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P V T Gas Laws

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Learning Objectives TLW know the variables that influence the behavior of gases (TEKS 9) TLW be able to describe interrelationships between temperature, number of moles, pressure, and volume of gases in an enclosed system (TEKS 9.A) TLW perform stoichiometric calculations to determine mass and volume relationships between reactants and products involving gases (TEKS 9.B) TLW describe the postulates of kinetic molecular theory (TEKS 9.C)

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**I. Gas Laws A. Four properties of gases 1. Volume - V 2. Pressure – P**

gases do not have a defined volume particles of a gas expand to fill their container volume is measured in L (liters) 2. Pressure – P collisions of particles with a surface P measured in atm, kPa, torr, mm Hg

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**3. Temperature – To 4. Quantity – n**

the measure of average particle speed gas particles are in constant motion To for gases are measured in K (Kelvin) 4. Quantity – n measure of how much there is of a gas MOLES!!!!! 22.4 L of gas = 1 mole

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**Postulates of Kinetic Molecular Theory**

Gases are composed of a large number of particles that behave like hard, spherical objects in a state of constant, random motion. These particles are much smaller than the distance between particles. Most of the volume of a gas is therefore empty space. There is no force of attraction between gas particles or between the particles and the walls of the container. These particles move in a straight line until they collide with another particle or the walls of the container. Collisions between gas particles or collisions with the walls of the container are perfectly elastic. None of the energy of a gas particle is lost when it collides with another particle or with the walls of the container. The average kinetic energy of a collection of gas particles depends on the temperature of the gas and nothing else.

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**Postulates of Kinetic Molecular Theory**

Check out this interactive tool which demonstrates the postulates in action

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**B. Gas laws are based mathematically. on the relationship of the four**

B. Gas laws are based mathematically on the relationship of the four properties of gas volume pressure temperature quantity

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**II. The Gas Laws (4 major ones)**

A. Boyle’s Law 1. Discovered that gas pressure and volume are related 2. If pressure is increased then volume decreases 3. Pressure and volume are inversely related 4. Meaning = whatever pressure does volume does the opposite

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NASA Video

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Boyle’s Law P1V1 = P2V2 V P

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5. Example of Boyle’s Law A sample of gas has a volume of 4.2 L and a pressure of 0.95 atm. If the pressure on the balloon increases to 1.90 atm what will the new volume be? 0.95 atm 1.90 atm 4.2 L P1V1 = P2V2 V = ? (.95 atm)(4.2L) = (1.90 atm)V2 V2 = 2.1 L

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B. Charles’ Law 1. Discovered the relationship between volume and temperature 2. If To increases then the volume increases 3. To and volume are directly proportional 4. Meaning = whatever volume does To does the exact same thing

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NASA Video

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**V1/T1 = V2/T2 oC + 273 = K Charles’ Law**

NOTE: All To must be Kelvin!!!! oC = K

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**5. Example of Charles’ Law**

Another sample of gas has a volume of 2.0 L and a To of 100 oC. If the To is increased to 200 oC, what will the new volume be? V = 2.0L V = ? 100ºC 200ºC V1/T1 = V2/T2 2.0L/(100 oC + 273) = V2/(200 oC + 273) V2 = 2.54 L KELVIN!!!!!!!!

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C. Gay-Lussac’s Law 1. Discovered the relationship between Pressure and To 2. If To increases then Pressure increases 3. To and P are directly proportional 4. Meaning = whatever To does pressure does the exact same thing

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Gay-Lussac’s Law P1/T1 = P2/T2 T P

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**Example of Gay-Lussac’s Law**

Another sample of gas has a volume of 2.0 L a To of 25 oC, and a pressure of 2.00 atm. If the To is increased to 75 oC, what will the new pressure be? 25ºC 2.00 atm V = 2.0L 75ºC V = 2.0L P = ? P1/T1 = P2/T2 2.00 atm/(25 oC + 273) = P2/(75 oC + 273) P2 = 2.34 atm

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D. Avogadro’s Law If pressure and temperature are kept constant, the volume of a gas is directly proportional to number of moles of a gas This is why a balloon gets larger as you blow it up… not the pressure 1 mole of gas = 22.4 L Mathematically speaking….. V1 = V2 n1 n2

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**Example of Avogadro’s Law**

I have a balloon with 0.25 moles of air in it and its volume is 0.30 L. If I blow it up more to 0.75 L, how many moles have I added of air? V1/n1 = V2/n L = 0.75 L = 0.63 moles 0.25 moles n2 moles

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**1. Sometimes the pressure, temperature, and/or change**

E. Combined Gas Law 1. Sometimes the pressure, temperature, and/or change 2. So must “combine” formulas from all three “dudes”. 3. Looks like this P1V1 = P2V2 T T2

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**Example of combined gas law**

8.0L of neon gas at 23 oC and 900 mm Hg is then compressed to 2.0 L and the To is raised to 225 oC. What will the new P be? P1V1/T1 = P2V2/T2 (900 mm Hg)(8.0 L)/(23 ºC + 273) = P2(2.0 L)/(225 ºC + 273) P2 = 6057 mm Hg

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**PV = nRT Where R = 0.08206 L atm/mol °K**

F. Ideal Gas Law PV = nRT Where R = L atm/mol °K

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**Web Exploration ASPIRE Animation Activity (link)**

Gas Law Investigation (link) Data Collection Sheet (link)

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**More Practice on Following Slides**

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**We will use Boyle’s Law: P1V1 = P2V2 (500.mm)(400.mL)=(250.mm)(V2)**

Sample problem #1 A gas occupies a volume of 400. mL at 500. mm Hg pressure. What will be its volume, at constant temperature, if the pressure is changed to 250 torr? (1 mm Hg = 1 torr) We will use Boyle’s Law: P1V1 = P2V (500.mm)(400.mL)=(250.mm)(V2) V2= (500)(400) = 800. mL 250

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**Sample #2 CHARLES’ LAW T V V2 = (V1T2)/T1 V2 = 562 cm3**

A gas occupies 473 cm3 at 36 °C. Find its volume at 94 °C. CHARLES’ LAW GIVEN: V1 = 473 cm3 T1 = 36°C = 309K V2 = ? T2 = 94°C = 367K T V WORK: V1/T1 = V2/T2 (473 cm3)/(309 K)=V2/(367K) V2 = (V1T2)/T1 V2 = 562 cm3

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**Sample #3 GAY-LUSSAC’S LAW P T**

A gas’ pressure is 765 torr at 23°C. At what temperature will the pressure be torr? GAY-LUSSAC’S LAW GIVEN: P1 = 765 torr T1 = 23°C = 296K P2 = 560. torr T2 = ? P T WORK: P1/T1 = P2/T2 765 torr/296K = 560torr/T2 T2 = (P2T1)/P1 T2 = 217 K

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**We will use the combined gas law:**

Sample problem #4 A gas occupies a volume of 410 mL at 27°C and 740 mm Hg pressure. Calculate the volume the gas would occupy at STP. (0 oC & 760 mm Hg) We will use the combined gas law: Oops…use Kelvin °C=300K; 0°C=273K

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**Independent Practice Calculations using four Gas Law Formulas**

Remember: oK = oC + 273 STP (Standard Temperature and Pressure) is 0oC and 760 mm Hg = 1 atm = kPa = 14.7 psi. 1 torr = 1 mm Hg 22.4 L = 1 mole of gas R = L atm/mol °K

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**Dalton’s Law of Partial Pressure**

Sum of the pressures of each gas equals total pressure of system P1 + P2 + P3 + …. + Pn = Ptotal A gas is 48% O2 & 52% N2. Total pressure is 100 kPa. What is the pressure of each gas? 100(.48) = 48 kPa for O2 and 100(.52) = 52 kPa for N2

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**Lab Gas Law Smorgasbord (link)**

In Periodic Groups, read the entire procedure Determine potential hazards, precautions to take, PPE that might be needed

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