How Do Gases Behave? - PowerPoint PPT Presentation

1 / 39
About This Presentation
Title:

How Do Gases Behave?

Description:

Title: How Do Gases Behave? Author: Karo Touloughuian Last modified by: testuser Created Date: 5/2/2006 10:13:18 PM Document presentation format: On-screen Show (4:3) – PowerPoint PPT presentation

Number of Views:102
Avg rating:3.0/5.0
Slides: 40
Provided by: KaroToul
Category:

less

Transcript and Presenter's Notes

Title: How Do Gases Behave?


1
How Do Gases Behave?
2
What is a solid, liquid or gas?
  • Help Marvin the Martian understand what a solid,
    liquid and gas are!
  • Draw what solids, liquids, gases look like
  • Describe physical/chemical properties
  • What would happen if we changed pressure?
  • What would happen if we changed temperature?

3
What is Pressure?
  • Pressure Force/Area
  • 1 atmosphere (atm)
  • 760 Torr
  • 760 mmHg
  • 1.01 Bar
  • 101,327 Pascal
  • 101.3 Kpa
  • 14.7 lbs/in2
  • Measured with
  • a barometer

4
MANOMETER
  • Column of mercury to measure pressure.
  • h is how much lower or higher the pressure is
    than outside.
  • Pgas Patm - h
  • Pgas Patm h

h
h
5
What is Temperature?
  • Average Kinetic Energy (1/2 mv2) of an atom or
    molecule
  • Measured in Fahrenheit, Celsius or Kelvin (SI)
  • F (C x 1.8) 32
  • K C 273
  • 0 Kelvin absolute zero (atom stops moving
    completely)
  • Is there a maximum temperature in the universe?

6
Kinetic Molecular Theory
  • Theory explains why ideal gases behave the way
    they do.
  • Assumptions that simplify the theory, but dont
    work in real gases.
  • The particles are so small we can ignore their
    volume.
  • The particles are in constant motion and their
    collisions cause pressure.
  • The particles do not affect each other, neither
    attracting or repelling.
  • The average kinetic energy is proportional to the
    Kelvin temperature.
  • The molecules move in straight path and all
    collisions are elastic

7
What is an Ideal Gas?
  • An ideal gas or perfect gas is a hypothetical gas
    consisting of identical particles of
  • Negligible volume
  • With no intermolecular forces
  • Atoms or molecules undergo perfectly elastic
    collisions with the walls of the container
  • Ideal gas law calculations are favored at low
    pressures and high temperatures.
  • Real gases existing in reality do not exhibit
    these exact properties, although the
    approximation is often good enough to describe
    real gases.

8
What is Boyles Law?
  • In the mid 1600's, Robert Boyle studied the
    relationship between the pressure P and the
    volume V of a confined gas held at a constant
    temperature.
  • Boyle observed that the product of the pressure
    and volume are observed to be nearly constant.
  • The product of pressure and volume is exactly a
    constant for an ideal gas.
  • P V constant
  • This relationship between pressure and volume is
    called Boyle's Law in his honor.

9
BOYLES LAW
V
P (at constant T)
10
Slope k
V
1/P (at constant T)
11
22.41 L atm
O2
PV
CO2
P (at constant T)
12
  • 20.5 L of nitrogen at 25ºC and 742 torr are
    compressed to 9.8 atm at constant T. What is the
    new volume?
  • P1V1P2V2
  • (0.98 atm)(20.5 L) (9.8 atm)(V2)
  • 20.09 atmL/9.8 atm V2
  • 2.1 L V2
  • 30.6 mL of carbon dioxide at 740 torr is
    expanded at constant temperature to 750 mL. What
    is the final pressure in kPa?
  • (30.6mL)(740Torr)(750 mL)(P2)
  • 22,644 mLTorr/750 mL P2
  • 30.2 Torr P2
  • (30.2 Torr) (1 atm/760 Torr) (101.3 kPa/1 atm)
  • 3059.3 kPa/760 4.03 kPa

13
What is Charles Law?
  • The relationship between temperature and volume,
    at a constant number of moles and pressure, is
    called Charles and Gay-Lussac's Law in honor of
    the two French scientists who first investigated
    this relationship.
  • Charles did the original work, which was verified
    by Gay-Lussac. They observed that if the pressure
    is held constant, the volume V is equal to a
    constant times the temperature T, or
  • V / T constant

14
CHARLES LAW
He
CH4
H2O
V (L)
H2
T (ºC)
-273.15ºC
15
Examples
  • What would the final volume be if 247 mL of gas
    at 22ºC is heated to 98ºC , if the pressure is
    held constant?
  • 247 ml/295 K X ml/371 K
  • 91,637 mL K 295 X K
  • 91,637 mL K/295 K X
  • 310 mL X
  • If the volume of oxygen at 21 C is 785 L, at
    what temperature would oxygen occupy 804 L?
  • 785 L/294 K 804 L/X K
  • 785 X 236,376
  • X 236,376/785
  • X 301 K 28 C

16
Combined Gas Law
  • Combining Charless Law and Boyles Law in a
    single statement
  • P1V1/T1 P2V2/T2
  • 39.8 mg of caffeine gives 10.1 mL of nitrogen gas
    at 23C and 746 mmHg. What is the volume of
    nitrogen at 0C and 760 mmHg?
  • First change temperature to Kelvin
  • V1 10.1mL P1 746 mmHg K1 296 K
  • V2 ? P2 760 mmHg K2 273
    K
  • 10.1 746/296 V2 760/273
  • V2 9.14 mL

17
Other Gas Laws
  • Gay-Lussac Law
  • At constant volume, pressure and absolute
    temperature are directly related.
  • P/T k (constant)
  • Avogadros Law
  • At constant temperature and pressure, the volume
    of gas is directly related to the number of
    moles.
  • V /n k (n is the number of moles)

18
Gas Law Summary
Law Statement Equation Constant
Boyles P inversely proportional to V PV k1 T, n
Charles V directly proportional to T V/T k2 P, n
Gay-Lussac P directly proportional to T P/T k3 V, n
Avogadros V directly proportional to n V/n k4 P, T
What equation would we get if we combined them
all?
19
What is the Ideal Gas Law?
  • Combining Boyles Law, Charles law Avogadros
    Law we derive the Ideal Gas Law
  • P V n R T
  • P Pressure (atm)
  • V Volume (L)
  • n moles (mol)
  • R Gas Constant (0.0821 L atm /mol K)
  • T Temperature (K)
  • Ideal gas law calculations are favored at low
    pressures and high temperatures
  • Tells you about a gas NOW.
  • The other laws tell you about a gas when it
    changes.

20
Let Try It!
  • Example
  • If we had 1.0 mol of gas at 1.0 atm of pressure
    at 0C (STP), what would be the volume?
  • PV nRT
  • V nRT/P
  • V (1.0 mol)(0.0821 L atm/mol K)(273 K)/(1.0
    atm)
  • V 22.41 L
  • 1 mole of ANY gas at STP will occupy 22.4 Liters
    of volume

21
Gas Density and Molar Mass
  • D m/V
  • Let M stand for molar mass
  • M m/n
  • n m/M
  • PV nRT
  • PV (m/M) RT
  • P mRT/VM (m/V)(RT/M)
  • P d RT/M
  • PM/RT d (density)

22
Examples
  • What is the density of ammonia at 23ºC and 735
    torr?
  • Units must be atm, K
  • 735 torr(1 atm/760 torr) 0.967 atm
  • 23 273 296 K
  • Molar mass of NH3 17.0 g
  • d 0.967 17.0 g
  • (0.0821 L atm/mol K)(296 K)
  • d 0.676 g / L

23
Gases and Stoichiometry
  • Reactions happen in moles
  • At Standard Temperature and Pressure (STP, 0ºC
    and 1 atm) 1 mole of gas occupies 22.42 L.
  • If not at STP, use the ideal gas law to calculate
    moles of reactant or volume of product.

24
Examples
  • Consider the following reaction
  • Suppose you heat 0.0100 mol of potassium
    chlorate, KClO3, in a test tube. How many liters
    of oxygen can you produce at 298 K and 1.02 atm?
  • Break it into 2 problems, one involving
    stoichiometry and the other using the ideal gas
    law

25
0.0100 mol KClO3 X 3 mol O2/2 mol KClO3 0.0150
mol O2 Now that you have the moles of oxygen use
the ideal gas law to calculate the volume V
nRT/P 0.0150 mol x 0.0821 L atm (K mol) x
298 K 1.02 atm V 0.360 L
26
  • Using the following reaction
  • Calculate the mass of sodium hydrogen carbonate
    necessary to produce 2.87 L of carbon dioxide at
    25ºC and 2.00 atm.
  • n PV/RT (2.00 atm)(2.87 L)
  • (0.0821 Latm/Kmol)(298 K)
  • n 0.235 mol CO2
  • 0.235 mol CO2 (1 mol NaHCO3) ( 84.0 g)
  • (1 mol CO2 )
    (1 mol NaHCO3)
  • 19.7 g NaHCO3

27
Daltons Law
  • The total pressure in a container is the sum of
    the pressure each gas would exert if it were
    alone in the container.
  • The total pressure is the sum of the partial
    pressures.
  • PTotal P1 P2 P3 P4 P5 ...
  • For each P nRT/V

28
Dalton's Law
  • PTotal n1RT n2RT n3RT ... V
    V V
  • In the same container R, T and V are the same.
  • PTotal (n1 n2 n3...)RT V
  • PTotal (nTotal)RT V

29
The Mole Fraction
  • Ratio of moles of the substance to the total
    moles.
  • symbol is Greek letter chi c
  • Because pressure of a gas is proportional to
    moles, for fixed volume and temperature then,
  • c1 n1 P1 nTotal PTotal

30
Calculating the Partial Pressure and Mole
Fraction of a Gas Mixture
  • A 1.00 L sample of dry air at 25C and 786 mmHg
    contains 0.925 g N2, plus other gases including
    oxygen, argon and carbon dioxide.
  • What is the partial pressure (in mmHg) of N2 in
    the air sample?
  • What is the mole fraction and mole percent of N2
    in the mixture?

31
  • Convert grams into moles
  • 0.925 g N2 x (1 mol N2/28.0g N2)
  • 0.0330 mol N2
  • Substitute into ideal gas law
  • PN2 nN2RT/V
  • 0.0330mol x 0.0821 Latm/Kmol x 298
  • 1.00 L
  • 0.807 atm 613 mmHg

32
  • The mole fraction of N2 in the air is
  • PN2/P 613 mmHg/786 mmHg
  • 0.780
  • Mole percent equals mole fraction x 100
  • 0.780 x 100 78
  • Air contains 78.0 mole percent of N2

33
Vapor Pressure
  • Water evaporates!
  • When that water evaporates, the vapor has a
    pressure.
  • Gases are often collected over water so the vapor
    pressure of water must be subtracted from the
    total pressure.
  • Vapor pressure varies by temperature and must be
    given in the problem or in a table.

34
  • Hydrogen gas is produced by the reaction of
    hydrochloric acid, HCl, on zinc metal
  • 2HCl (aq) Zn (s) gt ZnCl2 (aq) H2 (g)
  • The gas is collected over water. If 156 mL of
    gas is collected at 19C and 769 mmHg total
    pressure, what is the mass of hydrogen collected?

35
  • First find the Partial Pressure. The vapor
    pressure of water at 19C is 16.5 mmHg
  • P PH2 PH2O
  • PH2 P - PH2O
  • PH2 769 16.5 752 mmHg
  • Use the ideal gas law to find the moles of
    hydrogen collected.
  • P 752 mmHg x (1 atm/760 mmHg) 0.989 atm
  • V 156 mL x (1 L/1000 mL) 0.156 L
  • T 19 273 292 K
  • R 0.0821 Latm/Kmol
  • n ?

36
  • Solve for moles
  • n PV/RT
  • 0.989 x 0.156/0.0821 x 292
  • 0.00644 mol H2
  • Convert moles to grams
  • 0.00644 mol H2 x (2.02g/1 mol H2)
  • 0.0130 g H2

37
Whats Diffusion and Effusion?
  • Only a few physical properties of gases depends
    on the identity of the gas.
  • Diffusion - The rate at which two gases mix.
  • Effusion - The rate at which a gas escapes
    through a pinhole into a vacuum.

38
What is Grahams Law?
  • We know that Kinetic energy 1/2 mv2
  • If two bodies of unequal mass have the same
    kinetic energy, which moves faster?
  • The lighter one!
  • Thus, for two gases at the same temperature, the
    one with lower molecular mass will diffuse/effuse
    faster.
  • The rate of effusion/diffusion of a gas is
    inversely proportional to the square root of its
    mass.

39
  • Calculate the ratio of effusion rates of
    molecules of carbon dioxide and sulfur dioxide
    from the same container and at the same
    temperature and pressure
  • Rate of effusion of CO2 vMm SO2
  • Rate of effusion of SO2 vMm CO2
  • v64.1/44.0 1.21
  • In other words, carbon dioxide effuses 1.21 times
    faster than sulfur dioxide.
Write a Comment
User Comments (0)
About PowerShow.com