Transcript No Slide Title

Chapter 6 Gases
1
6.3
Pressure and Volume
Boyle’s Law
Chemistry An Introduction to General, Organic, and Biological Chemistry, Eleventh Edition
Copyright © 2012 by Pearson Education, Inc.
Boyle’s Law
2
Boyle’s law states that
• the pressure of a gas is
inversely related to its
volume when T and n
are constant
• the product P  V is
constant when
temperature and moles
are held constant
• if volume decreases, the
pressure increases
P1V1 = P2V2
Chemistry An Introduction to General, Organic, and Biological Chemistry, Eleventh Edition
Copyright © 2012 by Pearson Education, Inc.
Boyle’s Law: PV = Constant
3
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, n constant)
Chemistry An Introduction to General, Organic, and Biological Chemistry, Eleventh Edition
Copyright © 2012 by Pearson Education, Inc.
Boyle’s Law and Breathing
4
During an inhalation,
• the lungs expand
• the pressure in the
lungs decreases
• air flows toward the lower
pressure in the lungs
Chemistry An Introduction to General, Organic, and Biological Chemistry, Eleventh Edition
Copyright © 2012 by Pearson Education, Inc.
Boyle’s Law and Breathing
5
During an exhalation,
• lung volume decreases
• pressure within the lungs
increases
• air flows from the higher
pressure in the lungs to
the outside
Chemistry An Introduction to General, Organic, and Biological Chemistry, Eleventh Edition
Copyright © 2012 by Pearson Education, Inc.
Solving for a Gas Law Factor
6
The equation for Boyle’s law can be rearranged to
solve for any factor.
P1V1 = P2V2
Boyle’s law
To solve for V2 , divide both sides by P2.
P1V1
P2
= P2V2
P2
V1 x P1 =
P2
V2
Chemistry An Introduction to General, Organic, and Biological Chemistry, Eleventh Edition
Copyright © 2012 by Pearson Education, Inc.
Barometer Measures Pressure
7
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
Chemistry An Introduction to General, Organic, and Biological Chemistry, Eleventh Edition
Copyright © 2012 by Pearson Education, Inc.
Atmospheric Pressure
8
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
• is 1 atm at sea level
• is higher on a rainy day
Chemistry An Introduction to General, Organic, and Biological Chemistry, Eleventh Edition
Copyright © 2012 by Pearson Education, Inc.
Guide to Using Gas Laws
9
Chemistry An Introduction to General, Organic, and Biological Chemistry, Eleventh Edition
Copyright © 2012 by Pearson Education, Inc.
Calculations Using Boyle’s Law
10
Freon-12, CCl2F2, is used in refrigeration systems. What
is the new volume (L) of a 8.0-L sample of Freon gas
initially at 550 mmHg after its pressure is changed to
2200 mmHg at constant T and n?
Step 1 Organize the data in a table of initial and final conditions.
Conditions
Initial
Final
P1 = 550 mmHg
P2 = 2200 mmHg
V1 = 8.0 L
V2 = ?
Chemistry An Introduction to General, Organic, and Biological Chemistry, Eleventh Edition
Copyright © 2012 by Pearson Education, Inc.
Solution
11
Step 2 When pressure increases, volume decreases.
Solve Boyle’s law for V2:
P1V1 = P2V2
V2 = V1 P1
P2
Step 3 Substitute values into the gas law equation and calculate.
V2 = 8.0 L  550 mmHg = 2.0 L
2200 mmHg
pressure ratio
decreases volume
Chemistry An Introduction to General, Organic, and Biological Chemistry, Eleventh Edition
Copyright © 2012 by Pearson Education, Inc.
Learning Check
12
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 (T and n constant)?
A. 200. mmHg
B. 400. mmHg
C. 1200 mmHg
Chemistry An Introduction to General, Organic, and Biological Chemistry, Eleventh Edition
Copyright © 2012 by Pearson Education, Inc.
Solution
13
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 (T and n constant)?
Step 1 Organize the data in a table of initial and final
conditions.
Data Table
Conditions 1
Conditions 2
P1 = 600. mmHg P2 = ?
V1 = 12.0 L
V2 = 36.0 L
Chemistry An Introduction to General, Organic, and Biological Chemistry, Eleventh Edition
Copyright © 2012 by Pearson Education, Inc.
Solution
14
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 (T and n constant)?
Step 2 Rearrange the gas law equation to solve for the
unknown quantity.
P2 = P1  V1
V2
Step 3 600. mmHg  12.0 L = 200. mmHg The answer is A.
36.0 L
The answer is A, 200. mmHg.
Chemistry An Introduction to General, Organic, and Biological Chemistry, Eleventh Edition
Copyright © 2012 by Pearson Education, Inc.
Learning Check
15
For a cylinder containing helium gas, indicate if cylinder A
or cylinder B represents the new volume for the following
changes (n and T are constant).
1. pressure decreases
2. pressure increases
Chemistry An Introduction to General, Organic, and Biological Chemistry, Eleventh Edition
Copyright © 2012 by Pearson Education, Inc.
Learning Check
16
For a cylinder containing helium gas, indicate if cylinder A
or cylinder B represents the new volume for the following
changes (n and T are constant).
1. pressure decreases
cylinder B
2. pressure increases
cylinder A
Chemistry An Introduction to General, Organic, and Biological Chemistry, Eleventh Edition
Copyright © 2012 by Pearson Education, Inc.
Learning Check
17
If a sample of helium gas has a volume of 120 mL and a
pressure of 850 mmHg, what is the new volume if the
pressure is changed to 425 mmHg?
A. 60 mL
B. 120 mL
C. 240 mL
Chemistry An Introduction to General, Organic, and Biological Chemistry, Eleventh Edition
Copyright © 2012 by Pearson Education, Inc.
Solution
18
If a sample of helium gas has a volume of 120 mL and a
pressure of 850 mmHg, what is the new volume if the
pressure is changed to 425 mmHg?
Step 1 Organize the data in a table of initial and final conditions.
Data Table
Conditions 1
Conditions 2
P1 = 850 mmHg
P2 = 425 mm Hg
V1 = 120 mL
V2 = ?
Step 2 Rearrange the gas law equation to solve for the
unknown quantity. V2 = V1  P1
P2
Chemistry An Introduction to General, Organic, and Biological Chemistry, Eleventh Edition
Copyright © 2012 by Pearson Education, Inc.
Solution
19
If a sample of helium gas has a volume of 120 mL and a
pressure of 850 mmHg, what is the new volume if the
pressure is changed to 425 mmHg?
Step 3 Substitute values into the gas law equation and
calculate.
V2 = V1  P1 = 120 mL  850 mmHg = 240 mL
P2
425 mmHg
Pressure ratio
increases volume
The answer is C, 240 mL.
Chemistry An Introduction to General, Organic, and Biological Chemistry, Eleventh Edition
Copyright © 2012 by Pearson Education, Inc.
Learning Check
20
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 is constant), is the new
volume represented by A, B, or C?
Chemistry An Introduction to General, Organic, and Biological Chemistry, Eleventh Edition
Copyright © 2012 by Pearson Education, Inc.
Solution
21
A sample of helium gas in a balloon has a volume of 6.4 L at a
pressure of 0.70 atm. At a higher pressure (T constant), the
new volume is represented by the smaller balloon A.
Chemistry An Introduction to General, Organic, and Biological Chemistry, Eleventh Edition
Copyright © 2012 by Pearson Education, Inc.