AN INTRODUCTION To Gases

What is a GAS? Solid Liquid Gas

A gas is a collection of molecules that move about freely!

FAST & THE FURIOUS!

IDEAL GASES vs. REAL GASES Particles in an ideal gas… –have no volume. –have elastic collisions. –are in constant, random, straight-line motion. –don’t attract or repel each other. –have an average kinetic energy directly related to Kelvin temperature.

IDEAL GASES vs. REAL GASES Particles in a REAL gas… –have their own volume –attract each other Gas behavior is most IDEAL… –at low pressures –at high temperatures –in nonpolar atoms/molecules

Standard Temperature & Pressure 0°C 273 K 1 atm kPa STP

Standard Ambient Temperature & Pressure 10°C 283 K 1 atm kPa SATP

Properties of a Gas A gas fills all of its container.

Gases are fluids (like liquids). –no attraction Gases have very low densities. –lots of empty space

Properties of a Gas Gases can be compressed. –no volume = lots of empty space

Properties of a Gas Gases undergo diffusion & effusion. –random motion

The physical characteristics of all gases are the same. VOLUME (V) The size of the container holding the gas. Always measured in LITERS

TEMPERATURE (T) The average amount of kinetic energy of the molecules of the gas. Always measured in KELVINS.

PRESSURE (P) The amount of force the gas exerts on the walls of the container. Measured in ATMOSPHERES.

760 mm of Hg 760 torr 29.9 in. of Hg 1 Atmosphere 14.7 lbs. per sq. in. CONVERSIONS All Equal Evangelista Torricelli

Pressure Which shoes create the most pressure?

Lab: Determining Weight of a Car

The physical characteristics of all gases are the same. # of ATOMS or MOLECULES (n) Measured in MOLES x 10^23

Lab: Gas Physical Relationships Interactive

PHYSICAL GAS RELATIONSHIPS PRESSUREVOLUME

hits 9 sec 1 hit sec = 18 hits 9 sec 2 hits sec = Seconds

V=0.5, P=2 V=0.1, P=10 V=10, P=0.1 V=6, P=5 V=3, P=10 V=30, P=2

The Gas Laws Boyle’s Law

Lab: Boyle’s Law Interactive

Boyle’s Law P V PV = k

Sample Problem A sample of gas occupies a volume of 47.3 liters at 20ºC when the pressure of 30 mm Hg. If the pressure is raised to 75 mm Hg, the sample will occupy ____ liters. Step 1: List all of your givens. P 1 = 30 mm Hg V 1 = 47.3 liters P 2 = 75 mm Hg V 2 = ? liters

Sample Problem A sample of gas occupies a volume of 47.3 liters at 20ºC when the pressure of 30 mm Hg. If the pressure is raised to 75 mm Hg, the sample will occupy ____ liters. Step 2: State & solve the equation. P 1 V 1 = P 2 V 2 (30)(47.3) = (75) V 2 V 2 = 18.9 liters

PHYSICAL GAS RELATIONSHIPS VOLUMETEMPERATURE

The Gas Laws Charles’ Law

V T Charles’ Law

Lab: Charles Law

Sample Problem A 250 cm^3 sample of neon is collected at 44.0ºC. Assuming constant pressure, what would be the volume at standard pressure? Step 1: List all of your givens. T 1 = 317K (ºC + 273) V 1 = 250 cm^3 T 2 = 273K V 2 = ? cm^3

Sample Problem A 250 cm^3 sample of neon is collected at 44.0ºC. Assuming constant pressure, what would be the volume at standard pressure? Step 2: State & solve the equation. T 1 V 2 = T 2 V 1 (250)(273) = (317) V 2 V 2 = 220 cm^3

PHYSICAL GAS RELATIONSHIPS PRESSURETEMPERATURE

Physical Gas Relationships Temperature (T) goes down… Pressure (p) goes down.

15 psi, 300 K 30 psi 3 psi 1 psi 600 K 60 K 20 K Gay-Lussac

P T Gay-Lussac’s Law

P T P 1 V 1 T 2 = P 2 V 2 T 1

Sample Problem P 1 V 1 T 2 = P 2 V 2 T 1 A gas at STP is cooled to -185ºC. What pressure, in atmospheres, will it have at this temperature if its volume remains constant?

GIVEN: P 1 = 1 atm. T 1 = = 273K P 2 = ? T 2 = -185°C = 88K WORK: P 1 V 1 T 2 = P 2 V 2 T 1 Sample Problem A gas at STP is cooled to -185ºC. What pressure, in atmospheres, will it have at this temperature if its volume remains constant? GAY-LUSSAC’S LAW PP TT (1 atm)(88K) = (?)(273K) P 2 = 0.32 atm.

Lab: Pressure Chamber Interactive

hits 9 sec 1 hit sec = Seconds 27 ºC = 300 K 0 K

hits 4.5 sec 2 hits sec = Seconds 27 ºC = 300 K 327 ºC = 600 K 0 K

The Ideal Gas Law PV = nRT P = Pressure (atm) V = Volume (l) n = Number of Moles R = Gas Constant T = Temperature (K)

Lab: Determining “R”

P is pressure measured in atmospheres. V is volume measured in Liters n is moles of gas present. R is a constant that converts the units. It's value is atmL/molK T is temperature measured in Kelvin. Simple algebra can be used to solve for any of these values. P = nRT V = nRT n = PV T = PV R = nT V P RT nR PV

Pressure=1 atmosphere Volume=1 Liter n = 1 mole R= What is the temperature?

Sample Problem What volume does one mole of a gas occupy at 1.00 atm of pressure and K? Step 1: Convert Celsius to Kelvin.

What volume does one mole of a gas occupy at 1.00 atm of pressure and K? Step 2: List the Given Quantities and the Unknown. P = 1.00 atm V = ? n = 1 R = atmL/molK T = K

Sample Problem What volume does one mole of a gas occupy at 1.00 atm of pressure and K? V = nRT/P V = (1.00)(0.0821)(273.15)/1.00 V = 22.4 liters Step 3: Choose the Correct Formula & Solve.

GIVEN: V 1 = 473 cm 3 T 1 = 36°C = 309K V 2 = ? T 2 = 94°C = 367K WORK: P 1 V 1 T 2 = P 2 V 2 T 1 Gas Law Review Problems A gas occupies 473 cm 3 at 36°C. Find its volume at 94°C. CHARLES’ LAW TT VV (473 cm 3 )(367 K)=V 2 (309 K) V 2 = 562 cm 3

GIVEN: V 1 = 100. mL P 1 = 150. kPa V 2 = ? P 2 = 200. kPa WORK: P 1 V 1 T 2 = P 2 V 2 T 1 Gas Law Review Problems A gas occupies 100. mL at 150. kPa. Find its volume at 200. kPa. BOYLE’S LAW PP VV (150.kPa)(100.mL)=(200.kPa)V 2 V 2 = 75.0 mL

GIVEN: V 1 = 7.84 cm 3 P 1 = 71.8 kPa T 1 = 25°C = 298 K V2 = ?V2 = ? P 2 = kPa T 2 = 273 K WORK: P 1 V 1 T 2 = P 2 V 2 T 1 (71.8 kPa)(7.84 cm 3 )(273 K) =( kPa) V 2 (298 K) V 2 = 5.09 cm 3 Gas Law Review Problems A gas occupies 7.84 cm 3 at 71.8 kPa & 25°C. Find its volume at STP. P TP T VV COMBINED CHARLES’ & BOYLE’S LAW

GIVEN: P 1 = 765 torr T 1 = 23°C = 296K P 2 = 560. torr T 2 = ? WORK: P 1 V 1 T 2 = P 2 V 2 T 1 Gas Law Review Problems A gas’ pressure is 765 torr at 23°C. At what temperature will the pressure be 560. torr? GAY-LUSSAC’S LAW PP TT (765 torr)T 2 = (560. torr)(309K) T 2 = 226 K = -47°C

When a H 2 gas is collected by water displacement, the gas in the collection bottle is actually a mixture of H 2 and water vapor.

Dalton’s Law of Partial Pressure The total pressure of a mixture of gases equals the sum of the partial pressures of the individual gases. P total = P 1 + P

Sample Problem #1 Hydrogen gas is collected over water at 22.5°C. Find the pressure of the dry gas if the atmospheric pressure is 94.4 kPa. The total pressure in the collection bottle is equal to atmospheric pressure and is a mixture of H 2 and water vapor.

GIVEN: P H2 = ? P total = 94.4 kPa P H2O = 2.72 kPa WORK: P total = P H2 + P H2O 94.4 kPa = P H kPa P H2 = 91.7 kPa Sample Problem #1 Look up water-vapor pressure for 22.5°C. Sig Figs: Round to least number of decimal places.

A gas is collected over water at a temp of 35.0°C when the barometric pressure is torr. What is the partial pressure of the dry gas? Sample Problem #2 The total pressure in the collection bottle is equal to barometric pressure and is a mixture of the “gas” and water vapor.

GIVEN: P gas = ? P total = torr P H2O = 42.2 torr WORK: P total = P gas + P H2O torr = P gas torr P gas = torr Look up water-vapor pressure for 35.0°C. Sig Figs: Round to least number of decimal places. Sample Problem #2

Graham’s Law Effusion –P–Passing of gas molecules through a tiny opening in a container.

Lab: Effusion Interactive

Graham’s Law Diffusion –S–Spreading of gas molecules throughout a container until evenly distributed.

Rate of diffusion of a gas is inversely related to the square root of its molar mass. The equation shows the ratio of Gas A’s speed to Gas B’s speed.

Determine the relative rate of diffusion for krypton and bromine. Sample Problem #1 The first gas is “Gas A” and the second gas is “Gas B”. Relative rate mean find the ratio “v A /v B ”.

Kr diffuses times faster than Br 2. Sample Problem #1

A molecule of oxygen gas has an average speed of 12.3 m/s at a given temp and pressure. What is the average speed of hydrogen molecules at the same conditions? Sample Problem #2

Put the gas with the unknown speed as “Gas A”.

Lab: Graham’s Law Interactive