Title: How Do Gases Behave?
1How Do Gases Behave?
2What 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?
3What 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
4MANOMETER
- 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
5What 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?
6Kinetic 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
7What 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.
8What 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.
9BOYLES LAW
V
P (at constant T)
10Slope k
V
1/P (at constant T)
1122.41 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
13What 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
14CHARLES LAW
He
CH4
H2O
V (L)
H2
T (ºC)
-273.15ºC
15Examples
- 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
16Combined 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
17Other 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)
18Gas 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?
19What 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.
20Let 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
21Gas 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)
22Examples
- 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
23Gases 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.
24Examples
- 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
250.0100 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
27Daltons 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
28Dalton'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
29The 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
30Calculating 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
33Vapor 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
37Whats 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.
38What 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.