chapter 10
DESCRIPTION
asdfasdfTRANSCRIPT
![Page 1: Chapter 10](https://reader035.vdocuments.net/reader035/viewer/2022062407/55cf9768550346d033917959/html5/thumbnails/1.jpg)
Chapter 10Gases and their properties
![Page 2: Chapter 10](https://reader035.vdocuments.net/reader035/viewer/2022062407/55cf9768550346d033917959/html5/thumbnails/2.jpg)
2-1213, 14, 21, 2327-3031-33, 35, 37, 39, 41, 4349, 51, 53, 57, 59, 6163-65, 67, 69, 71, 7577, 81, 83, 85, 87, 9193, 95, 96, 97104, 108, 110, 115, 116, 117, 121, 123, 129
Recommended problems – Ch 10
![Page 3: Chapter 10](https://reader035.vdocuments.net/reader035/viewer/2022062407/55cf9768550346d033917959/html5/thumbnails/3.jpg)
Gases Assume shape and volume of container Highly compressible Easily diffuse/mix
Liquids Assume shape of container Not very compressible Easily mix
Solids Keep shape Incompressible Diffusion (if any) occurs very slowly
The nature of matter
![Page 4: Chapter 10](https://reader035.vdocuments.net/reader035/viewer/2022062407/55cf9768550346d033917959/html5/thumbnails/4.jpg)
States of Matter
The fundamental difference between states of matter is the distance between particles. Because in the solid and liquid states particles are closer together, we refer to them as condensed phases.
![Page 5: Chapter 10](https://reader035.vdocuments.net/reader035/viewer/2022062407/55cf9768550346d033917959/html5/thumbnails/5.jpg)
The States of Matter
The state of a substance at a particular temperature and pressure depends on two antagonistic entities:
--- kinetic energy of the particles (proportional to the temperature of the system)--- potential energy between particles (IM attractions/repulsions)
![Page 6: Chapter 10](https://reader035.vdocuments.net/reader035/viewer/2022062407/55cf9768550346d033917959/html5/thumbnails/6.jpg)
Pressure – a defining characteristic of a gas
Pressure is the amount of force applied to an area.
Atmospheric pressure is the weight of air per unit area.
P =FA
![Page 7: Chapter 10](https://reader035.vdocuments.net/reader035/viewer/2022062407/55cf9768550346d033917959/html5/thumbnails/7.jpg)
Pascals◦ 1 Pa = 1 N/m2
Atmospheres◦ 1 atm = 14.7 lb/in2 (psi) = 101325 Pa
Torr (or mm Hg)◦ 760 torr = 760 mm Hg = 1 atm
Units of Pressure
![Page 8: Chapter 10](https://reader035.vdocuments.net/reader035/viewer/2022062407/55cf9768550346d033917959/html5/thumbnails/8.jpg)
Normal atmospheric pressure at sea level.
Standard Pressure
• It is equal to1.00 atm760 torr (760 mm Hg)101.325 kPa
![Page 9: Chapter 10](https://reader035.vdocuments.net/reader035/viewer/2022062407/55cf9768550346d033917959/html5/thumbnails/9.jpg)
Kinetic-Molecular Theory
A model that aids in our understanding of what happens to gas particles as environmental conditions change.
![Page 10: Chapter 10](https://reader035.vdocuments.net/reader035/viewer/2022062407/55cf9768550346d033917959/html5/thumbnails/10.jpg)
1. Gases consist of large numbers of molecules that are in continuous, random motion.
2. The combined volume of all the molecules of the gas is negligible relative to the total volume in which the gas is contained.
3. Attractive and repulsive forces between gas molecules are negligible.
Tenets of Kinetic-Molecular Theory
![Page 11: Chapter 10](https://reader035.vdocuments.net/reader035/viewer/2022062407/55cf9768550346d033917959/html5/thumbnails/11.jpg)
Tenets of Kinetic-Molecular Theory
4. Energy can be transferred between molecules during collisions, but the average kinetic energy of the molecules does not change with time, as long as the temperature of the gas remains constant.
![Page 12: Chapter 10](https://reader035.vdocuments.net/reader035/viewer/2022062407/55cf9768550346d033917959/html5/thumbnails/12.jpg)
Tenets of Kinetic-Molecular Theory
5. The average kinetic energy of the molecules is proportional to the absolute temperature.
![Page 13: Chapter 10](https://reader035.vdocuments.net/reader035/viewer/2022062407/55cf9768550346d033917959/html5/thumbnails/13.jpg)
What happens to pressure when volume decreases?
What happens when volume increases?
How does KMT explain gas behavior?
![Page 14: Chapter 10](https://reader035.vdocuments.net/reader035/viewer/2022062407/55cf9768550346d033917959/html5/thumbnails/14.jpg)
What happens to volume when temperature increases?
What happens when temperature decreases?
How does KMT explain gas behavior?
![Page 15: Chapter 10](https://reader035.vdocuments.net/reader035/viewer/2022062407/55cf9768550346d033917959/html5/thumbnails/15.jpg)
What happens to volume when amount of gas (moles) increases?
What happens when amount of gas decreases?
How does KMT explain gas behavior?
![Page 16: Chapter 10](https://reader035.vdocuments.net/reader035/viewer/2022062407/55cf9768550346d033917959/html5/thumbnails/16.jpg)
Boyle Charles Avogadro
Review of General Gas Laws
![Page 17: Chapter 10](https://reader035.vdocuments.net/reader035/viewer/2022062407/55cf9768550346d033917959/html5/thumbnails/17.jpg)
Boyle’s Law
The volume of a fixed quantity of gas at constant temperature is inversely proportional to the pressure.
![Page 18: Chapter 10](https://reader035.vdocuments.net/reader035/viewer/2022062407/55cf9768550346d033917959/html5/thumbnails/18.jpg)
PV = constant [when temperature and amount of gas (moles) stays the same]
As volume decreases, the pressure increases (such that product = constant)
P1V1 = P2V2
Boyle’s Law
![Page 19: Chapter 10](https://reader035.vdocuments.net/reader035/viewer/2022062407/55cf9768550346d033917959/html5/thumbnails/19.jpg)
P and V areinversely proportional
A plot of V versus P results in a curve.Since
V = k (1/P)
This means a plot of V versus 1/P will be a straight line.
PV = k
![Page 20: Chapter 10](https://reader035.vdocuments.net/reader035/viewer/2022062407/55cf9768550346d033917959/html5/thumbnails/20.jpg)
Charles’s Law
The volume of a fixed amount of gas at constant pressure is directly proportional to its absolute temperature.
A plot of V versus T will be a straight line.
VT
= k
![Page 21: Chapter 10](https://reader035.vdocuments.net/reader035/viewer/2022062407/55cf9768550346d033917959/html5/thumbnails/21.jpg)
V/T = constant (or V = kT)
As temperature increases, volume increases.
V1/T1 = V2/T2
Charles’s Law
![Page 22: Chapter 10](https://reader035.vdocuments.net/reader035/viewer/2022062407/55cf9768550346d033917959/html5/thumbnails/22.jpg)
Avogadro’s Law
The volume of a gas at constant temperature and pressure is directly proportional to the number of moles of the gas.
Mathematically, this means V = kn
![Page 23: Chapter 10](https://reader035.vdocuments.net/reader035/viewer/2022062407/55cf9768550346d033917959/html5/thumbnails/23.jpg)
So far we’ve seen that:V 1/P (Boyle)V T (Charles)V n (Avogadro)
We can combine these to get:
V
Ideal Gas Equation
nTP
![Page 24: Chapter 10](https://reader035.vdocuments.net/reader035/viewer/2022062407/55cf9768550346d033917959/html5/thumbnails/24.jpg)
The relationship
Ideal Gas Equation
then becomes
which has the more familiar form: PV = nRT
nTP
V
nTP
V = R
![Page 25: Chapter 10](https://reader035.vdocuments.net/reader035/viewer/2022062407/55cf9768550346d033917959/html5/thumbnails/25.jpg)
Ideal Gas Equation
… where the constant of proportionality is known as R, the gas constant.
k (Boltzmann constant) = 1.381 x 10-23 J/K
Note units!
![Page 26: Chapter 10](https://reader035.vdocuments.net/reader035/viewer/2022062407/55cf9768550346d033917959/html5/thumbnails/26.jpg)
From the ideal gas law, PV=nRT, remember that
So you can use this general equation in many instances…
Using the general gas law
nTPV
R
22
22
11
11
TnVP
TnVP
![Page 27: Chapter 10](https://reader035.vdocuments.net/reader035/viewer/2022062407/55cf9768550346d033917959/html5/thumbnails/27.jpg)
The long cylinder of a bicycle pump has a volume of 1131 cm3. The outlet valve is sealed shut and the pump handle is pushed down until the volume of the air is 517 cm3. What is the resulting pressure inside the pump?
A scientist studying the properties of hydrogen at low temperatures takes a volume of 2.50 L hydrogen at atmospheric pressure and a temperature of 25.00oC and cools the gas at constant pressure to -200.00oC. What is the resulting volume of the gas?
A 5.00 L sample of Argon gas is known to contain 0.965 mol. If the amount of gas is increased by the addition of 0.835 moles, what will the new volume be (at an unchanged temperature and pressure)?
Using the general gas law
![Page 28: Chapter 10](https://reader035.vdocuments.net/reader035/viewer/2022062407/55cf9768550346d033917959/html5/thumbnails/28.jpg)
Nitric acid acts on solid copper to give NO2 and dissolved copper ions according to the equation:
Cu(s) + 4H+(aq) + 2NO3-(aq) 2NO2(g) + Cu2+(aq) + 2 H2O(l)
Suppose that 6.80 g Cu is consumed in excess acid and that the NO2 is collected at a pressure of 0.970 atm and a temperature of 45 oC. What volume of NO2 is produced?
answer 5.76L
Stoichiometry using the Ideal Gas Equation
![Page 29: Chapter 10](https://reader035.vdocuments.net/reader035/viewer/2022062407/55cf9768550346d033917959/html5/thumbnails/29.jpg)
We can derive the density of a gas, if we divide both sides of the ideal-gas equation by V and by RT.
We know thatmoles molecular mass (M) = mass
n x M = m
Density of a Gas
nV
PRT
=
![Page 30: Chapter 10](https://reader035.vdocuments.net/reader035/viewer/2022062407/55cf9768550346d033917959/html5/thumbnails/30.jpg)
Density of a GasMultiplying both sides by the molecular mass ( ) gives
And since D = m/V (=g/L) D = PM/RT
Therefore, we can know the density of a gas if we measure its pressure and temperature.
PRT
mV
=
![Page 31: Chapter 10](https://reader035.vdocuments.net/reader035/viewer/2022062407/55cf9768550346d033917959/html5/thumbnails/31.jpg)
We can manipulate the density equation to enable us to find the molar mass of an known gas:
Molar Mass
becomes
PRT
d =
dRTP =
![Page 32: Chapter 10](https://reader035.vdocuments.net/reader035/viewer/2022062407/55cf9768550346d033917959/html5/thumbnails/32.jpg)
The total pressure of a mixture of gases equals the sum of the pressures that each would exert if it were present alone.
In other words Ptotal = P1 + P2 + P3 + …
Dalton’s Law of Partial Pressures
![Page 33: Chapter 10](https://reader035.vdocuments.net/reader035/viewer/2022062407/55cf9768550346d033917959/html5/thumbnails/33.jpg)
For a mixture of gases, we sometimes use a quantity called the mole fraction, Χ:
Xi = ni/ntotal
The relationship between partial pressure, pi, and Xi is:
pi = Xi Ptotal
Mole fractions
![Page 34: Chapter 10](https://reader035.vdocuments.net/reader035/viewer/2022062407/55cf9768550346d033917959/html5/thumbnails/34.jpg)
Partial Pressures
When one collects a gas over water, there is water vapor mixed in with the gas.To find only the pressure of the desired gas, one must subtract the vapor pressure of water from the total pressure.
![Page 35: Chapter 10](https://reader035.vdocuments.net/reader035/viewer/2022062407/55cf9768550346d033917959/html5/thumbnails/35.jpg)
From Kinetic-Molecular Theory, all molecules have the same average kinetic energy at the same temperature (regardless of their mass).
The KE of a molecule is given by ½ mv2
The avg KE depends upon T(Kelvin)
The avg KE of all molecules in a gas is related to urms
Molecular speed
![Page 36: Chapter 10](https://reader035.vdocuments.net/reader035/viewer/2022062407/55cf9768550346d033917959/html5/thumbnails/36.jpg)
The relationship between mass, urms, and T is:urms =
where
Note: urms has a slightly different value from the average speed
Root-mean-square speed
![Page 37: Chapter 10](https://reader035.vdocuments.net/reader035/viewer/2022062407/55cf9768550346d033917959/html5/thumbnails/37.jpg)
Boltzmann Distributions
![Page 38: Chapter 10](https://reader035.vdocuments.net/reader035/viewer/2022062407/55cf9768550346d033917959/html5/thumbnails/38.jpg)
Diffusion
The spread of one substance throughout a space or throughout a second substance.
![Page 39: Chapter 10](https://reader035.vdocuments.net/reader035/viewer/2022062407/55cf9768550346d033917959/html5/thumbnails/39.jpg)
Effusion
The escape of gas molecules through a tiny hole into an evacuated space.
![Page 40: Chapter 10](https://reader035.vdocuments.net/reader035/viewer/2022062407/55cf9768550346d033917959/html5/thumbnails/40.jpg)
Graham’s law of effusion
![Page 41: Chapter 10](https://reader035.vdocuments.net/reader035/viewer/2022062407/55cf9768550346d033917959/html5/thumbnails/41.jpg)
Real Gases
In the real world, the behavior of gases conforms to the ideal-gas equation only at certain conditions, such as relatively high temperature and low pressure.
![Page 42: Chapter 10](https://reader035.vdocuments.net/reader035/viewer/2022062407/55cf9768550346d033917959/html5/thumbnails/42.jpg)
Deviations from Ideal Behavior
The assumptions made in the kinetic-molecular model break down at high pressure and/or low temperature.
![Page 43: Chapter 10](https://reader035.vdocuments.net/reader035/viewer/2022062407/55cf9768550346d033917959/html5/thumbnails/43.jpg)
Deviations from Ideal Behavior
![Page 44: Chapter 10](https://reader035.vdocuments.net/reader035/viewer/2022062407/55cf9768550346d033917959/html5/thumbnails/44.jpg)
The ideal-gas equation can be adjusted to take these deviations from ideal behavior into account.
Corrections for Nonideal Behavior
The corrected ideal-gas equation is known as the van der Waals equation.
![Page 45: Chapter 10](https://reader035.vdocuments.net/reader035/viewer/2022062407/55cf9768550346d033917959/html5/thumbnails/45.jpg)
Whereas ideal gas equation posits
van der Waals accounts for attraction btw molecules AND finite volume of molecules by
van der Waals Equation
![Page 46: Chapter 10](https://reader035.vdocuments.net/reader035/viewer/2022062407/55cf9768550346d033917959/html5/thumbnails/46.jpg)
The van der Waals Equation
) (V − nb) = nRTn2aV2(P +