Gas Laws

Physical Properties of Gases Have mass Easily compressed Fill containers completely Different gases move through each other rapidly – diffusion Exert pressure Pressure depends on temperature

The Kinetic-Molecular Theory Small particles with mass Separated by large distances In constant rapid motion Exert pressure by colliding with walls of container Elastic: collisions lose no energy of motion

The Kinetic-Molecular Theory Pressure = force per unit area More gas = more collisions = more pressure Increase temp causes increase pressure Temperature is a measure of kinetic energy KE = mv2/2 Increase velocity causes increased force on container

Measuring Gases Amount (n) in moles = mass/molar mass Volume (v) : 1L = 1000cm3 Temperature (T) – use K T(K) = T(c) + 273 Pressure (P)

Atmospheric Pressure and the Barometer Atmosphere exerts pressure Pump air out of can and see it crush Air has mass – attracted by earths gravity Force exerted on a unit area of earths surface = atmospheric pressure SI units: force = newton pressure = pascal (Pa) 1Pa = 1 newton of force per square meter Atmosphere (atm) = another unit of pressure 1 atm is close to average pressure at sea level 1 atm = 101,325 Pa or 101.3 kPa

Atmospheric Pressure and the Barometer Pressure varies with altitude: lower altitude = longer and heavier column of air Altimeter converts pressure to altitude Water vapor is lighter than nitrogen and oxygen So high water vapor = low pressure = rain storm likely.

Barometer Glass tube sealed at end, filled with mercury inverted in a reservoir of mercury. Hg in tube seeks a height so pressure exerted on surface of Hg in reservoir is balanced by pressure of Hg in column. 1 atm = 760mm up column at sea level.

Units of Pressure 1 atmosphere (atm) = 101,325 Pa 1 atm = 760 mm Hg = 760 torr 1 atm = 14.70 lb/in2 1 bar = 100,000 Pa = 0.9869 atm

Sample Problem The column of mercury in a barometer is 745 mm above the mercury reservoir at the bottom. What is the atmospheric pressure in pascals? Ans = 99,300 Pa

Practice Problems The air pressure inside the cabin of an airplane is 8.3 lb/in2. What is this pressure in atmosphere units? Ans = 0.56 atm

Practice Problems Pressure is considered the most accurate measure of storm strength, with lower pressure indicating a stronger storm. One of the lowest recorded pressures in the Western Hemisphere is 88.86 kPa. How high a column of mercury would be balanced by this atmospheric pressure? Ans = 666.5 mm Hg

Enclosed Gases Pressure of open container = pressure of atmosphere. Manometer: measures pressure in closed container.

Sample Problem You have a closed container attached to a U-tube. The mercury in the open-ended side of the tube is higher, and the difference between the heights of the mercury columns is 27 mm. Atmospheric pressure is 755 mm Hg. What is the pressure of the gas in the container in atmospheres? Ans = pressure in container is 27 + 755 mm Hg = 782 mm Hg. Convert this to atm = 1.03 atm

Practice Problems A balloon is attached to an open-ended manometer. The mercury level in the manometer is 13 mm lower on the side attached to the balloon than on the side open to the atmosphere. The pressure of the atmosphere is measured to be 755 mm Hg in a separate measurement. What is the gas pressure in the balloon? Ans = 768 mm Hg

Practice Problem Suppose you have a gas container fitted with a manometer. You measure the height of the mercury on the side of the manometer open to the atmosphere. Then the atmospheric pressure drops and you measure the height of the mercury on the open side again. Will the level of the mercury on the open side have moved, and if so, in which direction? Ans = it will have moved upward

The Gas Laws

Reminder of STP Standard temperature and pressure = 0oC or 273 K 1 atm = 760 mm Hg = 101,325 Pa

Boyle’s Law: The Pressure – Volume Relationship Robert Boyle 1627-1691 Trapped fixed amount of air, changing its pressure, and measuring its volume. Temperature was held constant.

Boyle’s Law: The Pressure – Volume Relationship Boyle found volume decrease as pressure increased. Boyle’s Law: If temp is constant, the product of pressure x volume has a constant value. PV=k1 So P1V1=P2V2 for a given amount at constant temp.

Practice Problems A gas at a pressure of 608 mm Hg is held in a container with a volume of 545 cm3. The volume of the container is then increased to 1065 cm3 without a change in temperature. Calculate the new pressure of the gas. Ans = 311 mm Hg

Sample Problem You need to fill 300 helium balloons for a party. A store that will rent a 25-L tank filled with helium gas at a pressure of 30.0 atm. Each balloon holds 2.5 L of helium at a pressure of 1.04 atm. Will one tank be enough to fill all of the balloons? Assume unchanged temperature. Ans = 290 balloons can be filled

Practice Problems A partially inflated helium weather balloon contains 150 L of gas. The balloon’s internal gas pressure is 1.0 atm when it is released. The research team wants to place a payload of measurement instruments at an altitude of 41 km, where the atmospheric pressure (and therefore the pressure inside the balloon is only 0.4 atm. How large must the balloon be to accommodate the gas volume at 41 km, assuming the gas temperature does not change and the balloon does not leak. Ans = 375L

Gay-Lussac Law P1/T1=P2/T2 Before a trip from New York to Boston, the pressure in an automobile tire was 1.8 atm at 20o C. At the end of the trip, the tire pressure gauge reads 1.9 atm. What is the new Celsius temperature in the tire? (Assume tires with constant volume.) Ans: 36 oC

Gay-Lussac Law At 120o C, the pressure of a sample of nitrogen is 1.07 atm. what will the pressure be at 205o C, assuming constant volume? Ans: 1.30 atm

Charles’s Law: The Temperature – Volume Relationship Used a cylinder with a movable piston. Immersed in water baths of different temperatures. Pressure and amount held constant.

Charles’s Law: The Temperature – Volume Relationship Calculated the lower limit for temperature to be –273.15oC Absolute zero K = oC + 273 Charles’s Law: V = k2T or k2 = V/T So V1/T1 = V2/T2

Sample Problem On a cool morning (10.0oC) a group of hot-air balloonists start filling their balloon with air, using a large fan. After the balloon’s envelope is three-fourths filled, they turn on the propane burner to heat the air. At what Celsius temperature will the air completely fill the envelope to its maximum capacity of 1700. m3. (assume constant pressure) Ans = 104oC

Practice Problems What will be the volume of a gas sample at 355 K if its volume at 273 K is 8.57 L? Assume constant pressure. Ans = 11.1 L

Practice Problems A gas can be used as a thermometer. If it is known that a sample of gas has a volume of 1.00 L at 255 K, what is the temperature if the volume of the same gas sample is changed to 0.45 L at constant pressure? Ans = 110 K

Combined Gas Law P1V1 = P2V2 T1 T2

Avogadro’s Law: The Amount – Volume Relationship Equal volumes of gases at the same temperature and pressure contain an equal number of particles. V = k3n

Dalton’s Law of Partial Pressures Dalton looked at mixtures of gases. Sum of partial pressures of all components in gas mixture = total pressure of mixture. PT = pa + pb + pc …

Sample Problem What is the atmospheric pressure if the partial pressures of nitrogen, oxygen, and argon are 604.5 mm Hg, 162.8 mm Hg, and 0.5 mm Hg, respectively? Ans = 767.8 mm Hg

Practice Problems Oxygen gas from the decomposition of potassium chlorate was collected by water displacement. The barometric pressure and the temperature during the experiment were 731.0 torr and 20.0oC, respectively. What was the partial pressure of the oxygen collected. Table A-8 gives partial pressure of water vapor Answer: 713.5 torr

Practice Problems The gases carbon dioxide, oxygen, nitrogen, neon, and krypton are mixed in a container. All gases have the same partial pressure and the total pressure in the container is 33,500 Pa. What is the partial pressure of nitrogen? Ans = 6700 Pa

The Ideal Gas Law PV = nRT Applies most of the time accept at low temperatures or high pressure. R = gas constant 0.0821 if units are atm-L/mol-K 8.314 if units are Pa-m3/mol-K 8.314 if units are J/mol-K

The Ideal Gas Law PV = nRT As n increases P increases As T increases P increases As V decreases P increases

Sample Problems How many moles of a gas at 100.oC does it take to fill a 1.00 L flask to a pressure of 1.50 atm? Ans = 0.0490 mol

Practice Problems What is the volume occupied by 9.45 g of C2H2 at STP? Ans = 8.15 L

Practice Problems A camping stove uses a 5.0 L propane tank that holds 3.0 kg of liquid C3H8. How large a container would be needed to hold the same amount of propane as a gas at 25oC and a pressure of 3.0 atm? Ans = 560 L

Gas Stoichiometry

Practice Problem An airbag inflates in less than 50 msec by the reaction of NaN3 to produce Na and nitrogen gas at 25C. NaN3  Na + N2 The volume of the airbag is about 30 liters, and it is filled to a pressure of 1.4 atm. How much NaN3 must be used for each air bag? Ans: 74.5 grams

Practice Problem Calculate the volume of methane (CH4) produced by the bacterial breakdown of 2.32 kg of sugar (C6H12O6) at 321 K and 707 torr C6H12O6  3 CH4 + 3 CO2 Ans 1095 L