecular activityTemperature – measurement of the degree of molecular activity Volume – “space occupied by matter” For a gas it is the volume of the container because gases will always fill the container.Volume – “space occupied by matter” For a gas it is the volume of the container because gases will always fill the container.

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Gas Law - Summary Table Law:Boyle’sCharles’s Gay Lussac’s Combined Formula:P1xV1=P2xV2 V1 = V2 T1 T2 P1 = P2 T1 T2 P1xV1 = P2xV2 T1 T2 T1 T2 Constant: Temperature & Mass Pressure & Mass Volume & Mass Mass Relationship:Inverse: P = V Direct: T = V Direct: T = P Variable Rearranged: V2=P1xV1 P2 P2 P2=P1xV1 V2 V2 V2=V1xT2 T1 T1 P2=P1xT2 T1 T1 V2=V1xP1xT2 P2xT1 P2xT1 P2=V1xP1xT2 V2xT1 V2xT1 T2=P2xV2xT1 P1xV1 P1xV1

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Memory Game “What remains constant?” Boyle’s = “Boiling”Boyle’s = “Boiling” (Temperature constant)(Temperature constant) Charles’s = Charlie watches TV.Charles’s = Charlie watches TV. (Pressure constant)(Pressure constant) Gay Lussac’s = GV Gas volumeGay Lussac’s = GV Gas volume (Volume constant)(Volume constant)

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Boyle’s Law Constants: Mass & TemperatureConstants: Mass & Temperature Measured under Isothermic conditionsMeasured under Isothermic conditions Constant temperatureConstant temperature Difficult to accomplishDifficult to accomplish P 1 x V 1 = P 2 x V 2 Opposite of Isothermic: “Adiabatic”Opposite of Isothermic: “Adiabatic” means a varying temperaturemeans a varying temperature

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Boyle’s Law Inverse relationship:Inverse relationship: P 1 x V 1 = P 2 x V 2 As pressure exerted on a gas is increased, volume will decrease.As pressure exerted on a gas is increased, volume will decrease. As pressure exerted on a gas is decreased, volume will increase.As pressure exerted on a gas is decreased, volume will increase.

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Boyle’s Law Solve for the unknown :Solve for the unknown : P 1 x V 1 = P 2 x V 2 P 1 x V 1 = P 2 x V 2 P 1 x V 1 = P 2 x V 2 (both known) (one known & one unknown) (both known) (one known & one unknown)

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NBRC Question You have 3 liters of gas at 770 mmHg. The volume is changed to 2.5 liters. (The mass and temperature are constant.) Which of the following statements would be true concerning this situation?You have 3 liters of gas at 770 mmHg. The volume is changed to 2.5 liters. (The mass and temperature are constant.) Which of the following statements would be true concerning this situation? I.The pressure has increased II.The pressure has decreased III.The pressure is now 924 mmHg IV.The pressure is now 641.7 V.The pressure has not changed

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Calculation P 1 x V 1 = P 2 x V 2P 1 x V 1 = P 2 x V 2 V 1 = 3 liters of gasV 1 = 3 liters of gas P 1 = 770 mmHgP 1 = 770 mmHg V 2 = 2.5 liters (volume decrease)V 2 = 2.5 liters (volume decrease) P 2 = ______________?P 2 = ______________? Rearrange the formula P 2 = P 1 xV 1 = V 2 V 2 increase or decrease?

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Choose an answer I The pressure will increaseI The pressure will increase II The pressure will decreaseII The pressure will decrease III The pressure will be 924 mmHgIII The pressure will be 924 mmHg IV The pressure will be 641.7IV The pressure will be 641.7 V The pressure will not changeV The pressure will not change a. I & II b. I & III c. II & III d. II & IV e. V only

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Practice Sibberson’s Practical Math for RC:Sibberson’s Practical Math for RC: Chapter 2: Boyle’s Law, pgs, 17-19, Sample Problems Fourth Set.Chapter 2: Boyle’s Law, pgs, 17-19, Sample Problems Fourth Set.

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Problem #1 P 1 x V 1 = P 2 x V 2P 1 x V 1 = P 2 x V 2 V 1 =6.4LV 1 =6.4L P 1 = 720 mmHgP 1 = 720 mmHg V 2 = 4.75LV 2 = 4.75L P 2 = __________? increase or decrease?P 2 = __________? increase or decrease? Rearrange the formula P 2 = P 1 xV 1 = V 2 V 2

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Examples Closed syringeClosed syringe Close off the end of a syringe and pull back.Close off the end of a syringe and pull back. Vacuum is formed with pressure decrease and volume increase.Vacuum is formed with pressure decrease and volume increase. Normal breathingNormal breathing Muscle contraction and inspiration causes decreased pressure in the pleural space and lungs.Muscle contraction and inspiration causes decreased pressure in the pleural space and lungs. Decreased pressure yields volume movement into the lungs and increase in volume.Decreased pressure yields volume movement into the lungs and increase in volume.

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Temp constant Pressure change = Volume change

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Charles’s Law Constants: Mass & PressureConstants: Mass & Pressure Direct Relationship – as temperature increases, volume increases

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Charles’s Law Rearrange the formula to find V 2Rearrange the formula to find V 2

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NBRC Question If you have 2 liters of a gas at 37°C and 752 mmHg and you change the temperature to 68°C without changing the pressure (constant pressure is Charles’s Law), what is the new volume of gas? Do you expect the volume to increase or decrease?If you have 2 liters of a gas at 37°C and 752 mmHg and you change the temperature to 68°C without changing the pressure (constant pressure is Charles’s Law), what is the new volume of gas? Do you expect the volume to increase or decrease? A 2.2 LitersA 2.2 Liters B 1.8 litersB 1.8 liters C 2 litersC 2 liters D 2.4 litersD 2.4 liters E 1.6 litersE 1.6 liters

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Temperature Scales When working with gas laws – always convert temperature to Kelvin.When working with gas laws – always convert temperature to Kelvin. ° Celsius (C) + 273 ° = ° Kelvin (K)° Celsius (C) + 273 ° = ° Kelvin (K)

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Calculation

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Practice Sibberson’s Practical Math for RC:Sibberson’s Practical Math for RC: Chapter 2: Charles’s Law, pgs, 19 - 20, Sample Problems Fifth Set.Chapter 2: Charles’s Law, pgs, 19 - 20, Sample Problems Fifth Set.

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Examples Balloon filled with airBalloon filled with air Put in refrigerator and it shrinksPut in refrigerator and it shrinks Put by heater and it expandsPut by heater and it expands Pulmonary Function TestingPulmonary Function Testing Patient exhales warm gas (37 ° C) into cold spirometer (room temp).Patient exhales warm gas (37 ° C) into cold spirometer (room temp). Measured gas volume will be less than actual volume in the lungs.Measured gas volume will be less than actual volume in the lungs. Measured volume must be corrected from ATPS to BTPS.Measured volume must be corrected from ATPS to BTPS.

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Gay-Lussac’s Law Constants: Mass & VolumeConstants: Mass & Volume Direct Relationship – as temperature increases, pressure increases

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Gay-Lussac’s Law Rearrange the formula to find P 2Rearrange the formula to find P 2

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NBRC Question You have 1.5 liters of a gas at 40° C and 750 mmHg pressure. The temperature of the gas is changed to 25° C without changing the volume (constant volume is Gay-Lussac’s Law), what is the new pressure of gas? Do you expect the pressure to increase or decrease?You have 1.5 liters of a gas at 40° C and 750 mmHg pressure. The temperature of the gas is changed to 25° C without changing the volume (constant volume is Gay-Lussac’s Law), what is the new pressure of gas? Do you expect the pressure to increase or decrease? A The new pressure will increase by a factor of 25A The new pressure will increase by a factor of 25 B The new pressure will increase by a factor of 15B The new pressure will increase by a factor of 15 C 417 mmHg will be the new pressureC 417 mmHg will be the new pressure D 714 mmHg will be the new pressureD 714 mmHg will be the new pressure E There will not be a pressure changeE There will not be a pressure change

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Temperature Scales When working with gas laws – always convert temperature to Kelvin.When working with gas laws – always convert temperature to Kelvin. ° Celsius (C) + 273 ° = ° Kelvin (K)° Celsius (C) + 273 ° = ° Kelvin (K)

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Calculation

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Calculation

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Choose an answer A. The new pressure will increase by a factor of 25 B. The new pressure will increase by a factor of 15 C. 417 mmHg will be the new pressure D. 714 mmHg will be the new pressure E. There will not be a pressure change

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Practice Sibberson’s Practical Math for RC:Sibberson’s Practical Math for RC: Chapter 2: Gay Lussac’s Law, pgs, 20 - 21, Sample Problems Sixth Set.Chapter 2: Gay Lussac’s Law, pgs, 20 - 21, Sample Problems Sixth Set.

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Examples Gas cylinderGas cylinder Exposure to increased temperatures will cause the pressure in the cylinder to riseExposure to increased temperatures will cause the pressure in the cylinder to rise Bicycle tiresBicycle tires On a hot day the tire pressure will be higher than the pressure on a cold dayOn a hot day the tire pressure will be higher than the pressure on a cold day Automobile tiresAutomobile tires After driving a car for a while the tire pressure will increase as the tires heat up.After driving a car for a while the tire pressure will increase as the tires heat up.

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Combined Gas Law Mass is the only constantMass is the only constant This formula can replace all previous.This formula can replace all previous.

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Temperature & Pressure & Volume Relationships

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Guidelines Before doing any calculationsBefore doing any calculations Must correct temperature to KelvinMust correct temperature to Kelvin Before doing any calculationsBefore doing any calculations Must subtract water vaporMust subtract water vapor Use the “Temperature & Humidity Chart”Use the “Temperature & Humidity Chart”

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Sibberson Math Book – page 24

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Sibberson Math Book – page 25

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Set up a chart before you set up your formula P 1 – P H 2 O = ___P 1 – P H 2 O = ___ V 1 = ___V 1 = ___ T 1 (convert to °K) = ____T 1 (convert to °K) = ____ P 2 – P H 2 O = ___ V 2 =___ T 2 (convert to ° K) = ____ Fill in chart then set up formula:

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NBRC Question A gas is at 42 ° C and 760 mmHg pressure. It occupies a volume of 2.5 liters. The temperature is decreased to 37 ° C and the volume decreases to 2 liters. What is the new pressure? (decreased or increased?)A gas is at 42 ° C and 760 mmHg pressure. It occupies a volume of 2.5 liters. The temperature is decreased to 37 ° C and the volume decreases to 2 liters. What is the new pressure? (decreased or increased?) Set up the tableSet up the table Change temp. to KelvinChange temp. to Kelvin Subtract P H 2 O (if indicated)Subtract P H 2 O (if indicated) Rearrange formulaRearrange formula Solve for unknownSolve for unknown

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Set up a chart before you set up your formula P 1 – P H 2 O = ___P 1 – P H 2 O = ___ V 1 = ___V 1 = ___ T 1 (convert to °K) = ____T 1 (convert to °K) = ____ P 2 – P H 2 O = ___ V 2 =___ T 2 (convert to ° K) = ____ Fill in chart then set up formula:

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Practice Sibberson’s Practical Math for RC:Sibberson’s Practical Math for RC: Chapter 2: Combined Law, pgs, 22 - 26, Sample Problems Seventh & Eighth Set.Chapter 2: Combined Law, pgs, 22 - 26, Sample Problems Seventh & Eighth Set. Seventh set is dry gasesSeventh set is dry gases Eighth set is gases with water vaporEighth set is gases with water vapor

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Problem #1 page 26 (vapor) On hand is a gas volume of 5.8 L, at a temp. of 32C, and an atmospheric pressure of 722 mmHg, ATPS. Find the new volume if the gas was measured at STPD. P 1 – P H 2 O = ___P 1 – P H 2 O = ___ V 1 = ___V 1 = ___ T 1 (convert to °K) = ____T 1 (convert to °K) = ____ P 2 – P H 2 O = ___P 2 – P H 2 O = ___ V 2 =___V 2 =___ T 2 (convert to ° K) = ____T 2 (convert to ° K) = ____

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5. Universal Gas Law P 1 xV 1 = nRTP 1 xV 1 = nRT n = Gram molecular weight (mass)n = Gram molecular weight (mass) R = 22.4 L (molar volume)R = 22.4 L (molar volume) All parameters can varyAll parameters can vary PressurePressure TemperatureTemperature VolumeVolume MassMass Used in situations where mass is varyingUsed in situations where mass is varying Not used in Respiratory TherapyNot used in Respiratory Therapy

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Gas Law - Summary Table Law:Boyle’sCharles’s Gay Lussac’s Combined Formula: P 1 xV 1 =P 2 xV 2 V 1 = V 2 T 1 T 2 P 1 = P 2 T 1 T 2 P 1 xV 1 = P 2 xV 2 T 1 T 2 T 1 T 2 Constant: Temperature & Mass Pressure & Mass Volume & Mass Mass Relationship:Inverse: P = V Direct: T = V Direct: T = P Variable Rearranged: V 2 =P 1 xV 1 P 2 P 2 P 2 =P 1 xV 1 V 2 V 2 V 2 =V 1 xT 2 T 1 T 1 P 2 =P 1 xT 2 T 1 T 1 V 2 =V 1 xP 1 xT 2 P 2 xT 1 P 2 xT 1 P 2 =V 1 xP 1 xT 2 V 2 xT 1 V 2 xT 1 T 2 =P 2 xV 2 xT 1 P 1 xV 1 P 1 xV 1

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