Chapter 5 Gases. Chapter 5: Phenomena. Properties of Gases. Properties of Gases. Pressure. Pressure

Size: px

Start display at page:

Download "Chapter 5 Gases. Chapter 5: Phenomena. Properties of Gases. Properties of Gases. Pressure. Pressure"

Samuel Heath
5 years ago
Views:

Chapter 5: Phenomena Phenomena: To determine the

observations/measurements about different gases.

(atm) Odor Temperature ( C) Cl 2 Yellow 1.0 24.4 70.

5 Bleach Like 25 C CH 4 Colorless 0.5 12.2 16.0426 1.

0 Odorless 25 C H 3 Colorless 1.0 24.4 17.0307 1.

5 Feline Urine 25 C O 2 Brown 0.5 12.2 46.005 1.

0 Pungent 25 C Xe Colorless 1.0 24.4 131.29 1.

0 Odorless 919 C Mystery 1.0 24.4 1.0 25 C Mystery 12.

moles, and temperature are needed to classify a gas.

The ideal gas laws can be explained using a model of a

Equations of States Gas Stoichiometry Dalton s Law of

and Diffusion Properties of Gases Properties of Gases

In addition, many compounds with low molar masses (HCl,

Bulk Matter: Forms of matter consisting of large numbers

The properties of a gas sample emerge from the

particles. Properties of Gases Compressible.

1 Chapter 5: Phenomena Phenomena: To determine the properties of gases scientists recorded various observations/measurements about different gases. Analyze the table below looking for patterns between the gases. Use these patterns to fill in the information for the mystery gas. Gas Color Amount (mol) Volume (L) Molar Mass Pressure (atm) Odor Temperature ( C) Cl 2 Yellow Bleach Like 25 C Cl 2 Yellow Bleach Like 25 C CH 4 Colorless Odorless 25 C CH 4 Colorless Odorless 25 C H 3 Colorless Feline Urine 25 C H 3 Colorless Feline Urine 25 C O 2 Brown Pungent 25 C O 2 Brown Pungent 25 C Xe Colorless Odorless 25 C Xe Colorless Odorless 919 C Mystery C Mystery C Big Idea: The pressure, volume, number of moles, and temperature are needed to classify a gas. Knowing 3 of these quantities allows us to calculate the forth, using the ideal gas law. Generally these properties are independent of gas type. The ideal gas laws can be explained using a model of a gas in which the molecules are in ceaseless random motion and widely spread out. 2 Chapter 5 Gases Properties of Gases Pressure Other Equations of States Gas Stoichiometry Dalton s Law of Partial Pressures The Kinetic Model of Gases Effusion and Diffusion Properties of Gases Properties of Gases Eleven elements are gases under standard conditions. In addition, many compounds with low molar masses (HCl, CH 4, C 3 H 8 ) are also gases under standard conditions. Bulk Matter: Forms of matter consisting of large numbers of molecules. The properties of a gas sample emerge from the collective behavior of vast numbers of its individual particles. Properties of Gases Compressible. Fill up the space that is available (this implies that the molecules are moving quickly in a chaotic motion). ote: All elements that are gases at room temperature temperatures are diatomic with the exception of the 6 noble gases, which are monatomic. 3 4 Pressure Pressure A barometer is used to measure the pressure of the atmosphere. The pressure of the atmosphere is balanced by the pressure exerted by the column of mercury. The height of the column is proportional to the atmospheric pressure. Therefore, by measuring the height of the column, we can monitor the pressure of the atmosphere. P=dhg (a) An open-tube manometer. The pressure inside the apparatus to which the narrow horizontal tube is connected pushes against the external pressure. In this instance, the pressure inside the system is lower than the atmospheric pressure by an amount proportional to the difference in heights of the liquid in the two arms. (b) The pressure in the adjoining apparatus is proportional to the difference in heights of the liquid in the two arms. The space inside the closed end is a vacuum

2 Pressure Common Units of Pressure Units Conversion to atm Temperature and Moles Constant Boyle s Law: For a fixed amount of gas under constant temperature, the volume is inversely proportional to pressure. Pa* mm Hg Torr psi in Hg Pa = 1 atm 760 mm Hg = 1 atm 760 torr = 1 atm 14.7 psi = 1 atm in Hg = 1 atm Mathematically 1 *The SI derived unit of pressure is Pa. ote: A change that occurs at constant temperature is referred to as an isothermal change. 7 8 Pressure and Moles Constant Charles s Law: For a fixed amount of gas under constant pressure, the volume varies linearly with the temperature. Mathematically Temperature Conversions Units Conversion to Kelvin Kelvin (K)* Celsius ( C) Fahrenheit ( F) *SI unit ote: Temperature conversions involve both multiplication/division and addition/subtraction, therefore, be very careful when using a unit other than Kelvin. ote: A change that occurs at constant pressure is referred to as an isobaric change Implications of Charles s Law A balloon containing 1.0 L of air at 25 C is put in liquid nitrogen which is at a temperature of -196 C. What is the final volume of the balloon?

3 Pressure and Temperature Constant Avogadro s Law: At constant pressure and temperature, the volume of a gas varies linearly with the number of moles. Mathematically PV=nRT Boyle s, Charles's, and Avogadro s Law are just special cases of ideal gas law Boyle s Law Charles s Law Avogadro s Law How do they get R? Three pistons all with different gases. (P = 1 atm, T = K, n = 1 mol) Student Question What is the volume (in L) occupied by 35.2 g of nitrogen gas at 35 C and atm? Helpful Information: He 2 O 2 = = =24.5L R= Ideal Gas Constant (P(atm),V(L), n(mol) and T(K)) (P(Pa),V(m3 ), n(mol) and T(K)) a) 26.8 L b) 18.7 L c) 21.8 L d) 32.6 L e) one of the above Other Equations of State Equation of State: A mathematical expression relating the pressure, volume, temperature, and amount of substance present in a sample. ote: The ideal gas law is an example of an equation of state. Limiting Law: A law that is accurately obeyed only at the limit of a property, which is when a property (the pressure of a gas, for example) is made very small. ote: The ideal gas law is a limiting law

Other Equations of State Other Equations of State A common procedure in chemistry to

equation (such as nrt in PV=nRT of the ideal gas law) are just the leading (and

Virial Equation: 1 B,C, are called the second virial coefficient, third virial coefficient

The virial coefficients are found by fitting experimental data and are temperature

Parameter a corrects for attractions (intermolecular forces) between particles; particles

Parameter b corrects for the size of the particle; it can be thought of as representing the

0322 Kr 2.32 0.0398 Xe 4.19 0.0511 H 2 0.244 0.0266 2 1.39 0.0391 O 2 1.36 0.0318 Cl 2 6.

0428 Dalton s Law of Partial Pressure Dalton wondered if he had a certain amount of oxygen

60 atm and he had another container of the same size of nitrogen that had a pressure of 0.

pressure would be. He found that the pressure would be 1.00 atm.

mixture would exert if it alone occupied the container.

$mixture expressed as a fraction of the total amount of particles in the mixture.$ compared with the distances between them that the volume of the individual particles can be

compared with the distances between them that the volume of the individual particles can be

The collisions of the particles with the walls of the container are the cause of the

4 Other Equations of State Other Equations of State A common procedure in chemistry to improve the ideal gas law is to suppose that the terms on the right-hand side of an equation (such as nrt in PV=nRT of the ideal gas law) are just the leading (and predominant) term of a more complicated expression. Virial Equation: 1 B,C, are called the second virial coefficient, third virial coefficient and so on. The virial coefficients are found by fitting experimental data and are temperature dependent. Parameter a corrects for attractions (intermolecular forces) between particles; particles with strong intermolecular forces (large molecules with many electrons)have larger a values. Parameter b corrects for the size of the particle; it can be thought of as representing the volume of an individual molecule Gas a b He e Ar Kr Xe H O Cl CO CH Dalton s Law of Partial Pressure Dalton wondered if he had a certain amount of oxygen in a container that has a pressure of 0.60 atm and he had another container of the same size of nitrogen that had a pressure of 0.40 atm, if he combined the two gases in a third container of the same size, what the pressure would be. He found that the pressure would be 1.00 atm. Dalton s Law of Partial Pressure Partial Pressure (P x ): The pressure that a gas (X) in a mixture would exert if it alone occupied the container. Law of Partial Pressures: The total pressure of gases is the sum of the partial pressures of its components. Mole Fraction (χ): The amount of particles (molecules, atoms, or ions) of a substance in a mixture expressed as a fraction of the total amount of particles in the mixture Assumptions Made for the Kinetic Model of Gases 1) The particles are so small compared with the distances between them that the volume of the individual particles can be assumed to be negligible (zero). 2) The particles are in constant motion. The collisions of the particles with the walls of the container are the cause of the pressure exerted by the gas. 3) The particles are assumed to exert no forces on each other; they are assumed to neither attract nor repel each other. 4) The average kinetic energy of a collection of gas particles is assumed to be directly proportional to the Kelvin temperature of the gas. Purpose: Want to show that ideal gas law and kinetic model of gases are consistent with each other PV n T Calculate the Pressure in a Rectangular Prism (Kinetic Model) 1) P F= Force, A=Area 2 z y x A x = Area of a side on x F A y = Area of a side on y (ewton's second law) A z = Area of a side on z p=momentum ( u=velocity)

Goal: Calculate Change in Momentum 3) Calculate of Δp of 1 molecule

p before hits wall p mu p after hits wall p m u Change in p p m u mu

speed) p p 2mu col = number of molecules that collide with wall

distributed pos = number of molecules that could hit wall V pos =

rectangular prism tot = total number of molecules ote: V tot is the

expressions for the rest of the variables.

which particles have the potential of hitting the wall (V pos ) x u

A x A u t Goal: Calculate Change in Momentum 8) Plug col into Δp tot

on 1 side of rectangle prism 7) Plug expression into pos F A mu t V

we originally calculated the change in momentum it was with respect

When we calculate the force, we need the change in momentum with

27 28 Goal: Calculate Pressure 10) Calculate pressure on 1 side of

12) Calculate P tot ote: The pressure inside the container is

5 Goal: Calculate Change in Momentum 3) Calculate of Δp of 1 molecule hitting 1 of the walls. p before hits wall p mu p after hits wall p m u Change in p p m u mu 2mu 4) Calculate p for multiple molecules (traveling at the same speed) p p 2mu col = number of molecules that collide with wall Goal: Calculate Change in Momentum 5) How many molecules collide with wall in time period Δt? Kinetic Model: particles in random motion, therefore, roughly evenly distributed pos = number of molecules that could hit wall V pos = the volume that those particles are in V tot = total volume of rectangular prism tot = total number of molecules ote: V tot is the same volume used in the ideal gas law but we need to find expressions for the rest of the variables Goal: Calculate Change in Momentum 6) What is the volume in which particles have the potential of hitting the wall (V pos ) x u t x max = max distance away from wall and still collide with side V A x A u t Goal: Calculate Change in Momentum 8) Plug col into Δp tot p 2mu A u t 2V 2mu A mu t V Goal: Calculate Force 9) Calculate force on 1 side of rectangle prism 7) Plug expression into pos F A mu t V A mu t V Problem: Half of the molecules in that area are ote: When we originally calculated the change in momentum it was with respect to moving toward the wall and half are moving away. the molecules. When we calculate the force, we need the change in momentum with respect to the wall, therefore, the sign must be flipped Goal: Calculate Pressure 10) Calculate pressure on 1 side of the rectangular prism A mu P F A V A mu V Goal: Calculate Pressure 12) Calculate P tot ote: The pressure inside the container is constant. P P mu V 11) Remove requirement that all molecules are traveling at the same speed. P mu V ote: A line over a variable represents the average value. 12) Change to overall velocity instead of velocity in x u u u 3u u u u P mu V m V

6 Goal: Calculate Pressure 14) Change to number of moles A = Avogadro s Constant Goal: Calculate Pressure 15) Kinetic Model: The average kinetic energy of a collection of gas particles is assumed to be directly proportional to the Kelvin temperature of the gas ote: The variables boxed in green are proportional to the kinetic energy and the variables boxed in red are constants. Kinetic Theory Maxwell Distribution ( ) Δ = umber of molecules with a speeds in the narrow range between u and u+ ΔU 4 f(u) = Maxwell distribution of speeds James Clerk Maxwell Wrote the equations that unified electricity, magnetism, and optics. The heavier the atom, the slower the average speed and the closer the speeds are to the average speed. As the temperature increases, the average speed increases and the spread of speeds widens Most Probable Velocity (u mp ) 0solve for u Average Velocity (u ave ) Root Mean Square Velocity (u rms ) Student Question Consider three 1.0-L flasks at STP. Flask A contains He gas, flask B contains O 2 gas, and flask C contains H 2 gas. In which flask do the gas particles have the lowest average kinetic energy? a) Flask A b) Flask B c) Flask C d) All are the same

Effusion and Diffusion Effusion and Diffusion Diffusion:

Effusion: The escape of a substance (particularly a gas)

Determining the relationship between rates of effusion of

1 1 Divide the two quantities by each other.

rate of effusion of a gas is inversely proportional to

ote: This law was determined experimentally.

A sample of an unknown gas effuses in 8.2 minutes.

same temperature and pressure effuses in 4.0 minutes.

Helpful Information: 83.80, 39.95, 352.03, 20.18, and 159.

6 b) Br 2 c) Ar d) e e) one of the Above otice that the

HCl. 39 40 Take Away From Chapter 5 Take Away From

The ideal gas law can be explained using a model of a gas

42 Know how to use : Boyle s Law 1 1 2 2 Charles's Law

(11,33,34,36,37,40,43,55,56) Know the condition in which

7 Effusion and Diffusion Effusion and Diffusion Diffusion: The spreading of one substance through another substance. Effusion: The escape of a substance (particularly a gas) through a small hole. Determining the relationship between rates of effusion of different substances. 1 1 Divide the two quantities by each other. Graham s Law of Effusion: At constant temperature, the rate of effusion of a gas is inversely proportional to the square root of its molar mass. ote: This law was determined experimentally. 1 1 ote: r Effusion and Diffusion Student Question A sample of an unknown gas effuses in 8.2 minutes. An equal volume of krypton in the same apparatus at the same temperature and pressure effuses in 4.0 minutes. What is the likely identity of the gas? Helpful Information: 83.80, 39.95, , 20.18, and Effusion and Diffusion H 3 (g) +HCl(g) H 4 Cl(s) a) UF 6 b) Br 2 c) Ar d) e e) one of the Above otice that the ammonium chloride initially forms closer to the end with HCl Take Away From Chapter 5 Take Away From Chapter 5 41 Big Idea: The pressure, volume, number of moles, and temperature are needed to classify a gas. Knowing 3 of these quantities allows us to calculate the forth by using the ideal gas law. Generally these properties are independent of gas type. The ideal gas law can be explained using a model of a gas in which the molecules are in ceaseless random motion and widely spread out. Properties of Gases Pressure (22) Know how to convert between different pressure units. Know the conditions of STP (1 atm and 0 C) and SATP (1 atm and 25 C). umbers correspond to end of chapter questions. 42 Know how to use : Boyle s Law Charles's Law (41) Avogadro s Law (42) Ideal gas Law (11,33,34,36,37,40,43,55,56) Know the condition in which the ideal gas law is a good approximation. (93) Other Equations of State Know the advantages and disadvantages of the Virial equation. Know how to use the Van der Waal equation and what the Van der Waal constants correct for. (91,92) Gas Stoichiometry (8) Be able to use the gas laws to perform stoichiometry problems. (60,62,65,66,73,119) umbers correspond to end of chapter questions. 7

8 Take Away From Chapter 5 Dalton s Law of Partial Pressure Be able to calculate the partial pressures of gases. (29,46,49,127) χ Know what assumptions are made for kinetic model of gases. Know the relationship between kinetic energy, temperature, and velocity.(79,80) (81) Know how the shape of the Maxwell distribution of speeds changes with mass and temperature. (94) Know the difference and how to calculate u rms, u mp, and u ave. (82,83,86,99) Take Away From Chapter 5 Effusion and Diffusion Know the difference between effusion and diffusion Be able to use the effusion equation: (89,90) The time equation only works if the number of particles that effused are the same Be able to use the diffusion equation: 43 umbers correspond to end of chapter questions. 44 umbers correspond to end of chapter questions. 8

Chapter 5: Phenomena. Chapter 5: Gases. Molar Mass. Volume (L) Amount (mol) Pressure (atm) Temperature ( C) Odor

Chapter 5: Phenomena. Chapter 5: Gases. Molar Mass. Volume (L) Amount (mol) Pressure (atm) Temperature ( C) Odor Chapter 5: Phenomena Phenomena: To determine the properties of gases scientists recorded various observations/measurements about different gases. Analyze the table below looking for patterns between the