Gas Laws

Gases No definite shape or volume Easily compressible Kinetic Theory of Matter - All particles are moving all the time.

What do we know about gas particles? Can be either molecules or atoms; e.g. He, O2, C3H8 Very far apart from one another. Between particles is empty space. No attractive or repulsive forces between particles. Move randomly. Move at high speeds (O2 at 20oC moves at 1700 km/h). Travel in straight paths. Only change direction when collide with another particle/object. Collide elastically (no kinetic energy lost).  Ideal Gas

Gas Pressure The force exerted by a gas per unit of surface area.  Created by the collision of gas particles with a surface.

Atmospheric Pressure Atmospheric Pressure: created by the gases that make up Earth’s atmosphere.  Atmospheric pressure decreases as elevation increases (lower density of gases).  Measured using a Barometer.

Units of Pressure SI Unit = pascal (Pa) Other units: atmospheres (atm) millimeters of mercury (mmHg) torr pounds per square inch (psi) Standard Pressure: 101.3 kPa = 1 atm = 760 mmHg = 760 torr = 14.7 lb/in2 (psi) Rmv psi

Pressure Conversion Practice 7.31 psi = _______ mmHg 7.31 psi x 760 mm Hg = 378 mm Hg 14.7 psi 1140 torr = _______ kPa 1140 torr x 101.3 kPa = 152 kPa 760 torr 19.0 psi = ________ kPa 19.0 psi x 101.3 kPa = 131 kPa 202 kPa = ________ atm 202 kPa x 1 atm = 1.99 atm 101.3 kPa Rmv psi

Temperature Temperature: average kinetic energy of particles The faster the particles are moving, the higher the temperature. Kelvin temperature is directly proportional to the average kinetic energy of the particles of the substance. Particles at 200K have twice the average KE of particles at 100K. Absolute Zero: KE = 0; all motion of particles stops  TK = TC + 273

Vacuum empty space  no particles no pressure A vacuum pump is a device that removes gas molecules from a sealed volume in order to leave behind a partial vacuum

Gas Laws P1V1 P2V2 T1 T2 = (FOR A FIXED AMOUNT OF GAS) (COMBINED GAS LAW)

Boyle’s Law Boyle’s Law: At constant temperature, the pressure and volume of a gas are inversely proportional. P1V1 = P2V2 Graph:

Boyle’s Law

Boyle’s Law Conceptual Problems If the volume of a gas is decreased by half, what happens to its pressure? Pressure is doubled 2) If the pressure tripled, what must have happened to the volume of the gas? Volume decreases by a third If the volume doubles, what happens to pressure? Pressure decreases by half

Boyle’s Law -. Both Pressures must be in the same unit Boyle’s Law - *Both Pressures must be in the same unit. *Both Volumes must be in the same unit. Math Problems The volume of a gas at 99 kPa is 300 mL. If the pressure is increased to 188 kPa, what will be the new volume? 99 ( 300) = 188 V2 158 mL = V2 2) The pressure of a sample of helium in a 1.0-L container is 0.988 atm. What is the new pressure if the sample is placed in a 2.0-L container? 0.988 (1) = P2 (2) 0.494 atm = P2

Cartesian Diver How does it work???

Charles’s Law Charles’s Law: At constant pressure, the volume of a gas is directly proportional to its Kelvin temperature. V1 = V2 T1 T2 Graph:

Charles’s Law

Liquid Nitrogen

Charles’s Law Conceptual Problems If the temperature of a gas is doubled, what must happen to volume in order for pressure to remain constant? Pressure is doubled 2) If the volume of a gas decreases to one-third its original volume, what happens to the temperature in order for pressure to remain constant? Temperature decreases one-third

Charles’s Law The Math… The Kelvin temperature of a 3.0-L sample of gas is lowered from 353 K to 303 K. What will be the resulting volume of this gas? 3.0 = V2 353 303 3.0(303) = 353V2 2.58 L = V2 2) A gas at 89oC occupies a volume of 0.67 L. At what Celsius temperature will the volume increase to 1.12 L? Change temp to K: 89 + 273 = 362 K 0.67 = 1.12 362 T2 0.67T2 = 1.12 (362) T2 = 605 K Change temp back to Celsius: 605 = C + 273 332 oC = T2

Gay-Lussac’s Law Gay-Lussac’s Law: At constant volume, the pressure of a gas is directly proportional to its Kelvin temperature. P1 = P2 T1 T2

Gay-Lussac’s Law What happens to pressure if temperature increases and volume is held constant? Pressure increases The pressure in an automobile tire is 1.88 atm at 25oC. What will be the pressure if the temperature warms up to 37oC?

Combined Gas Law Combined Gas Law: for a fixed amount of gas. P1V1 = P2V2 T1 T2   STP = 273 K (0 oC), 1 atm

Use gas laws to solve the following problems A gas occupies 12.3 liters at a pressure of 40.0 mmHg. What is the volume when the pressure is increased to 60.0 mmHg? The temperature of a 4.00 L sample of gas is changed from 10.0 °C to 20.0 °C. What will the volume of this gas be at the new temperature if the pressure is held constant? If a gas is cooled from 323.0 K to 273.15 K and the volume is kept constant what final pressure would result if the original pressure was 750.0 mmHg?

Combined Gas Law Conceptual Problems What happens to temperature if volume and pressure are both doubled? Temperature is multiplied by 4 What happens to pressure if volume and temperature are both tripled? Temp increases by multiple of 9 What must happen to volume if pressure is halved and temperature is doubled? Volume is multiplied by 4

Combined Gas Law Math Problems A helium-filled balloon at sea level has a volume of 2.1 L at 0.998 atm and 36oC. If it is released and rises to an elevation at which the pressure is 0.9 atm and the temperature is 28oC, what will be the new volume of the balloon? V1 = 2.1 L V2 = ? P1 = 0.998 atm P2 = 0.9 atm T1 = 36 + 273 = 309 K T2 = 28 + 273 = 301 K V2 = 2.27L At STP, a sample of gas occupies 30 mL. If the temperature is increased to 30 oC and the entire gas sample is transferred to a 20 mL container what will be the gas pressure inside the container? P1 = 1 atm P2 = ? T1 = 273 K T2 = 30 + 273 = 303 K V1 = 30 mL V2 = 20 mL P2 = 1.67 atm

Ideal Gas Law n = number of moles Ideal Gas Law – Amount of Gas Varies PV = nRT n = number of moles R = Gas constant (see reference tables for different values)

Ideal Gas Law What pressure is exerted by 0.450 mol of a gas at 25oC if the gas is in a 0.650-L container? PV = nRT P = ? P (.650) = .450(0.0821)(298) V = 0.650 L .650P = 11 n = 0.450 mol P = 16.9 atm T = 25 + 273 = 298 K R = 0.0821 L-atm/(mol K) 2) Determine the volume occupied by 0.582 mol of a gas at 15oC if the pressure is 81.8 kPa.

Ideal Gases vs Real Gases What we know about Ideal Gases: No attractive/repulsive forces Collide elastically (no loss of KE) Ideal gas behavior occurs at HIGH temps and LOW pressure. This keeps gases moving and far apart, causing no intermolecular forces Real Gases: Attractive/repulsive forces are present Collide in-elastically More collisions will occur at HIGH pressures Attractive/repulsive forces increase as temperatures DECREASE

Ideal Gas Law Problems How many moles of gas are contained in 890.0 mL at 21.0 °C and 750.0 mmHg pressure?

At what pressure would 0.150 mole of nitrogen gas at 23.0 °C occupy 8.90 L?

Calculate the volume 3. 00 moles of a gas will occupy at 24 Calculate the volume 3.00 moles of a gas will occupy at 24.0 °C and 762.4 mmHg.

What volume will 1.27 moles of helium gas occupy at STP?

Avogadro’s Law Avogadro’s Law – the amount of gas (# of moles) is directly proportional to the volume of the gas. n1 = n2 V1 V2

Avogadro’s Law Assuming that pressure and temperature remain constant, what happens to the volume of a gas if the number of moles doubles? Volume doubles If you have two moles of a gas in a 4-liter container, how many moles of the gas would occupy a 3-liter container and retain the same pressure and temperature.

Mixtures of Gases Dalton’s Law of Partial Pressures: the total pressure of a mixture of gases is equal to the sum of the pressures of all the gases in the mixture. Ptotal = P1 + P2 + P3 + … Partial Pressure of a Gas: the portion of the total pressure contributed by a single gas.

Dalton’s Law of Partial Pressures What is the partial pressure of hydrogen gas in a mixture of hydrogen and helium if the total pressure is 600 mmHg and the partial pressure of helium is 439 mmHg? PT = P1 + P2 600 = 439 + P2 161 mmHg = P2

Dalton’s Law Problem Ex. A mixture of neon and argon gases exerts a total pressure of 2.39 atm.   The partial pressure of the neon alone is 1.84 atm, what is the partial pressure of the argon?

Dalton’s Partial Pressure Example A synthetic atmosphere is created by blending 2 mol percent CO2, 0.2 mol O2 and 1.5 mol N2. If the total pressure is 750 torr, calculate the partial pressure of each component. (Hint: What percent of the mixture is each gas?)

Dalton’s Partial Pressure Example Consider the flask diagramed below with the following pressures: 492 torr for H2 and 286 torr for N2. What are the final partial pressures of H2 and N2 after the stopcock between the 2 flask is opened? (Assume the final volume is 3.00L) What is the total pressure in torr?

Gas Laws Question 1996 FRQ Represented above are five identical balloons, each filled to the same volume at 25°C and 1.0 atmosphere pressure with the pure gases indicated. Which balloon contains the greatest mass of gas? Explain. (b) Compare the average kinetic energies of the gas molecules in the balloons. Explain. (c) Which balloon contains the gas that would be expected to deviate most from the behavior of an ideal gas? Explain. (d) Twelve hours after being filled, all the balloons have decreased in size. Predict which balloon will be the smallest. Explain your reasoning. CO2 All the same He

Bellwork Complete the following problems: 1. If 4 moles of a gas are at a pressure of 5.4 atm and have a volume of 120 L, what is the temperature? 2. My car has an internal volume of 2600 L. If the sun heats my car from 20oC to 55oC, what will the pressure inside my car be? (Assume the initial pressure was 760 mmHg). How many moles of gas are in my car?