ASSESS Reviewing Main Ideas 1. Relate the effect of temperature and pressure on a gas to the model of a gas given by the kinetic- molecular theory. 4. Agas occupies 2.0 mat 100.0 Kand exerts a pressure of 100.0 kPa. What volume will the gas occupy if the temperature is increased to 400.0 K and the pressure is increased to 200.0 kPa? 2. A sample of helium gas has a volume of 200.0 ml. at 0.960 atm. What pressure, in atmospheres, is needed to reduce the volume at constant tem- perature to 50.0 mL? Critical Thinking 5. ANALYZING RESULTS A student has the fol- lowing data: V= 822 ml, T; = 75°C, and T2=-25°C. He calculates Vz and gets -274 ml. Is this value correct? Explain why or why not. 6. APPLYING MODELS Explain Charles's law in terms of the kinetic-molecular theory. 3. A sample of nitrogen gas occupies 1.55 Lat 27.0°C and 1.00 atm. What will the volume be at -100.0°C and the same pressure?

Physical Chemistry
2nd Edition
ISBN:9781133958437
Author:Ball, David W. (david Warren), BAER, Tomas
Publisher:Ball, David W. (david Warren), BAER, Tomas
Chapter1: Gases And The Zeroth Law Of Thermodynamics
Section: Chapter Questions
Problem 1.21E: Pressures of gases in mixtures are referred to as partial pressures and are additive. 1.00 L of He...
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Gas Laws
GO ONLINE
Using Gay-Lussac's Law (continued)
Using the Combined Gas Law
Solve It! Cards
O SOLVE
Sample Problem F A helium-filled balloon has a volume of 50.0 L
at 25°C and 1.08 atm. What volume will it have at 0.855 atm and 10.0°C?
Substitute known values for T, P, and P, to calculate the new temperature.
HMHScience.com
T, P, 298 Kx 6.50 am- 40 K
T, =-
P,
= 440 K
4.40 atm
O ANALYZE
Given:
V, of He = 50.0 L
Convert back to "C.
440 K = (440 – 273) °C = 167°C
T, of He = 25°C + 273 = 298 K; T of He = 10°C + 273 = 283 K
%3D
P, of He = 1.08 atm; P, of He = 0.855 atm
9 CHECK YOUR
WORK
The units cancel to give Kelvin temperature, which was converted to °C. The
number of significant figures is correct because the data were given to three
significant figures. The pressure increases, so the temperature must also increase.
Unknown:
V, of He
2 PLAN
Because the gas remains at constant pressure, an increase in temperature will
cause an increase in volume. To obtain V2 , rearrange the equation for
Practice
1. At 120.0°C, the pressure of a sample of nitrogen is 1.07 atm. What will the pressure be at 205°C,
assuming constant volume?
2. A cylinder of compressed gas has a pressure of 4.882 atm on one day. The next day, the same
cylinder of gas has a pressure of 4.690 atm, and its temperature is 8°C. What was the temperature on
the previous day in "C?
3. A mylar balloon is filled with helium gas to a pressure of 107 kPa when the temperature is 22°C. If the
temperature changes to 45°C, what will be the pressure of the helium in the bailoon?
Charles's law.
P,V, P,V.
т,
P,V,T,
V,=
P,T,
=
T,
3 SOLVE
Substitute the known values to obtain the new volume, V,.
(1.08 atm)(50.0 L He)(283 K)
(0.855 atm)(298 K)
= 60.0 L He
O MAIN IDEA
Gas pressure, temperature, and volume are
interrelated.
The pressure factor 1.80/0.855 predicts a larger volume, and the temperature
factor 283/298 predicts a smaller volume. The pressure factor predominates,
increasing the volume from 50.0 L to 60.0 L. Units cancel appropriately. The
answer is correctly expressed to three significant figures.
CHЕCK YOUR
WORK
A gas sample often undergoes changes in temperature, pressure, and
volume all at the same time. When this happens, three variables must be
dealt with at once. Boyle's law, Charles's law, and Gay-Lussac's law can be
combined into a single expression that is useful in such situations. The
combined gas law expresses the relationship between pressure, volume, and
temperature of a fixed amount of gas. The combined gas law can be ex-
pressed as follows:
Practice
Answers in Appendix E
1 The volume of a gas is 27.5 mL at 22.0°C and 0.974 atm. What will the volume be at 15.0°C
and 0.993 atm?
2. A 700.0 mL gas sample at STP is compressed to a volume of 200.0 ml., and the temperature
is increased to 30.0°C. What is the new pressure of the gas in Pa?
PV
= k
T
In the equation, k is constant and depends on the amount of gas. The
combined gas law can also be written as follows:
V CHECK FOR UNDERSTANDING
Assess What advantage does the
combined gas law have over the
three individual gas laws?
SECTION 2 FORMATIVE ASSESSMENT
P,V,
P,V.
,
2 2
Combined gas law
Reviewing Main ldeas
1. Relate the effect of temperature and pressure on
a gas to the model of a gas given by the kinetic-
molecular theory.
4. A gas occupies 2.0 m at 100.0 K and exerts a
pressure of 100.0 kPa. What volume will the gas
occupy if the temperature is increased to 400.0K
and the pressure is increased to 200.0 kPa?
The subscripts in the equation above indicate two different sets of
conditions, and Trepresents the temperature in Kelvins.
From this expression, any value can be calculated if the other five are
known. Note that each of the gas laws can be obtained from the com-
bined gas law when the proper variable is constant. For example, Boyle's
law is obtained when the temperature is constant. Because T, = T,, T,
and T, will cancel out on both sides of the combined gas law equation,
2. A sample of helium gas has a volume of 200.0 mL
at 0.960 atm. What pressure, in atmospheres, is
Critical Thinking
5. ANALYZING RESULTS A student has the fol-
lowing data: V = 822 ml., T, = 75°C, and
T2=-25°C. He calculates V2 and gets -274 mL.
Is this value correct? Explain why or why not.
needed to reduce the volume at constant tem-
perature to 50.0 mL?
3. A sample of nitrogen gas occupies 1.55 Lat
giving Boyle's law.
27.0°C and 1.00 atm. What will the volume be at
6. APPLYING MODELS Explain Charles's law in
terms of the kinetic-molecular theory.
-100.0°C and the same pressure?
P,V, = P,V,
Gases
363
362
Chapter 11
Transcribed Image Text:Gas Laws GO ONLINE Using Gay-Lussac's Law (continued) Using the Combined Gas Law Solve It! Cards O SOLVE Sample Problem F A helium-filled balloon has a volume of 50.0 L at 25°C and 1.08 atm. What volume will it have at 0.855 atm and 10.0°C? Substitute known values for T, P, and P, to calculate the new temperature. HMHScience.com T, P, 298 Kx 6.50 am- 40 K T, =- P, = 440 K 4.40 atm O ANALYZE Given: V, of He = 50.0 L Convert back to "C. 440 K = (440 – 273) °C = 167°C T, of He = 25°C + 273 = 298 K; T of He = 10°C + 273 = 283 K %3D P, of He = 1.08 atm; P, of He = 0.855 atm 9 CHECK YOUR WORK The units cancel to give Kelvin temperature, which was converted to °C. The number of significant figures is correct because the data were given to three significant figures. The pressure increases, so the temperature must also increase. Unknown: V, of He 2 PLAN Because the gas remains at constant pressure, an increase in temperature will cause an increase in volume. To obtain V2 , rearrange the equation for Practice 1. At 120.0°C, the pressure of a sample of nitrogen is 1.07 atm. What will the pressure be at 205°C, assuming constant volume? 2. A cylinder of compressed gas has a pressure of 4.882 atm on one day. The next day, the same cylinder of gas has a pressure of 4.690 atm, and its temperature is 8°C. What was the temperature on the previous day in "C? 3. A mylar balloon is filled with helium gas to a pressure of 107 kPa when the temperature is 22°C. If the temperature changes to 45°C, what will be the pressure of the helium in the bailoon? Charles's law. P,V, P,V. т, P,V,T, V,= P,T, = T, 3 SOLVE Substitute the known values to obtain the new volume, V,. (1.08 atm)(50.0 L He)(283 K) (0.855 atm)(298 K) = 60.0 L He O MAIN IDEA Gas pressure, temperature, and volume are interrelated. The pressure factor 1.80/0.855 predicts a larger volume, and the temperature factor 283/298 predicts a smaller volume. The pressure factor predominates, increasing the volume from 50.0 L to 60.0 L. Units cancel appropriately. The answer is correctly expressed to three significant figures. CHЕCK YOUR WORK A gas sample often undergoes changes in temperature, pressure, and volume all at the same time. When this happens, three variables must be dealt with at once. Boyle's law, Charles's law, and Gay-Lussac's law can be combined into a single expression that is useful in such situations. The combined gas law expresses the relationship between pressure, volume, and temperature of a fixed amount of gas. The combined gas law can be ex- pressed as follows: Practice Answers in Appendix E 1 The volume of a gas is 27.5 mL at 22.0°C and 0.974 atm. What will the volume be at 15.0°C and 0.993 atm? 2. A 700.0 mL gas sample at STP is compressed to a volume of 200.0 ml., and the temperature is increased to 30.0°C. What is the new pressure of the gas in Pa? PV = k T In the equation, k is constant and depends on the amount of gas. The combined gas law can also be written as follows: V CHECK FOR UNDERSTANDING Assess What advantage does the combined gas law have over the three individual gas laws? SECTION 2 FORMATIVE ASSESSMENT P,V, P,V. , 2 2 Combined gas law Reviewing Main ldeas 1. Relate the effect of temperature and pressure on a gas to the model of a gas given by the kinetic- molecular theory. 4. A gas occupies 2.0 m at 100.0 K and exerts a pressure of 100.0 kPa. What volume will the gas occupy if the temperature is increased to 400.0K and the pressure is increased to 200.0 kPa? The subscripts in the equation above indicate two different sets of conditions, and Trepresents the temperature in Kelvins. From this expression, any value can be calculated if the other five are known. Note that each of the gas laws can be obtained from the com- bined gas law when the proper variable is constant. For example, Boyle's law is obtained when the temperature is constant. Because T, = T,, T, and T, will cancel out on both sides of the combined gas law equation, 2. A sample of helium gas has a volume of 200.0 mL at 0.960 atm. What pressure, in atmospheres, is Critical Thinking 5. ANALYZING RESULTS A student has the fol- lowing data: V = 822 ml., T, = 75°C, and T2=-25°C. He calculates V2 and gets -274 mL. Is this value correct? Explain why or why not. needed to reduce the volume at constant tem- perature to 50.0 mL? 3. A sample of nitrogen gas occupies 1.55 Lat giving Boyle's law. 27.0°C and 1.00 atm. What will the volume be at 6. APPLYING MODELS Explain Charles's law in terms of the kinetic-molecular theory. -100.0°C and the same pressure? P,V, = P,V, Gases 363 362 Chapter 11
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