chapter 5 the gaseous state. g as p roperties خصائص الغازات 5 | 2 gases differ from...
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Chapter 5The Gaseous
State
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GAS PROPERTIESالغازات خصائص
5 | 2
Gases differ from liquids and solids:: يلي بما والصلب السوائل عن يختلف الغاز
They are compressible. االنضغاط او للضغط القابلية
The variables pressure, volume, temperature, and amount are related.
جميعها هي والكميات الحرارة، الحجم، الضغط، ناحية من التنوععالقة ذات
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PRESSUREبالضغط Pressure, Pلنبدأ
The force exerted per unit area بالرمز له ويرمز من Pالضغط وحدة عل المؤثرة القوة هو
المساحة
It can be given by two equations: توضيحها يمكن بمعادلتين
The SI unit for pressure is the pascal, Pa.
5 | 3(pascal)Pasm
kgm
s
m
m
kg223
dgh P A
FP
(pascal)Pasm
kg
ms
mkg
22
2
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PRESSURE
Other Pressure Unitsatmosphere, atmmmHgtorrBar
العادي الجوي زئبق 760الضغط ملم هو الضغط هذا عل الغاز مل 100حجم
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PRESSURE
A barometer is a device for measuring the pressure of the atmosphere.
الجوي الضغط لقياس جهازA manometer is a device for measuring the pressure of a gas or liquid in a vessel. االنابيب في السائل او الغاز ضغط لقياس جهاز
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EXAMPLE 1
The water column would be higher because its density is less by a factor equal to the density of mercury to the density of water.
بعامل اكثر وسترتفع اقل الماء كثافة طبعاكثافة بنسبو مضروب الزئبق لكثافة مساوي
معادلة حسب الماء كثافة الى الزئبقالضغط
5 | 6
OHOHHgHg 22hgdhgd
gdhP
OH
HgHgOH
2
2
d
dhh
اكثر سيرتفع العمودين اي بالماء وواحد بالزئبق مليء واحد الجوي الضغط لقياس بارميتر جهازين لديك ان لنفترض
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GAS LAWSالغاز قانون
5 | 7
Empirical Gas Laws التجريبي الغازات قانون
All gases behave quite simply with respect to temperature, pressure, volume, and molar amount. By holding two of these physical properties constant, it becomes possible to show a simple relationship between the other two properties.
والحجم الضغط الحرارة لدرجة تعرضها بحسب الغازات تتصرف . الخواص هذه من اثنان تثبيت تم اذا الموالت كمية و فيه الموضوعة
المتبقيتين الخاصيتين بين العالقة اظهار فباالمكان للغازات الفيزيائيةThe studies leading to the empirical gas laws occurred from the mid-17th century to the mid-19th century.
من موجودة التجريبية الغازات نظرية على الموجودة الدراسات. عشر التاسع القرن وحتى عشر السابع القرن منتصف
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BOYLE’S LAW
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Boyle’s Law بويل قانون
The volume of a sample of gas at constant temperature varies inversely with the applied pressure.
الذي الضغط مع عكسيا تختلف ثابتة حرارة درجات في الغاز عينة حجمله تتعرض
The mathematical relationship:
In equation form:
وعليه معين غاز حجم هناك كان فلو مترافقين دائما والضغط الحجم اذنفي اختالف او زيادة اي مع متناسبة الحجم محصلة تبقى معين ضغط
الضغط
PV
1
ffii
constant
VPVP
PV
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BOYLE’S LAW
5 | 9
Figure A shows the plot of V versus P for 1.000 g O2 at 0°C. This plot is nonlinear.
Figure B shows the plot of (1/V) versus P for 1.000 g O2 at 0°C. This plot is linear, illustrating the inverse relationship.
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BOYLE’S LAW
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At one atmosphere the volume of the gas is 100 mL. When pressure is doubled, the volume is halved to 50 mL. When pressure is tripled, the volume decreases to one-third, 33 mL.
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BOYLE’S LAW
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When a 1.00-g sample of O2 gas at 0C is placed in a containerat a pressure of 0.50 atm, it occupies a volume of 1.40 L.
When the pressure on the O2 is doubled to 1.0 atm, the volume is reduced to 0.70 L, half the original volume.
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EXAMPLE 2
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A volume of oxygen gas occupies 38.7 mL at 751 mmHg and 21°C. What is the volume if the pressure changes to 359 mmHg while the temperature remains constant?
Vi = 38.7 mLPi = 751 mmHgTi = 21°C
Vf = ?Pf = 359 mmHgTf = 21°C
f
iif P
VPV
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f
iif P
VPV
5 | 13
Vi = 38.7 mLPi = 751 mmHgTi = 21°C
Vf = ?Pf = 359 mmHgTf = 21°C
mmHg)(359
mmHg)mL)(751(38.7f V
= 81.0 mL(3 significant figures)
Example 2 (Cont)
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VOLUME - TEMPERATURE
5 | 14A graph of V versus T is linear. Note that all lines cross
zero volume at the same temperature, -273.15°C.
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ABSOLUTE ZEROالمطلق الصفر ظارة
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The temperature -273.15°C is called absolute zero. It is the temperature at which the volume of a gas is hypothetically zero.
- حرارة درجة درجة 273.15تسمى وهي المطلق الصفر بدرجة. صفر نظريا الغازات احجام تكون عندها التي الحرارة
This is the basis of the absolute temperature scale, the Kelvin scale (K). لتدريج االساسية الدرجة بالمناسبة وهي
الحراري كالفن
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CHARLES’ LAWتشارل قانون
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Charles’ LawThe volume of a sample of gas at constant pressure is directly proportional to the absolute temperature (K).
مع مباشرة يتناسب ثابت ضغط درجة على الغاز من عينة حجم. بالكالفن المطلقة الحرارة قيمة
The mathematical relationship:
In equation form:
TV
f
f
i
i
constant
T
V
T
VT
V
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CHARLES’ LAW
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A balloon was immersed in liquid nitrogen (black container) and is shown immediately after being removed. It shrank because air inside contracts in volume.
As the air inside warms, the balloon expands to its orginial size.
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CHARLES’ LAW
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A 1.0-g sample of O2 at a temperature of 100 K and a pressure of 1.0 atm occupies a volume of 0.26 L.
When the absolute temperature of the sample is raised to 200 K, the volume of the O2 is doubled to 0.52 L.
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EXAMPLE 3
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You prepared carbon dioxide by adding HCl(aq) to marble chips, CaCO3. According to your calculations, you should obtain 79.4 mL of CO2 at 0°C and 760 mmHg. How many milliliters of gas would you obtain at 27°C?
Vi = 79.4 mLPi = 760 mmHgTi = 0°C = 273 K
Vf = ?Pf = 760 mmHgTf = 27°C = 300. K
i
iff T
VTV
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i
iff T
VTV
5 | 20
Vi = 79.4 mLPi = 760 mmHgTi = 0°C = 273 K
Vf = ?Pf = 760 mmHgTf = 27°C = 300. K
K)(273
mL)K)(79.4(300.f V
= 87.3 mL(3 significant figures)
Example 3 (Cont)
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GAY-LUSSAC’S LAWلوساك جاي قانون
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Gay-Lussac’s Law
There is an analogous relationship to Charles’ Law that relates pressure and temperature. This relationship is called Gay-Lussac’s Law, and is described as follows:
قيم منخاللها ترتبط والتي شارل لقانون متناظرة عالقة هناكبالحرارة الضعط
The mathematical relationship:
In equation form:
P T
P
Tconstant
Pi
Ti
Pf
Tf
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GAY-LUSSAC’S LAW
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Interestingly, a plot of pressure versus temperature can also be extrapolated to estimate absolute zero, and values from Charles’ Law and Gay-Lussac’s Law give equivalent estimates.
نقطة تقدير الممكن من والحرارة الضغط بين العالقة رسمومنها والحجم الحرارة بين تشارلز وقيم فيها المطلق الصفر
غاي قانون اشراك يمكن ايضاProblems using Gas-Lussac’s Law are done in the
same fashion as Charles’ Law, and though we will not do any here, you will be accountable for solving them as well.
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COMBINED GAS LAWالمشترك الغازات قانون الى ينقلنا هذا
القوانين هذه من
5 | 23
Combined Gas LawThe volume of a sample of gas at constant pressure is inversely proportional to the pressure and directly proportional to the absolute temperature.
ثابتة ضغط قيمة عند الغاز عينة حجم بان القانون هذا وينصبالكالفن المطلقة الحرارة مع وطرديا الضغط مع عكسيا تتناسب
The mathematical relationship:
In equation form:
P
TV
f
ff
i
ii
constant
T
VP
T
VPT
PV
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EXAMPLE 4
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Divers working from a North Sea drilling platform experience pressure of 5.0 × 101 atm at a depth of 5.0 × 102 m. If a balloon is inflated to a volume of 5.0 L (the volume of the lung) at that depth at a water temperature of 4°C, what would the volume of the balloon be on the surface (1.0 atm pressure) at a temperature of 11°C?
Vi = 5.0 LPi = 5.0 × 101 atmTi = 4°C = 277 K
Vf = ?Pf = 1.0 atmTf = 11°C = 284 K
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EXAMPLE 4 (CONT)
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Vi = 5.0 LPi = 5.0 × 101 atmTi = 4°C = 277 K
Vf = ?Pf = 1.0 atmTf = 11°C = 284. K
fi
iiff PT
VPTV
atm)K)(1.0(277
L)atm)(5.010xK)(5.0(284 1
f V
= 2.6 x 102 L(2 significant figures)
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EXAMPLE 5
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EXAMPLE 5 (CONT)
a. Decreasing the temperature at a constant pressure results in a decrease in volume. Subsequently increasing the volume at a constant temperature results in a decrease in pressure.
b. Increasing the temperature at a constant pressure results in an increase in volume. Subsequently decreasing the volume at a constant temperature results in an increase in pressure.
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AVOGADRO’S LAWافوجادرو قانون
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Avogadro’s LawEqual volumes of any two gases at the same temperature and pressure contain the same number of molecules. We could also say,
الحرارة درجة نفس على مختلفين غازين من المتسوية االحجامنقول ان ونستطيع الجزيئات، من العدد نفس على تحتوي والضغط
ايضا:
V n and V
n = K
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STANDARD TEMPERATURE AND PRESSURE والضغط الحرارة ظروف المثالية
5 | 29
Standard Temperature and Pressure (STP)The reference condition for gases, chosen by convention to be exactly 0°C and 1 atm pressure.
مئوي صفر بحرارة تكون ان على اتفق للغازات المرجعية الظروف هياتموسفير وواحد
The molar volume, Vm, of a gas at STP is 22.4 L/mol. هو المثالية الظروف في للغاز المولي مول 22.4الجم لكل لتر
The volume of the yellow box is 22.4 L. To its left is a basketball.
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IDEAL GAS CONSTANT
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Ideal Gas Law
المثالي الغاز قانونThe ideal gas law is given by the
equation
PV=nRT
The molar gas constant, R, is the constant of proportionality that relates the molar volume of a gas to T/P.
التناسب ثابت هو المولي الغاز ثابتللغاز المولي الحجم بين يربط الذي
والضغط الحرارة T/Pمع
constant. is whereRT
V
RT
VP n
nRT PV
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EXAMPLE 6
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You put varying amounts of a gas into a given container at a given temperature. Use the ideal gas law to show that the amount (moles) of gas is proportional to the pressure at constant temperature and volume.
. معينة حرارة بدرجة وعاء في الغاز من مختلفة كميات وضعتتتناب بالموالت الغاز كمية بأن الظهار المثالي الغاز قانون اتخدم
ثابتين وحجم حرارة درجات في الضغط مع
constant. is whereRT
V
RT
VP n
nRT PV
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EXAMPLE 7
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A 50.0-L cylinder of nitrogen, N2, has a pressure of 17.1 atm at 23°C. What is the mass of nitrogen in the cylinder?
50 ضغطها النيترجين على تحتوي اسطوانة على 17.1لتر اتموسفيرحرارة . 23درجة النيتروجين؟ كتلة ماهي V = 50.0 Lمئوية
P = 17.1 atmT = 23°C = 296 K
RT
PVn
K)(296Kmol
atmL0.08206
L)atm)(50.0(17.1
n
mass = 986 g(3 significant figures)mol
g28.01mol35.20mass
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MOLAR MASS AND DENSITYوالكثافة المولية الكتلة
5 | 33
P
dRTM
RT
PMd m
m or
Gas Density and Molar Mass
Using the ideal gas law, it is possible to calculate the moles in 1 L at a given temperature and pressure. The number of moles can then be converted to grams (per liter).
الموالت حساب الممكن من المثالي الغاز قانون باستخدامنحول وبعدها معينين، وضغط حرارة درجة على لتر في
غرامات الى الموالت
To find molar mass, find the moles of gas, and then find the ratio of mass to moles.
In equation form:
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EXAMPLE 8
5 | 34
What is the density of methane gas (natural gas), CH4, at 125°C and 3.50 atm?
Mm = 16.04 g/molP = 3.50 atmT = 125°C = 398 K
RT
PMd m
K)(398Kmol
atmL0.08206
atm))(3.50mol
g(16.04
dfigures)tsignifican(3L
g1.72d
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EXAMPLE 9
5 | 35
A 500.0-mL flask containing a sample of octane (a component of gasoline) is placed in a boiling water bath in Denver, where the atmospheric pressure is 634 mmHg and water boils at 95.0°C. The mass of the vapor required to fill the flask is 1.57 g. What is the molar mass of octane? (Note: The empirical formula of octane is C4H9.) What is the molecular formula of octane?
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EXAMPLE 9 (CONT)
5 | 36
P = 634 mmHg = 0.8342 atm P
dRTM m
atm)(0.8342
K368.2Kmol
atmL0.08206
L
g3.140
m
M
figures)tsignifican(3mol
g114mM
d = 1.57 g/0.5000 L = 3.140 g/L
T = 95.0°C = 368.2 K
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EXAMPLE 9 (CONT)
2
mol
g57
mol
g114
n
5 | 37
Molecular formula: C8H18
Molar mass = 114 g/molEmpirical formula: C4H9
Empirical formula molar mass = 57 g/mol
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EXAMPLE 10
5 | 38
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EXAMPLE 10 (CONT)
Assume the flasks are closed.
a. All flasks contain the same number of atoms.
b. The gas with the highest molar mass, Xe, has the greatest density.
c. The flask at the highest temperature (the one containing He) has the highest pressure.
d. The number of atoms is unchanged.
5 | 39
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STOICHIOMETRY AND THE GAS LAWS
5 | 40
Stoichiometry and Gas VolumesUse the ideal gas law to find moles from a given volume, pressure, and temperature, and vice versa.
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EXAMPLE 11
5 | 41
When a 2.0-L bottle of concentrated HCl was spilled, 1.2 kg of CaCO3 was required to neutralize the spill. What volume of CO2 was released by the neutralization at 735 mmHg and 20.°C?
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EXAMPLE 11 (CONT)
1.2 x103g CaCO3 1mol CaCO3
100.09 g CaCO3
1mol CO2
1mol CaCO3
5 | 42
First, write the balanced chemical equation:
CaCO3(s) + 2HCl(aq) CaCl2(aq) + H2O(l) + CO2(g)
Moles of CO2 produced = 11.99 mol
Second, calculate the moles of CO2 produced:
Molar mass of CaCO3 = 100.09 g/mol
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EXAMPLE 11 (CONT)
5 | 43
n = 12.0 molP = 735 mmHg = 0.967 atmT = 20°C = 293 K
P
nRTV
atm)(0.967
K)(293Kmol
atmL0.08206mol12.0
V
= 3.0 × 102 L(2 significant figures)
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DALTON’S LAW
5 | 44
Gas MixturesDalton found that in a mixture of unreactive gases each gas acts as if it were the only the only gas in the mixture as far as pressure is concerned.
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DALTON’S LAW
5 | 45
Originally (left), flask A contains He at 152 mmHg and flask B contains O2 at 608 mmHg. Flask A is then filled with oil forcing the He into flask B (right). The new pressure in flask B is 760 mmHg
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DALTON’S LAW
Partial PressureThe pressure exerted by a particular gas in a mixture
Dalton’s Law of Partial PressuresThe sum of the partial pressures of all the different gases in a mixture is equal to the total pressure of the mixture:
P = PA + PB + PC + . . .
5 | 46
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EXAMPLE 12
5 | 47
A 100.0-mL sample of air exhaled from the lungs is analyzed and found to contain 0.0830 g N2, 0.0194 g O2, 0.00640 g CO2, and 0.00441 g water vapor at 35°C. What is the partial pressure of each component and the total pressure of the sample?
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EXAMPLE 12 (CONT)
5 | 48
mL10
L1mL100.0
K308Kmol
atmL0.08206
Ng28.01
Nmol1Ng0.0830
3
2
22
N2P
mL10
L1mL100.0
K308Kmol
atmL0.08206
Og32.00
Omol1Og0.0194
3
2
22
O2P
mL10
L1mL100.0
K308Kmol
atmL0.08206
COg44.01
COmol1COg0.00640
3
2
22
CO2P
mL10
L1mL100.0
K308Kmol
atmL0.08206
OHg18.01
OHmol1OHg0.00441
3
2
22
OH2P
atm0.749
atm0.153
atm0.0368
atm0.0619
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EXAMPLE 12 (CONT)
OHCOON 2222PPPPP
5 | 49
atm0.7492N P
atm0.1532O P
atm0.03682CO P
atm0.0619OH2P
P = 1.00 atm
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EXAMPLE 13
5 | 50
The partial pressure of air in the alveoli (the air sacs in the lungs) is as follows: nitrogen, 570.0 mmHg; oxygen, 103.0 mmHg; carbon dioxide, 40.0 mmHg; and water vapor, 47.0 mmHg. What is the mole fraction of each component of the alveolar air?
mmHg40.02CO P
Hg103.02O P
mmHg570.02N P
mmHg47.0OH2P
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EXAMPLE 13 (CONT)
5 | 51
OHCOON 2222PPPPP
570.0 mmHg103.0 mmHg
40.0 mmHg47.0 mmHg
P = 760.0 mmHg
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EXAMPLE 13 (CONT)
5 | 52
Mole fraction of N2
Mole fraction of H2OMole fraction of CO2
Mole fraction of O2
mmHg760.0
mmHg47.0
mmHg760.0
mmHg40.0
mmHg760.0
mmHg103.0
mmHg760.0
mmHg570.0
Mole fraction N2 = 0.7500
Mole fraction O2 = 0.1355
Mole fraction CO2 = 0.0526
Mole fraction O2 = 0.0618
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EXAMPLE 14
5 | 53
a. Nothing happens to the pressure of H2.b. The pressures are equal because the moles are
equal.c. The total pressure is the sum of the pressures of the
two gases. Because the pressures are equal, the total pressure is double the individual pressures.
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DALTON’S LAW AND WATER VAPOR
5 | 54
Collecting Gas Over WaterGases are often collected over water. The result is a mixture of the gas and water vapor. The total pressure is equal to the sum of the gas pressure and the vapor pressure of water. The partial pressure of water depends only on temperature and is known (Table 5.6).The pressure of the gas can then be found using Dalton’s law of partial pressures
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COLLECTING GAS OVER WATER
5 | 55
The reaction of Zn(s) with HCl(aq) produces hydrogen gas according to the following reaction:
Zn(s) + 2HCl(aq) ZnCl2(aq) + H2(g)
The next slide illustrates the apparatus used to collect the hydrogen. The result is a mixture of hydrogen and water vapor.
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APPARATUS FOR TRAPPING GAS
5 | 56
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WATER VAPOR
5 | 57
5.6)Table(See
mmHg16.5PC,19At
mmHg769
OH2
P
mmHg16.5mmHg7692
22
22
H
OHH
OHH
P
PPP
PPP
mmHg752.52H P
places)decimal(no
mmHg7532H P
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EXAMPLE 15
5 | 58
You prepare nitrogen gas by heating ammonium nitrite:NH4NO2(s) N2(g) + 2H2O(l)
If you collected the nitrogen over water at 23°C and 727 mmHg, how many liters of gas would you obtain from 5.68 g NH4NO2?
Molar mass NH4NO2
= 64.05 g/mol
P = 727 mmHgPvapor = 21.1 mmHgPgas = 706 mmHgT = 23°C = 296 K
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3
2
3
33 CaCOmol1
COmol1
CaCOg64.04
CaComol1CaCOg5.68
5 | 59
P = 727 mmHgPvapor = 21.1 mmHgPgas = 706 mmHgT = 23°C = 296 K P
nRTV
Molar mass NH4NO2
= 64.04 g/mol
= 0.8869 mol CO2 gas
Example 15 (Cont)
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5 | 60
P = 727 mmHgPvapor = 21.1 mmHgPgas = 706 mmHgT = 23°C = 296 Kn = 0.8869 mol
P
nRTV
mmHg760atm1
mmHg706
K)(296Kmol
atmL0.08206mol0.0887
V
= 2.32 L of CO2
(3 significant figures)
Example 15 (Cont)