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11/10/2015
1
General, Organic, and Biological Chemistry: Structures of Life, 5/eKaren C. Timberlake
© 2016 Pearson Education, Inc.
Karen C. Timberlake
Lecture Presentation
Chapter 8
Gases
General, Organic, and Biological Chemistry: Structures of Life, 5/eKaren C. Timberlake
© 2016 Pearson Education, Inc.
Chapter 8 Readiness
Key Math Skills
• Solving Equations (1.4D)
Core Chemistry Skills
• Using Significant Figures in Calculations (2.3)
• Writing Conversion Factors from Conversion Equalities (2.5)
• Using Conversion Factors (2.6)
• Using Molar Mass as a Conversion Factor (7.5)
• Using Mole–Mole Factors (7.6)
General, Organic, and Biological Chemistry: Structures of Life, 5/eKaren C. Timberlake
© 2016 Pearson Education, Inc.
8.1 Properties of Gases
Generally molecules with fewer than five atoms from the first two periods in the periodic table are gases at room temperature. In addition, the following are also gases:
Learning Goal Describe the kinetic molecular theory of gases and the units of measurement used for gases.
• H2, N2, O2, F2, and Cl2
• oxides of the nonmetals on the upper-right corner of the periodic table: CO, CO2, NO, NO2, SO2, and SO3
• noble gases
He
Ne
Ar
Kr
Xe
Rn
FONC
S Cl
H
General, Organic, and Biological Chemistry: Structures of Life, 5/eKaren C. Timberlake
© 2016 Pearson Education, Inc.
Kinetic Molecular Theory
A gas consists of small particles that
1. move randomly with high velocities.
2. have very small attractive (or repulsive) forces between molecules.
3. occupy a much larger volume than the volume of the molecules alone.
4. are in constant motion, moving rapidly in straight lines.
5. have a Kelvin temperature proportionate to the average kinetic energy of the molecules.
Gas particles which
move in straight lines within a container, exert
pressure when they
collide with the walls of the container.
General, Organic, and Biological Chemistry: Structures of Life, 5/eKaren C. Timberlake
© 2016 Pearson Education, Inc.
Properties That Describe a Gas
Gases can be quantified in terms of four properties: pressure (P), volume (V), temperature (T), and amount of particles (n = moles).
General, Organic, and Biological Chemistry: Structures of Life, 5/eKaren C. Timberlake
© 2016 Pearson Education, Inc.
Gas Volume
The volume of a gas
• is the same as the volume of the container it occupies.
• is usually measured in liters or milliliters.
• increases with an increase in temperature at a constant pressure. Gas particles which
move in straight lines within a container, exert
pressure when they
collide with the walls of the container.
11/10/2015
2
General, Organic, and Biological Chemistry: Structures of Life, 5/eKaren C. Timberlake
© 2016 Pearson Education, Inc.
Gas Temperature
The temperature of a gas is directly related to the average kinetic energy (motion) of the molecules and is measured in the Kelvin (K) temperature scale.
**Note: The Kelvin scale must used as calculations using the
Celsius scale could result in negative volume or pressure of a
gas � that’s impossible!!!
When the temperature of a gas is
• decreased, the particles are moving more slowly and have fewer collisions.
• increased, the particles are moving faster have more collisions.
General, Organic, and Biological Chemistry: Structures of Life, 5/eKaren C. Timberlake
© 2016 Pearson Education, Inc.
Gas Pressure
Gas Pressure is a measure the number of collisions of the gas particles with the walls of its container, and the force of those collisions, and is measured in various units:
• millimeters of mercury, mmHg or torr.
• atmospheres, atm.
• pascals, Pa, or kilopascals, kPa (the SI unit of measurement)
• pounds per square inch, psi.
• At weather stations in the U.S., inches of Hg are used
General, Organic, and Biological Chemistry: Structures of Life, 5/eKaren C. Timberlake
© 2016 Pearson Education, Inc.
Gas Pressure
Gas particles in the air exert pressure on us called atmospheric pressure.
In 1643, Italian physicist EvangilistaTorricelli invented a device to measure the pressure of the atmosphere = Barometer
General, Organic, and Biological Chemistry: Structures of Life, 5/eKaren C. Timberlake
© 2016 Pearson Education, Inc.
Barometers Measure Pressure
A barometer
• measures the pressure exerted by the gases in the atmosphere.
• indicates atmospheric pressure as the height in mm of the mercury column.
760 mmHg = 1 atm = 760 Torr
The barometer was invented by
Evangelista Torricelli, at exactly 1 atmthe barometer tube measures exactly
760 mm high.
General, Organic, and Biological Chemistry: Structures of Life, 5/eKaren C. Timberlake
© 2016 Pearson Education, Inc.
Units of Pressure
General, Organic, and Biological Chemistry: Structures of Life, 5/eKaren C. Timberlake
© 2016 Pearson Education, Inc.
Atmospheric Pressure
Atmospheric pressure
• is the pressure exerted by a column of air from the top of the atmosphere to the
surface of Earth.
• decreases as altitude increases.
• about 1 atm at sea level.
11/10/2015
3
General, Organic, and Biological Chemistry: Structures of Life, 5/eKaren C. Timberlake
© 2016 Pearson Education, Inc.
Altitude and Atmospheric Pressure
Atmospheric pressure changes with variations in weather and altitude.
• On a hot, sunny day, the mercury column rises, indicating a higher atmospheric pressure.
• On a rainy day, the atmosphere exerts less pressure, which causes the mercury column to fall.
General, Organic, and Biological Chemistry: Structures of Life, 5/eKaren C. Timberlake
© 2016 Pearson Education, Inc.
Study Check
1. What is 475 mmHg expressed in atm?
A. 475 atmB. 0.625 atmC. 3.61 × 105 atm
2. The pressure in a tire is 2.00 atm. What is thispressure in mmHg?A. 2.00 mmHgB. 1520 mmHg
C. 22 300 mmHg
General, Organic, and Biological Chemistry: Structures of Life, 5/eKaren C. Timberlake
© 2016 Pearson Education, Inc.
8.2 Gas Pressure and Volume, (Boyle’s
Law)
The inverse relationship between the pressure and volume of a gas is known as Boyle’s law.
Changes occur in opposite directions. When volume increases, the pressure decreases, provided the temperature and moles of the gas remains constant.
Learning Goal Use the pressure–volume relationship (Boyle’s law) to determine the final pressure or volume when the temperature and amount of gas are constant.
The anesthetic N2O gas,
is used for pain relief.
General, Organic, and Biological Chemistry: Structures of Life, 5/eKaren C. Timberlake
© 2016 Pearson Education, Inc.
8.2 Gas Pressure and Volume, (Boyle’s
Law)
In the late 1600s, Irish chemist Robert Boyle performed experiments in order to determine the relationship of the pressure of a gas and its volume under conditions of constant pressure and amount of gas. When he graphed the pressure of a gas as a function of its volume, the result was the graph to the right
Notice that there is not a linear relationship between the variables. This downward sloping curve can indicate an inverse relationship
General, Organic, and Biological Chemistry: Structures of Life, 5/eKaren C. Timberlake
© 2016 Pearson Education, Inc.
8.2 Gas Pressure and Volume, (Boyle’s
Law)
Boyle re-graphed his data, this time plotting the pressure of the gas as a function of the inverse of its volume.
Notice the graph to the right now shows a linear relationship
So, the pressure of a gas, P, at constant temperature and amount of gas, varies directly with the inverse of its volume
General, Organic, and Biological Chemistry: Structures of Life, 5/eKaren C. Timberlake
© 2016 Pearson Education, Inc.
8.2 Pressure and Volume, (Boyle’s Law)
The inverse relationship between the pressure and volume of a gas is known as Boyle’s law.
Changes occur in opposite directions. When volume increases, the pressure decreases, provided the temperature and moles of the gas remains constant.
Mathematical Expression of Boyle’s Law: P1V1 = P2V2
11/10/2015
4
General, Organic, and Biological Chemistry: Structures of Life, 5/eKaren C. Timberlake
© 2016 Pearson Education, Inc.
Boyle’s Law
Boyle’s law states that
• the pressure of a gas is inversely related to its volume when T is constant.
• the product P × V is constant when temperature and amount of a gas is held constant
• if volume decreases, the pressure increases.
P1V1 = P2V2
General, Organic, and Biological Chemistry: Structures of Life, 5/eKaren C. Timberlake
© 2016 Pearson Education, Inc.
Boyle’s Law: PV = Constant
Pressure × volume is a constant, provided the temperature and amount of the gas remains
the same.
P1V1 = 8.0 atm × 2.0 L = 16 atm L
P2V2 = 4.0 atm × 4.0 L = 16 atm L
P3V3 = 2.0 atm × 8.0 L = 16 atm L
Boyle’s law can be stated as
P1V1 = P2V2 (T is constant.)
General, Organic, and Biological Chemistry: Structures of Life, 5/eKaren C. Timberlake
© 2016 Pearson Education, Inc.
Chemistry Link to Health:
Boyle’s Law and Breathing
During an inhalation,
• the lungs expand.
• the pressure in the lungs decreases.
• air flows toward the lower pressure in the lungs.
General, Organic, and Biological Chemistry: Structures of Life, 5/eKaren C. Timberlake
© 2016 Pearson Education, Inc.
Chemistry Link to Health:
Boyle’s Law and Breathing
During an exhalation,
• lung volume decreases.
• pressure within the lungs increases.
• air flows from the higher pressure in the lungs to
the outside.
General, Organic, and Biological Chemistry: Structures of Life, 5/eKaren C. Timberlake
© 2016 Pearson Education, Inc.
Guide to Using Gas Laws
General, Organic, and Biological Chemistry: Structures of Life, 5/eKaren C. Timberlake
© 2016 Pearson Education, Inc.
Calculations Using Boyle’s Law
Freon-12, CCl2F2, was used in refrigeration systems. What is the new volume of an 8.0 L sample of Freon gas initially at 550 mmHg after its pressure is changed to 2200 mmHg at constant temperature and moles?
STEP 1 Organize the data in a table of initial and final conditions.
Temperature and moles remain constant.
ANALYZE Conditions 1 Conditions 2 Know Predict
THE P1 = 550 mmHg P2 = 2200 mmHg P increases
PROBLEM V1 = 8.0 L V2 = ? V decreases
ANALYZE Conditions 1 Conditions 2 Know Predict
THE P1 = 550 mmHg P2 = 2200 mmHg P increases
PROBLEM V1 = 8.0 L V2 = ? V decreases
11/10/2015
5
General, Organic, and Biological Chemistry: Structures of Life, 5/eKaren C. Timberlake
© 2016 Pearson Education, Inc.
Calculations Using Boyle’s Law
STEP 2 Rearrange the gas law equation to solve for the
unknown quantity.
P1V1 = P2V2 Boyle’s lawTo solve for V2 , divide both sides by P2.
STEP 3 Substitute values into the gas law equation and calculate.
×
×
General, Organic, and Biological Chemistry: Structures of Life, 5/eKaren C. Timberlake
© 2016 Pearson Education, Inc.
Study Check
A sample of oxygen gas has a volume of 12.0 L at 600. mmHg. What is the new pressure when the volume changes to 36.0 L at a constant T and n?
A. 200. mmHg
B. 400. mmHg
C. 1200 mmHg
General, Organic, and Biological Chemistry: Structures of Life, 5/eKaren C. Timberlake
© 2016 Pearson Education, Inc.
Solution
A sample of oxygen gas has a volume of 12.0 L at 600. mmHg. What is the new pressure when the volume changes to 36.0 L at a constant T and n?
STEP 1 Organize the data in a table of initial and final conditions.
Temperature and moles remain constant.
General, Organic, and Biological Chemistry: Structures of Life, 5/eKaren C. Timberlake
© 2016 Pearson Education, Inc.
Solution
A sample of oxygen gas has a volume of 12.0 L at 600. mmHg. What is the new pressure when the volume changes to 36.0 L at a constant T and n?
STEP 2 Rearrange the gas law equation to solve for the unknown quantity.
×
General, Organic, and Biological Chemistry: Structures of Life, 5/eKaren C. Timberlake
© 2016 Pearson Education, Inc.
Solution
A sample of oxygen gas has a volume of 12.0 L at 600. mmHg. What is the new pressure when the volume changes to 36.0 L at a constant T and n?
STEP 3 Substitute values into the gas law equation and calculate.
The answer is A, 200. mmHg.
×
General, Organic, and Biological Chemistry: Structures of Life, 5/eKaren C. Timberlake
© 2016 Pearson Education, Inc.
Study Check
For a cylinder containing helium gas, indicate if cylinder A or cylinder B represents the new volume for the followingchanges (n and T are constant).
1. pressure decreases
2. pressure increases
11/10/2015
6
General, Organic, and Biological Chemistry: Structures of Life, 5/eKaren C. Timberlake
© 2016 Pearson Education, Inc.
Solution
For a cylinder containing helium gas, indicate if cylinder A or cylinder B represents the new volume for the followingchanges (n and T are constant).
1. pressure decreases cylinder B
2. pressure increases cylinder A
General, Organic, and Biological Chemistry: Structures of Life, 5/eKaren C. Timberlake
© 2016 Pearson Education, Inc.
Study Check
If a sample of helium gas has a volume of 120 mL and apressure of 850 mmHg, what is the new volume if the pressureis changed to 425 mmHg at a constant T and n?A. 60 mL
B. 120 mL
C. 240 mL
General, Organic, and Biological Chemistry: Structures of Life, 5/eKaren C. Timberlake
© 2016 Pearson Education, Inc.
Solution
If a sample of helium gas has a volume of 120 mL and apressure of 850 mmHg, what is the new volume if the pressureis changed to 425 mmHg at a constant T and n?
STEP 1 Organize the data in a table of initial and final conditions.
Temperature and moles remain constant.
General, Organic, and Biological Chemistry: Structures of Life, 5/eKaren C. Timberlake
© 2016 Pearson Education, Inc.
Solution
If a sample of helium gas has a volume of 120 mL and apressure of 850 mmHg, what is the new volume if the pressureis changed to 425 mmHg at a constant T and n?
STEP 2 Rearrange the gas law equation to solve for the unknown quantity.
STEP 3 Substitute values into the gas law equation and calculate.
×
×
General, Organic, and Biological Chemistry: Structures of Life, 5/eKaren C. Timberlake
© 2016 Pearson Education, Inc.
Study Check
A sample of helium gas in a balloon has a volume of 6.4 L at a pressure of 0.70 atm. At 1.40 atm (T and n are constant), is the new volume represented by A, B, or C?
General, Organic, and Biological Chemistry: Structures of Life, 5/eKaren C. Timberlake
© 2016 Pearson Education, Inc.
Solution
A sample of helium gas in a balloon has a volume of 6.4 L at a pressure of 0.70 atm. At 1.40 atm (T and n are constant), is the new volume represented by A, B, or C?
At a higher pressure (T and n constant), the new volume is represented by the smaller balloon A.
11/10/2015
7
General, Organic, and Biological Chemistry: Structures of Life, 5/eKaren C. Timberlake
© 2016 Pearson Education, Inc.
Solution
1. What is 475 mmHg expressed in atm?
The answer is B, 0.625 atm.
2. The pressure in a tire is 2.00 atm. What is this pressure in mmHg? The answer is B, 1520 mmHg.
×
×
General, Organic, and Biological Chemistry: Structures of Life, 5/eKaren C. Timberlake
© 2016 Pearson Education, Inc.
Study Check
1. The downward pressure on the Hg in a barometer is _____ the pressure of the atmosphere.
A. greater than B. less than C. the same as
2. A water barometer is 13.6 times taller than an Hg barometer (dHg = 13.6 g/mL) because
A. H2O is less dense than mercury.
B. H2O is heavier than mercury.
C. air is more dense than H2O.
General, Organic, and Biological Chemistry: Structures of Life, 5/eKaren C. Timberlake
© 2016 Pearson Education, Inc.
Solution
1. The downward pressure on the Hg in a barometer is _____ the pressure of the atmosphere.
The answer is C, the same as.
2. A water barometer is 13.6 times taller than an Hg barometer (dHg = 13.6 g/mL) because
The answer is A, H2O is less dense than mercury.
General, Organic, and Biological Chemistry: Structures of Life, 5/eKaren C. Timberlake
© 2016 Pearson Education, Inc.
8.3 Gas Temperature and Volume
(Charles’s Law)
If we increase the temperature of a gas sample, kinetic molecular theory states that the motion (kinetic energy) of the gas particles will also increase.
If the amount and pressure of the gas is held constant, the volume of the container will increase.
Learning Goal Use the temperature–volume relationship (Charles’s law) to determine the final temperature or volume when the pressure and amount of gas are constant.
General, Organic, and Biological Chemistry: Structures of Life, 5/eKaren C. Timberlake
© 2016 Pearson Education, Inc.
Charles’s Law
In Charles’s law,
• the Kelvin temperature (K) of a gas is directly related to its volume.
• pressure and moles of gas are constant.
• when the temperature of a sample of gas increases, its volume increases at constant pressure.
General, Organic, and Biological Chemistry: Structures of Life, 5/eKaren C. Timberlake
© 2016 Pearson Education, Inc.
Charles’s Law: V and T
• For two conditions, Charles’s law is written
(P and n are constant)
• Rearranging Charles’s law to solve for V2:
×
×
×
11/10/2015
8
General, Organic, and Biological Chemistry: Structures of Life, 5/eKaren C. Timberlake
© 2016 Pearson Education, Inc.
Study Check
Solve Charles’s law expression for T2.
General, Organic, and Biological Chemistry: Structures of Life, 5/eKaren C. Timberlake
© 2016 Pearson Education, Inc.
Solution
Solve Charles’s law expression for T2:
Cross-multiply to give V1T2 = V2T1
Isolate T2 by dividing through by V1:
×
General, Organic, and Biological Chemistry: Structures of Life, 5/eKaren C. Timberlake
© 2016 Pearson Education, Inc.
Calculations Using Charles’s Law
A balloon has a volume of 785 mL at 21 °C. If the temperature drops to 0 °C, what is the new volume of the balloon at constant pressure and moles?
STEP 1 Organize the data in a table of initial and final conditions.
Pressure and moles remain constant.
General, Organic, and Biological Chemistry: Structures of Life, 5/eKaren C. Timberlake
© 2016 Pearson Education, Inc.
Calculations Using Charles’s Law
STEP 2 Rearrange to solve for unknown quantity: V2.
STEP 3 Substitute the values into the gas law equation and calculate.
×
×
××
General, Organic, and Biological Chemistry: Structures of Life, 5/eKaren C. Timberlake
© 2016 Pearson Education, Inc.
Study Check
A sample of oxygen gas has a volume of 420 mL at a temperature of 18 °C. At what temperature (in °C) will the volume of the oxygen be 640 mL (P and n are constant)?
A. 443 °C
B. 170 °C
C. −82 °C
General, Organic, and Biological Chemistry: Structures of Life, 5/eKaren C. Timberlake
© 2016 Pearson Education, Inc.
Solution
A sample of oxygen gas has a volume of 420 mL at a temperature of 18 °C. At what temperature (in °C) will the volume of the oxygen be 640 mL (P and n are constant)?
STEP 1 Organize the data into a table of initial and final conditions.
Pressure and moles remain constant.
ANALYZE Conditions 1 Conditions 2 Know Predict
THE V1 = 420 mL V2 = 640 mL V increases
PROBLEM T1 = 18 °C = 291 K T2 = ? T increases
ANALYZE Conditions 1 Conditions 2 Know Predict
THE V1 = 420 mL V2 = 640 mL V increases
PROBLEM T1 = 18 °C = 291 K T2 = ? T increases
11/10/2015
9
General, Organic, and Biological Chemistry: Structures of Life, 5/eKaren C. Timberlake
© 2016 Pearson Education, Inc.
Solution
A sample of oxygen gas has a volume of 420 mL at a temperature of 18 °C. At what temperature (in °C) will the volume of the oxygen be 640 mL (P and n are constant)?
STEP 2 Rearrange to solve for unknown quantity: T2.
STEP 3 Substitute the values into the gas law equation and calculate.
The answer is B.
×
×
-
General, Organic, and Biological Chemistry: Structures of Life, 5/eKaren C. Timberlake
© 2016 Pearson Education, Inc.
Study Check
Use the gas laws to complete each sentence with increases or decreases.
A. Pressure _______ when V decreases at constant temperature and moles.
B. When T decreases, V _______ at constant pressure andmoles.
C. Pressure _______ when V changes from 12 L to 24 L at constant temperature and moles.
D. Volume _______when T changes from 15 °C to 45 °C at constant pressure and moles.
General, Organic, and Biological Chemistry: Structures of Life, 5/eKaren C. Timberlake
© 2016 Pearson Education, Inc.
Solution
Use the gas laws to complete each sentence with increases or decreases.
A. Pressure increases when V decreases at constant temperature and moles.
B. When T decreases, V decreases at constant pressure and moles.
C. Pressure decreases when V changes from 12 L to 24 L at constant temperature and moles.
D. Volume increases when T changes from 15 °C to 45 °C at constant pressure and moles.
General, Organic, and Biological Chemistry: Structures of Life, 5/eKaren C. Timberlake
© 2016 Pearson Education, Inc.
8.4 Temperature and Pressure
(Gay-Lussac’s Law)
Gay-Lussac’s law:
When the Kelvin temperature of a gas doubles at constant volume and amount of gas,
the pressure also doubles.
Learning Goal Use the temperature–pressure relationship (Gay-Lussac’s law) to determine the final temperature or pressure when the volume and amount of gas are constant.
General, Organic, and Biological Chemistry: Structures of Life, 5/eKaren C. Timberlake
© 2016 Pearson Education, Inc.
Gay-Lussac’s Law
In Gay-Lussac’s law,
• the pressure exerted by a gas is directly related to the Kelvin temperature of
the gas.
• volume and amount of gas are constant.
General, Organic, and Biological Chemistry: Structures of Life, 5/eKaren C. Timberlake
© 2016 Pearson Education, Inc.
Study Check
Solve Gay-Lussac’s law for P2.
11/10/2015
10
General, Organic, and Biological Chemistry: Structures of Life, 5/eKaren C. Timberlake
© 2016 Pearson Education, Inc.
Solution
Solve Gay-Lussac’s law for P2.
Multiply both sides by T2 and cancel:
××
×
General, Organic, and Biological Chemistry: Structures of Life, 5/eKaren C. Timberlake
© 2016 Pearson Education, Inc.
Calculations Using Gay-Lussac’s Law
A gas has a pressure at 2.0 atm at 18 °C. What is the new
pressure when the temperature is 62 °C (constant volume
and moles)?
STEP 1 Organize the data in a table of initial and final
conditions.
Volume and moles remain constant.
General, Organic, and Biological Chemistry: Structures of Life, 5/eKaren C. Timberlake
© 2016 Pearson Education, Inc.
Calculations Using Gay-Lussac’s Law
STEP 2 Rearrange to solve for unknown quantity P2.
Solve Gay-Lussac’s law for P2:
STEP 3 Substitute the values into the gas law equation
and calculate.
×
×
×
×
General, Organic, and Biological Chemistry: Structures of Life, 5/eKaren C. Timberlake
© 2016 Pearson Education, Inc.
Study Check
A gas has a pressure of 645 Torr at 128 °C.
What is the temperature in Celsius if the pressure increases to 824 Torr (V and n
remain constant)?
General, Organic, and Biological Chemistry: Structures of Life, 5/eKaren C. Timberlake
© 2016 Pearson Education, Inc.
Solution
A gas has a pressure of 645 Torr at 128 °C. What is the temperature in Celsius if the pressure increases to 824 Torr(V and n remain constant)?
STEP 1 Organize the data in a table of initial and final conditions.
Volume and moles remain constant.
General, Organic, and Biological Chemistry: Structures of Life, 5/eKaren C. Timberlake
© 2016 Pearson Education, Inc.
Solution
A gas has a pressure of 645 Torr at 128 °C. What is the temperature in Celsius if the pressure increases to 824 Torr(V and n remain constant)?
STEP 2 Rearrange to solve for unknown quantity T2
Solve Gay-Lussac’s law for T2:
STEP 3 Substitute the values into the gas law equation
and calculate.
×
×
-
11/10/2015
11
General, Organic, and Biological Chemistry: Structures of Life, 5/eKaren C. Timberlake
© 2016 Pearson Education, Inc.
Vapor Pressure and Boiling Point
When liquid molecules with sufficient kinetic energy break away from the surface of a liquid, they become a vapor.
• In an open container, all the liquid will eventually evaporate.• In a closed container, the vapor accumulates and creates
pressure called vapor pressure.
A liquid• exerts its own vapor pressure at a given temperature.• boils when its vapor pressure becomes equal to the external
pressure.
General, Organic, and Biological Chemistry: Structures of Life, 5/eKaren C. Timberlake
© 2016 Pearson Education, Inc.
Altitude and Boiling Point
At high altitudes,• atmospheric pressure is
lower than 1 atm, 760 Torr.• the boiling point of water is
lower than 100 °C.In a closed container, such as a pressure cooker, • a pressure greater than
1 atm, 760 Torr, can be obtained.
• water boils at a higher temperature than 100 °C.
Pressure and the boiling point of water.
General, Organic, and Biological Chemistry: Structures of Life, 5/eKaren C. Timberlake
© 2016 Pearson Education, Inc.
Vapor Pressure and Boiling Point
General, Organic, and Biological Chemistry: Structures of Life, 5/eKaren C. Timberlake
© 2016 Pearson Education, Inc.
Study Check
Explain why water boils at a lower
temperature in the mountains than at sea level.
General, Organic, and Biological Chemistry: Structures of Life, 5/eKaren C. Timberlake
© 2016 Pearson Education, Inc.
Solution
Explain why water boils at a lower
temperature in the mountains than at sea level.
Atmospheric pressure in the mountains is
less than at sea level. The vapor pressure of the water reaches the atmospheric pressure
at a lower temperature.
General, Organic, and Biological Chemistry: Structures of Life, 5/eKaren C. Timberlake
© 2016 Pearson Education, Inc.
8.5 The Combined Gas Law
Under water, the pressure on a diver is greater than the atmospheric pressure.
The combined gas law comes from the pressure–volume–temperature relationships for gases that we have studied.
Learning Goal Use the combined gas law to calculate the final pressure, volume, or temperature of a gas when changes in two of these properties are given and the amount of gas is constant.
11/10/2015
12
General, Organic, and Biological Chemistry: Structures of Life, 5/eKaren C. Timberlake
© 2016 Pearson Education, Inc.
The Combined Gas Law
The combined gas law uses the pressure–volume–temperature relationships from Boyle’s law, Charles’s law, and Gay-Lussac’s law where n is constant.
General, Organic, and Biological Chemistry: Structures of Life, 5/eKaren C. Timberlake
© 2016 Pearson Education, Inc.
Calculations Using Combined Gas Law
A gas has a volume of 675 mL at 35 °C and 646 mmHg pressure. What is the volume (mL) of the gas at −95 °C and a pressure of 802 mmHg (n is constant)?
STEP 1 Organize the data into a table of initial and final conditions.
Moles of gas remain the same.
ANALYZE Conditions 1 Conditions 2
THE P1 = 646 mmHg P2 = 802 mmHg
PROBLEM V1 = 675 mL V2 = ?
T1 = 35 °C + 273 T2 = −95 °C + 273
= 308 K = 178 K
ANALYZE Conditions 1 Conditions 2
THE P1 = 646 mmHg P2 = 802 mmHg
PROBLEM V1 = 675 mL V2 = ?
T1 = 35 °C + 273 T2 = −95 °C + 273
= 308 K = 178 K
General, Organic, and Biological Chemistry: Structures of Life, 5/eKaren C. Timberlake
© 2016 Pearson Education, Inc.
Calculations Using Combined Gas Law
STEP 2 Rearrange to solve for unknown quantity V2.
STEP 3 Substitute the values into the gas law equation and calculate.
××
×
×
General, Organic, and Biological Chemistry: Structures of Life, 5/eKaren C. Timberlake
© 2016 Pearson Education, Inc.
Study Check
A sample of helium gas has a volume of 0.180 L, a pressure of 0.800 atm, and a temperature of 29 °C. At what temperature (°C) will the helium have a volume of 90.0 mL and a pressure of 3.20 atm(n remains constant)?
General, Organic, and Biological Chemistry: Structures of Life, 5/eKaren C. Timberlake
© 2016 Pearson Education, Inc.
Solution
A sample of helium gas has a volume of 0.180 L, a pressure of
0.800 atm, and a temperature of 29 °C. At what temperature
(°C) will the helium have a volume of 90.0 mL and a pressure
of 3.20 atm (n remains constant)?
STEP 1 Organize the data into a table of initial and final conditions.
Moles of gas remain the same.
ANALYZE Conditions 1 Conditions 2
THE P1 = 0.800 atm P2 = 3.20 atm
PROBLEM V1 = 0.180 L (180 mL) V2 = 90.0 mL
T1 = 29 °C + 273 T2 = ?
= 302 K
ANALYZE Conditions 1 Conditions 2
THE P1 = 0.800 atm P2 = 3.20 atm
PROBLEM V1 = 0.180 L (180 mL) V2 = 90.0 mL
T1 = 29 °C + 273 T2 = ?
= 302 K
General, Organic, and Biological Chemistry: Structures of Life, 5/eKaren C. Timberlake
© 2016 Pearson Education, Inc.
Solution
A sample of helium gas has a volume of 0.180 L, a pressure of
0.800 atm, and a temperature of 29 °C. At what temperature
(°C) will the helium have a volume of 90.0 mL and a pressure
of 3.20 atm (n remains constant)?
STEP 2 Rearrange to solve for unknown quantity T2.
××
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General, Organic, and Biological Chemistry: Structures of Life, 5/eKaren C. Timberlake
© 2016 Pearson Education, Inc.
Solution
A sample of helium gas has a volume of 0.180 L, a pressure of
0.800 atm, and a temperature of 29 °C. At what temperature
(°C) will the helium have a volume of 90.0 mL and a pressure
of 3.20 atm (n remains constant)?
STEP 3 Substitute the values into the gas law equation and calculate.
×
×
-
General, Organic, and Biological Chemistry: Structures of Life, 5/eKaren C. Timberlake
© 2016 Pearson Education, Inc.
8.6 Volume and Moles, Avogadro’s Law
The molar volume of a gas at STP is about the same as the volume of three basketballs.
The volume of 1 mole of gas is 22.4 liters.
Learning Goal Use Avogadro’s law to calculate the amount or volume of a gas when the pressure and temperature are constant.
General, Organic, and Biological Chemistry: Structures of Life, 5/eKaren C. Timberlake
© 2016 Pearson Education, Inc.
Avogadro’s Law: Volume and Moles
In Avogadro’s law,
• the volume of a gas is directly related to the number of moles (n) of gas.
• T and P are constant.
General, Organic, and Biological Chemistry: Structures of Life, 5/eKaren C. Timberlake
© 2016 Pearson Education, Inc.
Calculations Using Avogadro’s Law
If 0.75 mole of helium gas occupies a volume of 1.5 L, what volume (L) will 1.2 moles of helium occupy at the same temperature and pressure?
A. 0.94 L
B. 1.8 L
C. 2.4 L
General, Organic, and Biological Chemistry: Structures of Life, 5/eKaren C. Timberlake
© 2016 Pearson Education, Inc.
Calculations Using Avogadro’s Law
If 0.75 mole of helium gas occupies a volume of 1.5 L, what volume (L) will 1.2 moles of helium occupy at the same temperature and pressure?
STEP 1 Organize the data into a table of initial and final conditions.
Pressure and temperature remain constant.
General, Organic, and Biological Chemistry: Structures of Life, 5/eKaren C. Timberlake
© 2016 Pearson Education, Inc.
Calculations Using Avogadro’s Law
STEP 2 Rearrange to solve for unknown quantity V2.
STEP 3 Substitute the values into the gas law equation and calculate.
The answer is C.
×
×
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General, Organic, and Biological Chemistry: Structures of Life, 5/eKaren C. Timberlake
© 2016 Pearson Education, Inc.
Standard Temperature and Pressure
The volumes of gases can be compared at STP, Standard Temperature and Pressure, when they have
• the same temperature.
• a standard temperature (T) of 0 °C or 273 K.
• the same pressure.
• a standard pressure (P) of 1 atm (760 mmHg).
General, Organic, and Biological Chemistry: Structures of Life, 5/eKaren C. Timberlake
© 2016 Pearson Education, Inc.
Molar Volume, STP
At standard temperature and pressure (STP), 1 mole of a gas occupies a volume of 22.4 L, which
is called its molar volume.
Use this equality as a conversion factor for gas at STP:
22.4 L = 1 mole gas
General, Organic, and Biological Chemistry: Structures of Life, 5/eKaren C. Timberlake
© 2016 Pearson Education, Inc.
Molar Volume
Avogadro’s law indicated that1 mole of
any gas at STP has a volume of 22.4 L.General, Organic, and Biological Chemistry: Structures of Life, 5/eKaren C. Timberlake
© 2016 Pearson Education, Inc.
Guide to Using Molar Volume
General, Organic, and Biological Chemistry: Structures of Life, 5/eKaren C. Timberlake
© 2016 Pearson Education, Inc.
Calculations Using Molar Volume
What is the volume occupied by 2.75 moles of N2 gas at STP?
STEP 1 State the given and needed quantities.
Pressure and temperature remain constant.
STEP 2 Write a plan to calculate the needed quantity.
Moles N2 Volume N2
General, Organic, and Biological Chemistry: Structures of Life, 5/eKaren C. Timberlake
© 2016 Pearson Education, Inc.
Calculations Using Molar Volume
STEP 3 Write conversion factors including 22.4 L/mole at STP.
At STP, 22.4 L = 1 mole N2.
STEP 4 Set up the problem with factors to cancel units.
×
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General, Organic, and Biological Chemistry: Structures of Life, 5/eKaren C. Timberlake
© 2016 Pearson Education, Inc.
Study Check
1. What is the volume at STP of 4.00 g of CH4?
A. 5.60 L B. 11.2 L C. 44.8 L
2. How many grams of He are present in 8.00 L of gas at STP?
A. 25.6 g B. 0.357 g C. 1.43 g
General, Organic, and Biological Chemistry: Structures of Life, 5/eKaren C. Timberlake
© 2016 Pearson Education, Inc.
Solution
STEP 1 State given and needed quantities.
1. What is the volume at STP of 4.00 g of CH4?
Pressure and temperature remain constant.
2. How many grams of He are present in 8.00 L of gas at STP? Pressure and temperature remain constant.
ANALYZE Given Need
THE 4.00 grams CH4(g) volume CH4(g)
PROBLEM at STP at STP
ANALYZE Given Need
THE 4.00 grams CH4(g) volume CH4(g)
PROBLEM at STP at STP
General, Organic, and Biological Chemistry: Structures of Life, 5/eKaren C. Timberlake
© 2016 Pearson Education, Inc.
Solution
STEP 2 Write a plan to calculate the needed quantity.
1. What is the volume at STP of 4.00 g of CH4?
mass CH4 moles CH4 volume CH4
2. How many grams of He are present in 8.00 L of
gas at STP?
volume He moles He mass He
General, Organic, and Biological Chemistry: Structures of Life, 5/eKaren C. Timberlake
© 2016 Pearson Education, Inc.
Solution
STEP 3 Write conversion factors including 22.4 L/mole at STP.
1. What is the volume at STP of 4.00 g of CH4?
22.4 L = 1 mole of CH4
1 mole of CH4 = 16.05 g CH4
General, Organic, and Biological Chemistry: Structures of Life, 5/eKaren C. Timberlake
© 2016 Pearson Education, Inc.
Solution
STEP 3 Write conversion factors including 22.4 L/mole at STP.
2. How many grams of He are present in 8.00 L of gas at STP?
22.4 L = 1 mole of He
1 mole of He = 4.00 g He
General, Organic, and Biological Chemistry: Structures of Life, 5/eKaren C. Timberlake
© 2016 Pearson Education, Inc.
Solution
STEP 4 Set up the problem with factors to cancel units.
1. What is the volume at STP of 4.00 g of CH4?
The answer is A, 5.60 L
2. How many grams of He are present in 8.00 L of gas at STP?
The answer is C, 1.43 g.
××
×
×
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General, Organic, and Biological Chemistry: Structures of Life, 5/eKaren C. Timberlake
© 2016 Pearson Education, Inc.
8.7 Ideal Gas Law
When camping, butane is used as a fuel for a portable gas stove. Given the pressure, volume, and temperature of the gas in the tank, we can use the ideal gas law equation to determine the amount of gas present.
Learning Goal Use the ideal gas law equation to solve for P, V, T, or n of a gas when given three of the four values in the ideal gas law equation. Calculate mass or volume of a gas in a chemical reaction.
General, Organic, and Biological Chemistry: Structures of Life, 5/eKaren C. Timberlake
© 2016 Pearson Education, Inc.
The Ideal Gas Law
The ideal gas law is the combination of the four properties used in the measurement of a gas—
pressure (P), volume (V), temperature (T), and amount of a gas (n)—to give a single expression, which is written as
Ideal Gas Law PV = nRT
Core Chemistry Skill Calculating Mass or Volume
of a Gas in a Chemical Reaction
General, Organic, and Biological Chemistry: Structures of Life, 5/eKaren C. Timberlake
© 2016 Pearson Education, Inc.
R, Ideal Gas Constant
Rearranging the ideal gas law equation showsthat the four gas properties equal a constant, R.
• To calculate the value of R, we substitute the STP conditions (273 K, 1 atm) for molar volume into the expression: 1 mole of gas = 22.4 L at STP.
• Real gases show some deviations in behavior; however, the ideal gas law closely approximates the behavior of real gases at typical conditions.
General, Organic, and Biological Chemistry: Structures of Life, 5/eKaren C. Timberlake
© 2016 Pearson Education, Inc.
R, Ideal Gas Constant
The value for the ideal gas constant, R, is 0.0821 L atm per mole K.
• If we use 760 mmHg for the pressure, we obtain another useful value for R of 62.4 mmHg per mole K.
• In working problems using the ideal gas law, the units of each variable must match the units in the R you select.
General, Organic, and Biological Chemistry: Structures of Life, 5/eKaren C. Timberlake
© 2016 Pearson Education, Inc.
Guide to Using the Ideal Gas Equation
General, Organic, and Biological Chemistry: Structures of Life, 5/eKaren C. Timberlake
© 2016 Pearson Education, Inc.
Study Check
Dinitrogen oxide, N2O, which is used in dentistry, is an anesthetic also called laughing gas. What is the
pressure, in atmospheres, of 0.350 mole of N2O at 22 °C in a 5.00-L container?
11/10/2015
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General, Organic, and Biological Chemistry: Structures of Life, 5/eKaren C. Timberlake
© 2016 Pearson Education, Inc.
Solution
Dinitrogen oxide, N2O, which is used in dentistry, is an anesthetic also called laughing gas. What is the
pressure, in atmospheres, of 0.350 mole of N2O at 22 °C in a 5.00-L container?
STEP 1 State the given and needed quantities.
General, Organic, and Biological Chemistry: Structures of Life, 5/eKaren C. Timberlake
© 2016 Pearson Education, Inc.
Solution
Dinitrogen oxide, N2O, which is used in dentistry, is an anesthetic also called laughing gas. What is the
pressure, in atmospheres, of 0.350 mole of N2O at 22 °C in a 5.00-L container?
STEP 2 Rearrange the ideal gas law equation to solve for the needed quantity.
General, Organic, and Biological Chemistry: Structures of Life, 5/eKaren C. Timberlake
© 2016 Pearson Education, Inc.
Solution
Dinitrogen oxide, N2O, which is used in dentistry, is an anesthetic also called laughing gas. What is the
pressure, in atmospheres, of 0.350 mole of N2O at 22 °C in a 5.00-L container?
STEP 3 Substitute the gas data into the equation and the needed quantity.
××
General, Organic, and Biological Chemistry: Structures of Life, 5/eKaren C. Timberlake
© 2016 Pearson Education, Inc.
R, Unit Summary for Ideal Gas Constant
General, Organic, and Biological Chemistry: Structures of Life, 5/eKaren C. Timberlake
© 2016 Pearson Education, Inc.
Gas Laws and Chemical Reactions
Gases are involved as reactants and products in many chemical reactions.
Typically, the information given for a gas in a reaction is its pressure (P), volume (V), and temperature (T).
We can use the ideal gas law equation to determine
• the moles of a gas in a reaction if we are given the number of moles for one of the gases in a reaction.
• the moles of any other substance using a mole–mole factor.
General, Organic, and Biological Chemistry: Structures of Life, 5/eKaren C. Timberlake
© 2016 Pearson Education, Inc.
Guide to Using the Ideal Gas Law
for Reactions
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General, Organic, and Biological Chemistry: Structures of Life, 5/eKaren C. Timberlake
© 2016 Pearson Education, Inc.
Study Check
Nitrogen gas reacts with hydrogen gas to produce ammonia (NH3) gas. How many liters of NH3 can be produced at 0.93 atm and 24 °C from a 16.0-g
sample of nitrogen gas and an excess of hydrogen gas? N2(g) + 3H2(g) � 2NH3(g)
General, Organic, and Biological Chemistry: Structures of Life, 5/eKaren C. Timberlake
© 2016 Pearson Education, Inc.
Solution
Nitrogen gas reacts with hydrogen gas to produce ammonia (NH3) gas. How many liters of NH3 can be produced at 0.93 atm and 24 °C from a 16.0-g sample of nitrogen gas and an excess of hydrogen gas? N2(g) + 3H2(g) � 2NH3(g)
STEP 1 State the given and needed quantities.
General, Organic, and Biological Chemistry: Structures of Life, 5/eKaren C. Timberlake
© 2016 Pearson Education, Inc.
Solution
Nitrogen gas reacts with hydrogen gas to produce ammonia (NH3) gas. How many liters of NH3 can be produced at 0.93 atm and 24 °C from a 16.0-g sample of nitrogen gas and an excess of hydrogen gas? N2(g) + 3H2(g) � 2NH3(g)
STEP 2 Write a plan to convert the given quantity to the needed moles.
grams Molar moles Mole−mole moles litersof N2 mass of N2 factor of NH3 of NH3
Ideal
gas law
General, Organic, and Biological Chemistry: Structures of Life, 5/eKaren C. Timberlake
© 2016 Pearson Education, Inc.
Solution
Nitrogen gas reacts with hydrogen gas to produce ammonia (NH3) gas. How many liters of NH3 can be produced at 0.93 atm and 24 °C from a 16.0-g sample of nitrogen gas and an excess of hydrogen gas? N2(g) + 3H2(g) � 2NH3(g)
STEP 3 Write the equalities for molar mass and mole–mole factors.
General, Organic, and Biological Chemistry: Structures of Life, 5/eKaren C. Timberlake
© 2016 Pearson Education, Inc.
Solution
Nitrogen gas reacts with hydrogen gas to produce ammonia (NH3) gas. How many liters of NH3 can be produced at 0.93 atm and 24 °C from a 16.0-g sample of nitrogen gas and an excess of hydrogen gas? N2(g) + 3H2(g) � 2NH3(g)
STEP 4 Set up the problem to calculate moles of needed quantity.
× ×
General, Organic, and Biological Chemistry: Structures of Life, 5/eKaren C. Timberlake
© 2016 Pearson Education, Inc.
Solution
Nitrogen gas reacts with hydrogen gas to produce ammonia (NH3) gas. How many liters of NH3 can be produced at 0.93 atm and 24 °C from a 16.0-g sample of nitrogen gas and an excess of hydrogen gas? N2(g) + 3H2(g) � 2NH3(g)
STEP 5 Convert moles of needed quantity to mass or volume using the molar mass or ideal gas law equation.
××
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General, Organic, and Biological Chemistry: Structures of Life, 5/eKaren C. Timberlake
© 2016 Pearson Education, Inc.
8.8 Partial Pressure (Dalton’s Law)
Our cells continuously use oxygen and produce carbon dioxide.
Both gases move in and out of the lungs through the membranes of the alveoli, the tiny air sacs at the ends of the airways in the lungs.
Learning Goal Use Dalton’s law of partial pressures to calculate the total pressure of a mixture of gases.
General, Organic, and Biological Chemistry: Structures of Life, 5/eKaren C. Timberlake
© 2016 Pearson Education, Inc.
Partial Pressure
The partial pressure of a gas is the pressure that each gas in a mixture would exert if it were by itself in the container.
Core Chemistry Skill Calculating Partial Pressure
General, Organic, and Biological Chemistry: Structures of Life, 5/eKaren C. Timberlake
© 2016 Pearson Education, Inc.
Dalton’s Law of Partial Pressures
Dalton’s law of partial pressures indicates that• pressure depends on the total number of gas
particles, not on the types of particles.• the total pressure exerted by gases in a mixture is
the sum of the partial pressures of those gases.
PT = P1 + P2 + P3 + ....
General, Organic, and Biological Chemistry: Structures of Life, 5/eKaren C. Timberlake
© 2016 Pearson Education, Inc.
Total Pressure
For example, at STP, 1 mole of a pure gas in a volume of 22.4 L will exert the same pressure as 1 mole of a gas mixture in 22.4 L.
Gas mixtures
1.0 mole N2
0.4 mole O2
0.6 mole He
1.0 mole
0.5 mole O2
0.3 mole He
0.2 mole Ar
1.0 mole
1.0 atm1.0 atm 1.0 atm
General, Organic, and Biological Chemistry: Structures of Life, 5/eKaren C. Timberlake
© 2016 Pearson Education, Inc.
Total Pressure
The air we breathe • is a mixture of different gases.• contains mostly N2 and O2, and contains small amounts of
other gases.What we call the atmospheric pressure is actually the sum of the partial pressures of the gases in the air
General, Organic, and Biological Chemistry: Structures of Life, 5/eKaren C. Timberlake
© 2016 Pearson Education, Inc.
Guide to Solving for Partial Pressure
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General, Organic, and Biological Chemistry: Structures of Life, 5/eKaren C. Timberlake
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Solving for Partial Pressure
A scuba tank contains O2 with a pressure of 0.450 atm and He
at 855 mmHg. What is the total pressure in mmHg in the tank (volume and temperature are constant)?
STEP 1 Write the equation for the sum of the partial pressures.
Ptotal = PO2+ PHe
STEP 2 Rearrange the equation to solve for the unknown pressure. Convert units to match.
Ptotal = PO2+ PHe
×
General, Organic, and Biological Chemistry: Structures of Life, 5/eKaren C. Timberlake
© 2016 Pearson Education, Inc.
Solving for Partial Pressure
A scuba tank contains O2 with a pressure of 0.450 atm and He
at 855 mmHg. What is the total pressure in mmHg in the tank (volume and temperature are constant)?
STEP 3 Substitute known pressures and calculate the unknown partial pressure.
Ptotal = PO2 + PHe
Ptotal = 342 mmHg + 855 mmHg
= 1.20 x 103 mmHg×
General, Organic, and Biological Chemistry: Structures of Life, 5/eKaren C. Timberlake
© 2016 Pearson Education, Inc.
Study Check
For a deep dive, a scuba diver uses a mixture of helium and oxygen with a pressure of 8.00 atm. If the
oxygen has a partial pressure of 1280 mmHg, what is the partial pressure of the helium (volume and temperature are constant)?
A. 520 mmHg
B. 2040 mmHg
C. 4800 mmHg
General, Organic, and Biological Chemistry: Structures of Life, 5/eKaren C. Timberlake
© 2016 Pearson Education, Inc.
Solution
For a deep dive, a scuba diver uses a mixture of helium andoxygen with a pressure of 8.00 atm. If the oxygen has a partial pressure of 1280 mmHg, what is the partial pressure of the helium (volume and temperature are constant)?
STEP 1 Write the equation for the sum of the partial pressures.
Ptotal = PO2+ Phe
STEP 2 Rearrange the equation to solve for the unknown pressure. Convert units to match.
PHe = Ptotal − PO2×
General, Organic, and Biological Chemistry: Structures of Life, 5/eKaren C. Timberlake
© 2016 Pearson Education, Inc.
Solution
For a deep dive, a scuba diver uses a mixture of helium andoxygen with a pressure of 8.00 atm. If the oxygen has a partial pressure of 1280 mmHg, what is the partial pressure of the helium (volume and temperature are constant)?
STEP 3 Substitute known pressures and calculate the unknown partial pressure.
PHe = 6080 mmHg – 1280 mmHg = 4800 mmHg or 4.80 × 103 mmHg
The answer is C, 4800 mm Hg.
General, Organic, and Biological Chemistry: Structures of Life, 5/eKaren C. Timberlake
© 2016 Pearson Education, Inc.
Chemistry Link to Health: Blood Gases
• In the lungs, O2 enters the blood, while CO2 from the blood is released.
• In the tissues, O2
enters the cells, which releases CO2 into the blood.
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General, Organic, and Biological Chemistry: Structures of Life, 5/eKaren C. Timberlake
© 2016 Pearson Education, Inc.
Chemistry Link to Health: Blood Gases
In the body,
• O2 flows into the tissues because the partial pressure of O2 is higher in blood and lower in the tissues.
• CO2 flows out of the tissues because the partial pressure of CO2 is higher in the tissues and lower in blood.
General, Organic, and Biological Chemistry: Structures of Life, 5/eKaren C. Timberlake
© 2016 Pearson Education, Inc.
Chemistry Link to Health:
Partial Pressures in Blood
Partial Pressures in Blood and Tissue
General, Organic, and Biological Chemistry: Structures of Life, 5/eKaren C. Timberlake
© 2016 Pearson Education, Inc.
Gas Exchange During Breathing