2Number of Particles Increases Defining Gas PressureHow are number of particles and pressure related?Pressure –force per unit area that particles exert on walls of their containerGas particles collide with walls = greater pressurePressure is directly proportional to number of particles.Number of Particles IncreasesPressure Increases
3Temperature & Pressure Higher temperature results in more kinetic energy!IF the volume of container remains constant and IF the amount of gas remains constant:the pressure of a gas increases in direct proportion to the Kelvin temperature.(Kelvin Temp = Celsius Temp + 273)Volume of a gas at constant pressure is directly proportional to Kelvin temp.Pressure of Gas IncreasesKelvin Temperature Increases
5Devices to Measure Pressure Barometer: an instrument that measures pressure exerted by the atmosphere.Invented in 1600’s by an Italian scientist,Evangelista TorricelliHeight of column ofmercury shows the atmospheric pressure.(atm)
6Atmospheric PressureWe live at the bottom of an ocean of air; highest pressure occurs at the lowest altitudes!Standard Atmosphere is pressure that supports a 760 mm column of mercury.1.00 atm = 760 mm Hg
7Devices to Measure Pressure Pressure Gauge: instrument used to measure pressure inside a tire or oxygen tank.Tire PressureBlood Pressure
8Absolute PressureWhen measuring tire pressure; you measure pressure ABOVE atmosphere pressure. Recommended pressures for tires are gauge pressures.Absolute pressure – the TOTAL pressure of all gases including the atmosphere.Q: How would you figure it for an inflated tire?A: Add barometric pressure to the gauge pressure.
9Pressure UnitsSI unit for measuring pressure is the pascal (pa) after the French physicist Blaise Pascal (1600s)A kilopascal (kPa) is 1000 pascals and is more commonly used.Equivalent Pressures1.00 atmPa101.3 kPa760 mm Hg760 Torr14.7 psi
10Sample Calculations Express 1.56 atm in kPa. Convert 801 mm Hg to Pa. How many psi are equivalent to 95.6 kPa?
11Answers 101.3 kPa 1.56 atm 801 mm Hg 95.6 kPa X = 158 kPa 1.00 atm 14.7 psiX=13.9 psi101.3 kPa
12Dalton’s Law of Partial Pressures The pressure exerted by each gas in a mixtureThe total pressure of a mixture of gases is equal to the sum of the partial pressures of the component gasesDalton’s Law:PT = P1 + P2 + P3 + …
13PracticeCalculate the partial pressure in mm Hg exerted by the four main gases in air at 760 mm Hg: nitrogen, oxygen, argon and carbon dioxide. Their abundance by volume is 78.08%, 20.95%, 0.934% and 0.035%, respectively.N2= mm HgO2= mm HgAr = 7.10 mm HgCO2= 0.27 mm Hg
14Gases Collected by Water Displacement Gases produced in the lab are often collected by the displacement of water in a collection bottleWater vapor will be present in the collected gas, and it exerts a pressureWater vapor pressure = PH20Water vapor pressure increases with temperature (Appendix A, Table-8)Pressure of the dry gasP atm = P gas + P H20so… P gas = P atm – P H2O
15PracticeA student has stored mL of neon gas over water on a day when the temperature if 27.0 °C. If the barometer in the room reads mm Hg, what is the pressure of the neon gas in its container?P atm = P Ne + P H2OP Ne = P atm – P H2OP Ne = mm Hg – 26.7 mm Hg=716.6 mm Hg
17Pressure & Volume are Inversely Proportional! In the 1600s, Robert Boyle did many experiments involving gases.He did these experiments at constant temperature.if pressure increases, volume decreasesif pressure decreases, volume increasesPressure & Volume are Inversely Proportional!
19Boyle’s Law V1P1=V2P2 Where: V1 = initial volume P1 = initial pressure V2 = final volumeP2 = final pressure
20Kinetic Explanation of Boyle’s Law As volume is reduced, number of particles and temperature remains constant but number of collisions with the walls of the container increases.There is a smaller area of space for the same number of particles to move around, so pressure increases.
22(5.5 L) x (1.6 atm) = (x L) x (1.2 atm) PracticeIf you have 5.5 L of gas at a pressure of 1.6 atm, and the pressure changes to 1.2 atm, what is your new volume?V1P1 = V2P2(5.5 L) x (1.6 atm) = (x L) x (1.2 atm)x = 7.3 L
23Temperature & Volume are Directly Proportional! Jacques Charles did experiments concerning gases held at constant pressure, while varying temperature.As Kelvin temperature increases, volume increases.As Kelvin temperature decreases, volume decreases.Temperature & Volume are Directly Proportional!
25Charles’s Law V1 V2 T1 T2 = Where: V1 = initial volume T1 = initial temperatureV2 = final volumeT2 = final temperature=
26Kinetic Explanation of Charles’s Law When a gas is heated, its temperature increases, which means the kinetic energy of the particles has increased.Then the particles begin to move faster, which causes its volume to increase.The reverse occurs as the temperature begins to fall.
27Practice3.0 L of Helium gas is in a balloon at 22 C and a pressure of 760 mm Hg. If the temperature rises to 31 C and the pressure remains constant, what will the new volume be?(remember to convert any temperatures to KELVIN!!!)V V2T T23.0 L V2( C) ( C )V2 = (3.0 L x 304 K) / 295 KV2 = 3.1 L==
28Pressure & Temperature From the prior relationships of volume & pressure, and temperature & volume, it could be concluded that a relationship exists between pressure & temperature.For a given mass of a dry gas, if the volume is constant, the pressure is directly proportional to the Kelvin temperaturePressure & Temperature are Directly Proportional!
30Gay-Lussac’s Law P1 P2 T1 T2 = Where: P1 = initial pressure T1 = initial temperatureP2 = final pressureT2 = final temperature=
31PracticeAt 27 C, Helium gas is in a balloon at pressure of 760 mm Hg. If the temperature rises to 31 C, what will the new pressure be?(remember to convert any temperatures to KELVIN!!!)P P2T T2760 mm Hg P2( C) ( C )P2 = (760 mm Hg x 304 K) / 300 KP2 = 770 mm Hg==
32Combined Gas LawAll 3 Gas Laws require one variable to be held constant.How can we solve a problem when all 3 variables; volume, pressure & temperature change?Since 2 out of the 3 laws always have a variable in common, there should be a way to relate these laws into one formula.This new formula is called the Combined Gas Law.
33Combined Gas Law P1 V1 = P2 V2 T1 T2 Gay-Lussac’s LawP1 V1 = P2 V2T T2Where: P1, V1 & T1 are initial valuesP2, V2 & T2 are final values*0C & 1 atm = Standard Temperature & Pressure, or STPBoyle’s LawCharles’s Law
34Practice154 mL of Carbon Dioxide gas is at a pressure of 121 kPa and a temperature of 117C. What volume would this gas occupy at STP? (Remember to convert your temps to Kelvin!!!)1 atm = kPaP1V1/ T1 = P2V2/ T2(154 mL)(121 kPa) = (101.3 kPa)(V2)(117C + 273) (0C + 273)V2 = (154 mL)(121 kPa)(273 K)(390 K)(101.3 kPa)V2 = 129 mL
3511.3 Gas Volumes & the Ideal Gas Law Chapter 11 Gases11.3 Gas Volumes & the Ideal Gas Law
36The Law of Combining Gas Volumes If one volume of water, H2O, is decomposed, one volume of oxygen will be formed and 2 volumes of hydrogen will be formed.How can 3 volumes be formed from only 1 initial volume?1 L H2O1 L O21 L H21 L H2++
37The Law of Combining Gas Volumes The law of combining volumes states that in chemical reactions involving gases, the ratio of the gas volumes is a small whole number.All of the gases are at the same temperature & pressure, each of the identical flasks contains the same number of molecules. Notice how the combining ratio:2 volumes H2 : 1 volume O2 : 2 volumes H2O leads to a result in which all the atoms present initially are accounted for in the product.
38The Law of Combining Gas Volumes Avogadro was the first to study this and concluded a water molecule is composed of particles.We now know that a water molecule is composed of 2 hydrogen atoms & 1 oxygen atom. When a molecule of water breaks down, it breaks down according to the ratio of particles that compose it; 2 volumes of H2 & 1 volume of O2 from 1 volume of H2O.
39The Law of Combining Gas Volumes My principle states that equal volumes of gases at the same temp & pressure contain equal numbers of particles.He reasoned that the volume of a gas depends on the number of gas particles, provided the temperature & pressure are constant.
40The Law of Combining Gas Volumes Under the same conditions of temperature and pressure, the volumes of reacting gases and their gaseous products are expressed in ratios of small whole numbers2 L H2 + 1 L O2 → 2 L H2O (g)2 volumes H2 + 1volume O2 → 2 volumes H2O (g)1 volume H2 + 1 volume Cl2 → 2 volumes HCl1 volume HCl + 1 volume NH3 → NH4Cl (s)
41Avogadro’s LawFor a gas at constant temperature and pressure, the volume is directly proportional to the number of moles of gas (at low pressures).V = ana = proportionality constantV = volume of the gasn = number of moles of gas
42Standard Molar VolumeEqual volumes of all gases at the same temperature and pressure contain the same number of molecules.- Amedeo Avogadro
44PracticeYou are planning an experiment that requires mol of nitrogen monoxide gas at STP. What volume would you need?mol x 22.4 L = 1.30 L1 mol
45Gas Stoichiometry Volume-Volume Calculations Assume: All products and reactants are at the same temp and pressureUnless otherwise stated, assume STPSolve by normal stoichiometric processesVolume ratios are the same as mole ratios
46Volume-Mass and Mass-Volume Calculations Order of CalculationsYou are given a gas volume and asked to find a mass:gas volume A →moles A →moles B → mass BYou are given a mass and asked to find a gas volume:mass A → moles A →moles B →gas volume B
47Ideal Gas Law PV = nRT P = pressure in atm V = volume in liters n = molesR = proportionality constant= L∙ atm/ mol·KFor units of kPa, L & K:R = 8.31 kPa ∙ LMol ∙ KT = temperature in Kelvin
48Calculate the Value of R Use all standard values!P = 1 atmV = 22.4 Ln = 1 moleT = 273 KTry substituting different standard pressures to obtain different values of R
49= 2.88 mol x 0.0821 (atm∙L/mol∙K) x 295 K PracticeA 2.07 L cylinder contains 2.88 mol of helium gas at 22.0 °C. What is the pressure in atmospheres of the gas in the cylinder?PV = nRTP = nRTV= 2.88 mol x (atm∙L/mol∙K) x 295 K2.07 L= 33.7 atm
51Variations on the Ideal Gas Law n = mass (m)molar mass (M)So replace n with m/MIf PV = nRT thenPV = mRTMSo rearrange for MM = mRTPV
52Variations on the Ideal Gas Law D = mass (m)volume (V)So replace m / V with DIf M = mRT thenVPM = DRTP
53Density and the Ideal Gas Law Combining the formula for density with the IdealGas law, substituting and rearranging algebraically:M = Molar MassP = PressureR = Gas ConstantT = Temperature in Kelvin
54PracticeAt 28°C and atm, 1.00 L of a gas has a mass of 5.16 g. What is the molar mass of this gas?What is the molar mass of a gas if 0.427g of the gas occupies a volume of 125 mL at 20.0°C and atm?What is the density of a sample of ammonia gas if the pressure is atm and the temp is 63.0°C?The density of a gas was found to be 2.0 g/L at 1.50 atm and 27°C. What is the molar mass of the gas?What is the density of argon gas at a pressure of 551 torr and a temp of 25°C?131 g/mol83.8 g/mol0.572 g/L33 g/mol1.18 g/L
58Graham’s LawDensity can replace molar mass in Graham’s formula, since density is directly proportional to molar mass.Isotopes of elements can be separated by vaporizing the element, and allowing it to effuse.The heavier isotope effuses more slowly than the lighter isotope
59PracticeAt 25 °C, the average velocity of oxygen molecules is 420 m/s. What is the average velocity of helium atoms at the same temperature?Rate of O2 is 420 m/s = √MHeRate of He √MO2420 m/s = √4 g/molx √32 g/mol420 m/s =xx = 1188 m/s ≈ 1200 m/s