Transcript Slide 1

EXAMPLE 11.1
Converting between Pressure Units
A high-performance road bicycle tire is inflated to a total pressure of 125 psi. What is this pressure in millimeters of
mercury?
You are given a pressure in psi and asked to convert it
to mm Hg. Find the required conversion factors in
Table 11.1.
Begin the solution map with the given units of psi.
Use the conversion factors to convert first to atm and
then to mm Hg.
Follow the solution map to solve the problem.
SKILLBUILDER 11.1
Given: 125 psi
Find: mm Hg
Conversion Factors:
1 atm = 14.7 psi
760 mm Hg = 1 atm
Solution Map:
Solution:
Converting between Pressure Units
Convert a pressure of 173 in. Hg into pounds per square inch.
Introductory Chemistry, Third Edition
By Nivaldo J. Tro
Copyright ©2009 by Pearson Education, Inc.
Upper Saddle River, New Jersey 07458
All rights reserved.
EXAMPLE 11.1
Converting between Pressure Units
Continued
SKILLBUILDER PLUS
Convert a pressure of 23.8 in. Hg into kilopascals.
FOR MORE PRACTICE
Introductory Chemistry, Third Edition
By Nivaldo J. Tro
Example 11.13; Problems 27, 28, 29, 30, 33, 34, 35, 36.
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Upper Saddle River, New Jersey 07458
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EXAMPLE 11.2
Boyle’s Law
A cylinder equipped with a moveable piston has an applied pressure of 4.0 atm and a volume of 6.0 L. What is the
volume of the cylinder if the applied pressure is decreased to 1.0 atm?
You are given an initial pressure, an initial
volume, and final pressure. You are asked to
find the final volume.
This problem requires the use of Boyle's law.
Given:
P1 = 4.0 atm
V1 = 6.0 L
V1 = 6.0 L
Find: V2
Equation: P1 V1 = P2 V2
Draw a solution map beginning with the
given quantities. Boyle’s law shows the
relationship necessary to get to the find
quantity.
Solution Map:
Solve the equation for the quantity you are
trying to find (V2)and then substitute the
numerical quantities into the equation to
compute the answer.
Solution:
Introductory Chemistry, Third Edition
By Nivaldo J. Tro
Copyright ©2009 by Pearson Education, Inc.
Upper Saddle River, New Jersey 07458
All rights reserved.
EXAMPLE 11.2
Boyle’s Law
Continued
SKILLBUILDER 11.2
Boyle’s Law
A snorkeler takes a syringe filled with 16 mL of air from the surface, where the pressure is 1.0 atm, to an
unknown depth. The volume of the air in the syringe at this depth is 7.5 mL. What is the pressure at this
depth? If the pressure increases by an additional 1 atm for every 10 m of depth, how deep is the snorkeler?
FOR MORE PRACTICE
Introductory Chemistry, Third Edition
By Nivaldo J. Tro
Example 11.14; Problems 37, 38, 39, 40.
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EXAMPLE 11.3
Charles’s Law
A sample of gas has a volume of 2.80 L at an unknown temperature. When the sample is submerged in ice water at
t = 0 °C its volume decreases to 2.57 L. What was its initial temperature (in kelvins and in Celsius)? Assume a
constant pressure. (To distinguish between the two temperature scales, use t for temperature in °C and T for
temperature in K.)
You are given an initial volume, a final
volume, and a final temperature. You are
asked to find the intitial temperature in both
kelvins (T1) and degrees Celsius (t1).
Given:
This problem requires the use of Charles's
law.
Find: T1 and t1
Equation:
Draw a solution map beginning with the
given quantities. Charles’s law shows the
relationship necessary to get to the find
quantity.
Solution Map:
Introductory Chemistry, Third Edition
By Nivaldo J. Tro
V1 = 2.80 L
V2 = 2.57
t2 = 0 °C
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EXAMPLE 11.3
Charles’s Law
Continued
Solve the equation for the quantity you are
trying to find (T1).
Solution:
Before you substitute in the numerical
values, you must convert the temperature to
kelvins. Remember, gas law problems must
always be worked using Kelvin temperatures.
Once you have converted the temperature to
kelvins, substitute into the equation to find
Convert the temperature to degrees Celsius
to find t1.
Introductory Chemistry, Third Edition
By Nivaldo J. Tro
Copyright ©2009 by Pearson Education, Inc.
Upper Saddle River, New Jersey 07458
All rights reserved.
EXAMPLE 11.3
Charles’s Law
Continued
SKILLBUILDER 11.3
Charles’s Law
A gas in a cylinder with a moveable piston with an initial volume of 88.2 mL is heated from 35°C to
155°C. What is the final volume of the gas in milliliters?
FOR MORE PRACTICE
Introductory Chemistry, Third Edition
By Nivaldo J. Tro
Problems 43, 44, 45, 46.
Copyright ©2009 by Pearson Education, Inc.
Upper Saddle River, New Jersey 07458
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EXAMPLE 11.4
The Combined Gas Law
A sample of gas has an initial volume of 158 mL at a pressure of 735 mm Hg and a temperature of 34°C. If the gas
is compressed to a volume of 108 mL and heated to a temperature of 85°C, what is its final pressure in millimeters
of mercury?
You are given an initial pressure,
temperature, and volume as well as a final
temperature and volume. You are asked to
find the final pressure.
Given:
Find: P2
P1 = 735 mm Hg
t1 = 34 °C
V1 = 158 mL
This problem requires the use of the
combined gas law.
Equation:
Draw a solution map beginning with the
given quantities. The combined gas law
shows the relationship necessary to get to the
find quantity.
Solution Map:
Introductory Chemistry, Third Edition
By Nivaldo J. Tro
t2 = 85 °C
V2 = 108 mL
Copyright ©2009 by Pearson Education, Inc.
Upper Saddle River, New Jersey 07458
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EXAMPLE 11.4
The Combined Gas Law
Continued
Solve the equation for the quantity you are
trying to find (P2).
Solution:
Before you substitute in the numerical
values, you must convert the temperatures to
kelvins.
Once you have converted the temperature
to kelvins, substitute into the equation to
find P2 .
Introductory Chemistry, Third Edition
By Nivaldo J. Tro
Copyright ©2009 by Pearson Education, Inc.
Upper Saddle River, New Jersey 07458
All rights reserved.
EXAMPLE 11.4
The Combined Gas Law
Continued
SKILLBUILDER 11.4
The Combined Gas Law
A balloon has a volume of 3.7 L at a pressure of 1.1 atm and a temperature of 30 °C. If the balloon is
submerged in water to a depth where the pressure is 4.7 atm and the temperature is 15 °C, what will its
volume be (assume that any changes in pressure caused by the skin of the balloon are negligible)?
FOR MORE PRACTICE
Introductory Chemistry, Third Edition
By Nivaldo J. Tro
Example 11.15; Problems 55, 56, 57, 58, 59, 60.
Copyright ©2009 by Pearson Education, Inc.
Upper Saddle River, New Jersey 07458
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EXAMPLE 11.5
Avogadro’s Law
A 4.8-L sample of helium gas contains 0.22 mol of helium. How many additional moles of helium gas must be
added to the sample to obtain a volume of 6.4 L? Assume constant temperature and pressure.
You are given an initial volume, an initial
number of moles, and a final volume. You
are (essentially) asked to find the final
number of moles.
This problem requires the use of Avogadro’s
law
Draw a solution map beginning with the
given quantities. Avogadro’s law shows the
relationship necessary to get to the find
quantity.
Introductory Chemistry, Third Edition
By Nivaldo J. Tro
Given:
Find: n2
Equation:
V1 = 4.8 L
n1 = 0.22 mol
V2 = 6.4 L
Solution Map:
Copyright ©2009 by Pearson Education, Inc.
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EXAMPLE 11.5
Avogadro’s Law
Continued
Solve the equation for the quantity you are
trying to find (n2)and substitute the
appropriate quantities to compute n2.
Solution:
Since the balloon already contains 0.22 mol,
subtract this quantity from the final number
of moles to determine how much must be
added
SKILLBUILDER 11.5
mol to add = 0.29 – 0.22 = 0.07 mol
Avogadro’s Law
A chemical reaction occurring in a cylinder equipped with a moveable piston produces 0.58 mol of a
gaseous product. If the cylinder contained 0.11 mol of gas before the reaction and had an initial volume of
2.1 L, what was its volume after the reaction?
FOR MORE PRACTICE
Introductory Chemistry, Third Edition
By Nivaldo J. Tro
Problems 49, 50, 51, 52.
Copyright ©2009 by Pearson Education, Inc.
Upper Saddle River, New Jersey 07458
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EXAMPLE 11.6
The Ideal Gas Law
Calculate the volume occupied by 0.845 mol of nitrogen gas at a pressure of 1.37 atm and a temperature of 315 K.
You are given the number of moles, the
pressure, and the temperature of a gas
sample. You are asked to find the volume.
This problem requires the use of the ideal
gas law.
Given:
n = 0.845 mol
P = 1.37 atm
T = 315 K
Find: V
Equation: PV = nRT
Draw a solution map beginning with the
given quantities. The ideal gas law shows the
relationship necessary to get to the find
quantity.
Solution Map:
Solve the equation for the quantity you are
trying to find (V) and substitute the
appropriate quantities to compute V.
Solution:
Introductory Chemistry, Third Edition
By Nivaldo J. Tro
Copyright ©2009 by Pearson Education, Inc.
Upper Saddle River, New Jersey 07458
All rights reserved.
EXAMPLE 11.6
The Ideal Gas Law
Continued
SKILLBUILDER 11.6
The Ideal Gas Law
An 8.5-L tire is filled with 0.55 mol of gas at a temperature of 305 K. What is the pressure of the gas in the
tire?
FOR MORE PRACTICE
Introductory Chemistry, Third Edition
By Nivaldo J. Tro
Example 11.16; Problems 63, 64, 65, 66.
Copyright ©2009 by Pearson Education, Inc.
Upper Saddle River, New Jersey 07458
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EXAMPLE 11.7
The Ideal Gas Law Requiring Unit Conversion
Calculate the number of moles of gas in a basketball inflated to a total pressure of 24.2 psi with a volume of 3.2 L at
25 °C.
You are given the pressure, the volume, and
the temperature of a gas sample. You are
asked to find the number of moles.
Given:
This problem requires the use of the ideal gas
law.
Find: n
Equation: PV = nRT
Draw a solution map beginning with the
given quantities. The ideal gas law shows the
relationship necessary to get to the find
quantity.
Solution Map:
Introductory Chemistry, Third Edition
By Nivaldo J. Tro
P = 24.2 psi
V = 3.2 L
t = 25 °C
Copyright ©2009 by Pearson Education, Inc.
Upper Saddle River, New Jersey 07458
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EXAMPLE 11.7
The Ideal Gas Law Requiring Unit Conversion
Continued
Solve the equation for the quantity you are
trying to find (n).
Solution:
Before substituting into the equation, you
must convert P and t into the correct units.
(Since 1.6462 is an intermediate answer,
mark the least significant digit, but don’t
round until the end.)
Finally, substitute into the equation to
compute n.
SKILLBUILDER 11.7
The Ideal Gas Law Requiring Unit Conversion
How much volume does 0.556 mol of gas occupy when its pressure is 715 mm Hg and its temperature is
58 °C?
Introductory Chemistry, Third Edition
By Nivaldo J. Tro
Copyright ©2009 by Pearson Education, Inc.
Upper Saddle River, New Jersey 07458
All rights reserved.
EXAMPLE 11.7
The Ideal Gas Law Requiring Unit Conversion
Continued
SKILLBUILDER PLUS
Find the pressure in millimeters of mercury of a 0.133-g sample of helium gas at
32 °C and contained in a 648-mL container.
FOR MORE PRACTICE
Introductory Chemistry, Third Edition
By Nivaldo J. Tro
Problems 67, 68, 71, 72.
Copyright ©2009 by Pearson Education, Inc.
Upper Saddle River, New Jersey 07458
All rights reserved.
EXAMPLE 11.8
Molar Mass Using the Ideal Gas Law and Mass Measurement
A sample of gas has a mass of 0.311 g. Its volume is 0.225 L at a temperature of 55 °C and a pressure of 886 mm
Hg. Find its molar mass.
You are given the mass, the volume, the
temperature, and the pressure of a gas
sample. You are asked to find the molar mass
of the gas.
This problem requires the use of the ideal gas
law and the definition of molar mass.
In the first part of the solution map, use the
ideal gas law to find the number of moles of
gas from the other given quantities. In the
second part, use the number of moles from
the first part, as well as the given mass, to
find the molar mass.
Introductory Chemistry, Third Edition
By Nivaldo J. Tro
Given:
m = 0.311 g
V = 0.225 L
t = 55 °C
P = 886 mm Hg
Find: molar mass (g/mol)
Equation:
Solution Map:
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EXAMPLE 11.8
Molar Mass Using the Ideal Gas Law and Mass Measurement
Continued
First, solve the ideal gas law for n.
Solution:
Before substituting into the equation, you
must convert the pressure to atm and
temperature to K.
Now, substitute into the equation to compute
n, the number of moles.
Finally, use the number of moles just found
and the given mass (m) to find the molar
mass.
Introductory Chemistry, Third Edition
By Nivaldo J. Tro
Copyright ©2009 by Pearson Education, Inc.
Upper Saddle River, New Jersey 07458
All rights reserved.
EXAMPLE 11.8
Molar Mass Using the Ideal Gas Law and Mass Measurement
Continued
SKILLBUILDER 11.8
Molar Mass Using the Ideal Gas Law and Mass Measurement
A sample of gas has a mass of 827 mg. Its volume is 0.270 L at a temperature of 88 °C and a pressure of
975 mm Hg. Find its molar mass.
FOR MORE PRACTICE
Introductory Chemistry, Third Edition
By Nivaldo J. Tro
Problems 73, 74, 75, 76.
Copyright ©2009 by Pearson Education, Inc.
Upper Saddle River, New Jersey 07458
All rights reserved.
EXAMPLE 11.9
Total Pressure and Partial Pressure
A mixture of helium, neon, and argon has a total pressure of 558 mm Hg. If the partial pressure of helium is
341 mm Hg and the partial pressure of neon is 112 mm Hg, what is the partial pressure of argon?
You are given the total pressure of a gas
mixture and the partial pressures of two (of
its three) components. You are asked to find
the partial pressure of the third component.
This problem requires the use of Dalton’s
law of partial pressures.
To solve this problem, simply solve Dalton’s
law for the partial pressure of argon and
substitute the correct values to compute it.
SKILLBUILDER 11.9
Given:
Ptot = 558 mm Hg
PHe = 341 mm Hg
PNe = 112 mm Hg
Find: PAr
Equation: Ptot = Pa + Pb + Pc + . . .
Solution:
Ptot = PHe + PNe + PAr
PAr = Ptot + PHe + PNe
= 558 mm Hg – 341 mm Hg – 112 mm Hg
= 105 mm Hg
Total Pressure and Partial Pressure
A sample of hydrogen gas is mixed with water vapor. The mixture has a total pressure of 745 torr, and the
water vapor has a partial pressure of 24 torr. What is the partial pressure of the hydrogen gas?
FOR MORE PRACTICE
Introductory Chemistry, Third Edition
By Nivaldo J. Tro
Example 11.17; Problems 77, 78, 79, 80.
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Upper Saddle River, New Jersey 07458
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EXAMPLE 11.10
Partial Pressure, Total Pressure, and Percent Composition
Calculate the partial pressure of oxygen that a diver breathes with a heliox mixture containing 2.0% oxygen at a
depth of 100 m where the total pressure is 10.0 atm.
You are given the percent oxygen in the
mixture and the total pressure. You are asked
to find the partial pressure of oxygen.
You will need the equation that relates partial
pressure to total pressure.
Calculate the fractional composition of O2
by dividing the percent composition by 100.
Calculate the partial pressure of O2 by
multiplying the fractional composition by the
total pressure.
SKILLBUILDER 11.10
Given:
O2 percent = 2.0%
Ptot = 10.0 atm
Find:
Equation:
Partial pressure of component
= Fractional composition of component × Total pressure
Solution:
Partial Pressure, Total Pressure, and Percent Composition
What must the total pressure be for a diver breathing heliox with an oxygen composition of 5.0% to breathe
= 0.21 atm?
FOR MORE PRACTICE
Introductory Chemistry, Third Edition
By Nivaldo J. Tro
Problems 83, 84, 85, 86.
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Upper Saddle River, New Jersey 07458
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EXAMPLE 11.11
Gases in Chemical Reactions
How many liters of oxygen gas form when 294 g of KClO3 completely react in the following reaction (which is
used in the ignition of fireworks)?
Assume that the oxygen gas is collected at P = 755 mm Hg and T = 305 K.
You are given the mass of a reactant in a
chemical reaction. You are asked to find
the volume of a gaseous product at a
given pressure and temperature.
You will need the molar mass of KClO3 and
the stoichiometric relationship between
KClO3 and O2 (from the balanced chemical
equation). You will also need the ideal gas
law.
The solution map has two parts. In the first
part, convert from g KClO3 to mol KClO3
and then to mol O2 In the second part, use
mol O2 as n in the ideal gas law to find the
volume of O2 .
Introductory Chemistry, Third Edition
By Nivaldo J. Tro
294 g KClO3
P = 755 mm Hg (of oxygen gas)
T = 305 K
Find: Volume of O2 in liters
Equations and Conversion Factors:
1 mol KClO3 = 122.6 g
2 mol KClO3 = 3 mol O2
PV = nRT
Given:
Solution Map:
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EXAMPLE 11.11
Gases in Chemical Reactions
Continued
Begin by converting mass KClO3 to mol
KClO3 and then to mol O2.
Solution:
Then solve the ideal gas equation for V.
Before substituting the values into this
equation, you must convert the pressure to
atm.
Finally, substitute the given quantities along
with the number of moles just calculated to
compute the volume.
SKILLBUILDER 11.11
Gases in Chemical Reactions
In the following reaction, 4.58 L of O2 were formed at 745 mm Hg and 308 K. How many grams of Ag2O must
have decomposed?
FOR MORE PRACTICE
Introductory Chemistry, Third Edition
By Nivaldo J. Tro
Problems 93, 94, 95, 96, 97, 98.
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Upper Saddle River, New Jersey 07458
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EXAMPLE 11.12
Using Molar Volume in Calculations
How many grams of water form when 1.24 L of H2 gas at STP completely reacts with O2?
You are given the volume of a reactant at
STP and asked to find the mass of the
product formed.
You will need the molar volume at STP, the
stoichiometric relationship between H2 and
H2O (from the balanced chemical equation),
and the molar mass of H2O.
Given: 1.24 L H2
The solution map has two parts. In the first
part, convert from g KClO3 to mol KClO3
and then to mol O2 In the second part, use
mol O2 as n in the ideal gas law to find the
volume of O2 .
Solution Map:
Introductory Chemistry, Third Edition
By Nivaldo J. Tro
Find: g H2O
Conversion Factors:
1 mol = 22.4 L (at STP)
2 mol H2 = 2 mol H2O
18.02 g H2O = 1 mol H2O
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EXAMPLE 11.12
Using Molar Volume in Calculations
Continued
Begin with the volume of H2 and follow the
solution map to arrive at mass H2O in grams.
SKILLBUILDER 11.12
Solution:
Using Molar Volume in Calculations
How many liters of oxygen (at STP) are required to form 10.5 g of H2O?
FOR MORE PRACTICE
Introductory Chemistry, Third Edition
By Nivaldo J. Tro
Problems 99, 100, 101, 102.
Copyright ©2009 by Pearson Education, Inc.
Upper Saddle River, New Jersey 07458
All rights reserved.
EXAMPLE 11.13
Pressure Unit Conversion
Convert 18.4 in. Hg to torr.
Given: 18.4 in. Hg
Find: torr
Conversion Factors:
1 atm = 29.92 in. Hg
760 torr = 1 atm
Solution Map:
Solution:
Introductory Chemistry, Third Edition
By Nivaldo J. Tro
Copyright ©2009 by Pearson Education, Inc.
Upper Saddle River, New Jersey 07458
All rights reserved.
EXAMPLE 11.14
Simple Gas Laws
A gas has a volume of 5.7 L at a pressure of 3.2 atm. What is its volume at 4.7 atm? (Assume constant temperature.)
Given:
P1 = 3.2 atm
V1 = 5.7 L
P2 = 4.7 atm
Find: V2
Equation: P1V1 = P2V2
Solution Map:
Solution:
Introductory Chemistry, Third Edition
By Nivaldo J. Tro
Copyright ©2009 by Pearson Education, Inc.
Upper Saddle River, New Jersey 07458
All rights reserved.
EXAMPLE 11.15
The Combined Gas Law
A sample of gas has an initial volume of 2.4 L at a pressure of 855 mm Hg and a temperature of 298 K. If the gas is
heated to a temperature of 387 K and expanded to a volume of 4.1 L, what is its final pressure in millimeters of
mercury?
Given: P1 = 855 mm Hg
V1 = 2.4 L
T1 = 298 K
V2 = 4.1 L
T2 = 387 K
Find: P2
Equation:
Solution Map:
Introductory Chemistry, Third Edition
By Nivaldo J. Tro
Copyright ©2009 by Pearson Education, Inc.
Upper Saddle River, New Jersey 07458
All rights reserved.
EXAMPLE 11.15
The Combined Gas Law
Continued
Solution:
Introductory Chemistry, Third Edition
By Nivaldo J. Tro
Copyright ©2009 by Pearson Education, Inc.
Upper Saddle River, New Jersey 07458
All rights reserved.
EXAMPLE 11.16
The Ideal Gas Law
Calculate the pressure exerted by 1.2 mol of gas in a volume of 28.2 L and at a temperature of 334 K.
Given:
n = 1.2 mol
V = 28.2 L
T = 334 K
Find: P
Equation:
PV = nRT
Solution Map:
Solution:
Introductory Chemistry, Third Edition
By Nivaldo J. Tro
Copyright ©2009 by Pearson Education, Inc.
Upper Saddle River, New Jersey 07458
All rights reserved.
EXAMPLE 11.17
Total Pressure and Partial Pressure
A mixture of three gases has the following partial pressures.
What is the total pressure of the mixture?
Given:
Find: Ptot
Equation: Ptot = Pa + Pb + Pc + . . .
Solution:
= 289 mm Hg + 342 mm Hg + 122 mm H
= 289 mm Hg + 342 mm Hg + 122 mm Hg
Introductory Chemistry, Third Edition
By Nivaldo J. Tro
Copyright ©2009 by Pearson Education, Inc.
Upper Saddle River, New Jersey 07458
All rights reserved.