. Pressure CHAPER GASES AND KINEIC-MOLECULAR HEORY. Boyle s Law: he -P Relationship 3. Charles Law: he - Relationship 4. Standard &P 5. he Combined Gas Law Equation 6. Avogadro s Law and the Standard Molar olume 7. Summary of Gas Laws: he Ideal Gas Equation 8. Dalton s Law of Partial Pressures 9. he Kinetic-Molecular heory 0. Diffusion and Effusion of Gases. Real Gases: Deviations from Ideality
Pressure Pressure is force per unit area. lb/in N/m Gas pressure as most people think of it. Atmospheric pressure is measured using a barometer. Definitions of standard pressure 76 cm Hg 760 mm Hg 760 torr atmosphere 0.3 kpa Hg density 3.6 g/ml
Boyle s Law: he olume-pressure Relationship /P or k (/P) or P k P k for one sample of a gas. P k for a second sample of a gas. k k for the same sample of a gas at the same. hus we can write Boyle s Law mathematically as P P 3
Boyle s Law: he olume-pressure Relationship At 5 o C a sample of He has a volume of 4.00 x 0 ml under a pressure of 7.60 x 0 torr. What volume would it occupy under a pressure of.00 atm at the same? P P P P ( 760 torr)( 400 ml) 50 torr.00 0 ml 4
35 Charles Law: he olume-emperature Relationship; he Absolute emperature Scale 30 5 0 5 0 5 0 Gases liquefy before reaching 0K 0 50 00 50 00 50 300 350 400 absolute zero -73.5 0 C olume (L) vs. emperature (K) 5
Charles Law: he olume-emperature Relationship; he Absolute emperature Scale Charles s law states that the volume of a gas is directly proportional to the absolute temperature at constant pressure. Gas laws must use the Kelvin scale to be correct. Relationship between Kelvin and centigrade. o K C + 73 6
Charles Law: he olume-emperature Relationship; he Absolute emperature Scale Mathematical form of Charles law. k and or k or k however the k's are equalso k in the most useful form 7
Charles Law: he olume-emperature Relationship; he Absolute emperature Scale A sample of hydrogen, H, occupies.00 x 0 ml at 5.0 o C and.00 atm. What volume would it occupy at 50.0 o C under the same pressure? 5 + 73 98 50 + 73 33.00 0 ml 33 K 98 K 08 ml 8
Standard emperature and Pressure Standard temperature and pressure is given the symbol SP. Standard P.00000 atm or 0.3 kpa Standard 73.5 K or 0.00 o C 9
he Combined Gas Law Equation Boyle s and Charles Laws combined into one statement is called the combined gas law equation. Useful when the,, and P of a gas are changing. Boyle' s Law Charles' Law For a P P given sample of gas : he combined gas law is : P k P P 0
he Combined Gas Law Equation A sample of nitrogen gas, N, occupies 7.50 x 0 ml at 75.0 0 C under a pressure of 8.0 x 0 torr. What volume would it occupy at SP? P 348 80 Solve 750 K torr for ( 80 torr )( 750 ml )( 73 K ) ( 760 torr )( 348 K ) ml 67 P ml 73 760 P P? K torr
he Combined Gas Law Equation A sample of methane, CH 4, occupies.60 x 0 ml at 3 o C under a pressure of 0.500 atm. At what temperature would it occupy 5.00 x 0 ml under a pressure of.0 x 0 3 torr? P 60 ml 0.500 atm 380 torr P 500 00 ml torr 305 K P P 85 K 580 ( 305 K )( 00 torr )( 500 ml ) ( 380 torr )( 60 ml ) o C?
Avogadro s Law and the Standard Molar olume Avogadro s Law states that at the same temperature and pressure, equal volumes of two gases contain the same number of molecules (or moles) of gas. If we set the temperature and pressure for any gas to be SP, then one mole of that gas has a volume called the standard molar volume. he standard molar volume is.4 L at SP. his is another way to measure moles. For gases, the volume is proportional to the number of moles. 3
Summary of Gas Laws: he Ideal Gas Law Boyle s Law - /P (at constant & n) Charles Law (at constant P & n) Avogadro s Law n (at constant & P) Combine these three laws into one statement n/p Convert the proportionality into an equality. nr/p his provides the Ideal Gas Law. P nr R is a proportionality constant called the universal gas constant. 4
Summary of Gas Laws: he Ideal Gas Law We must determine the value of R. Recognize that for one mole of a gas at.00 atm, and 73 K (SP), the volume is.4 L. Use these values in the ideal gas law. R P n (.00 atm )(. 4 L) (.00 mol )( 73 K) L atm 0. 08 mol K 5
Summary of Gas Laws: he Ideal Gas Law R has other values if the units are changed. R 8.34 J/mol K Use this value in thermodynamics. R 8.34 kg m /s K mol Use this later in this chapter for gas velocities. R 8.34 dm 3 kpa/k mol his is R in all metric units. R.987 cal/k mol his the value of R in calories rather than J. 6
Summary of Gas Laws: he Ideal Gas Law What volume would 50.0 g of ethane, C H 6, occupy at.40 x 0 o C under a pressure of.8 x 0 3 torr?. 40 + 73 43 K. P 80 torr ( atm/760 torr).39 atm 3. 50 g ( mol/30 g).67 mol n R P (.67 mol) 0.08 ( 43K) 3.6 L L atm molk.39 atm 7
Summary of Gas Laws: he Ideal Gas Law Calculate the number of moles in, and the mass of, an 8.96 L sample of methane, CH 4, measured at standard conditions. ( )( ) n P.00 atm 896. L R 0.08 L atm 0.400 mol CH ( K) 73 mol K 6.0 g? g CH 4 0400. mol 6.40 g mol 4 8
Summary of Gas Laws: he Ideal Gas Law Calculate the pressure exerted by 50.0 g of ethane, C H 6, in a 5.0 L container at 5.0 o C. n.67 mol and 98 K P n R P L atm mol K 5.0 L P.63 atm (.67 mol ) 0.08 ( 98 K ) 9
Dalton s Law of Partial Pressures Dalton s law states that the pressure exerted by a mixture of gases is the sum of the partial pressures of the individual gases. P total P A + P B + P C +... 0
Dalton s Law of Partial Pressures apor Pressure is the pressure exerted by a substance s vapor over the substance s liquid at equilibrium.
he Kinetic-Molecular heory he basic assumptions of kineticmolecular theory are: Postulate Gases consist of discrete molecules that are relatively far apart. Gases have few intermolecular attractions. he volume of individual molecules is very small compared to the gas s volume. Proof - Gases are easily compressible.
he Kinetic-Molecular heory Postulate Gas molecules are in constant, random, straight line motion with varying velocities. Proof - Brownian motion displays molecular motion. Postulate 3 Gas molecules have elastic collisions with themselves and the container. otal energy is conserved during a collision. Proof - A sealed, confined gas exhibits no pressure drop over time. 3
he Kinetic-Molecular heory Postulate 4 he kinetic energy of the molecules is proportional to the absolute temperature. he average kinetic energies of molecules of different gases are equal at a given temperature. Proof - Brownian motion increases as temperature increases. 4
he Kinetic-Molecular heory he kinetic energy of the molecules is proportional to the absolute temperature. he kinetic energy of the molecules is proportional to the absolute temperature. Displayed in a Maxwellian distribution. 5
he Kinetic-Molecular heory Boyle s Law P / As the increases the molecular collisions with container walls decrease and the P decreases. Dalton s Law P total P A + P B + P C +... Because gases have few intermolecular attractions, their pressures are independent of other gases in the container. Charles Law An increase in temperature raises the molecular velocities, thus the increases to keep the P constant. 6
Diffusion and Effusion of Gases Diffusion is the intermingling of gases. Effusion is the escape of gases through tiny holes. 7
Diffusion and Effusion of Gases he rate of effusion is inversely proportional to the square roots of the molecular weights or densities. R R M M or R R D D 8
Real Gases: Deviations from Ideality Real gases behave ideally at ordinary temperatures and pressures. At low temperatures and high pressures real gases do not behave ideally. he reasons for the deviations from ideality are:. he molecules are very close to one another, thus their volume is important.. he molecular interactions also become important. 9
Real Gases: Deviations from Ideality van der Waals equation accounts for the behavior of real gases at low and high P. P + na ( nb) nr he van der Waals constants a and b take into account two things:. a accounts for intermolecular attraction. b accounts for volume of gas molecules 30