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CHEMISTRY - OPENSTAX 2015E

CH.9 - GASES

CONCEPT: UNITS OF PRESSURE

Pressure is defined as the force exerted per unit of surface area.

The SI unit for Pressure is the ________________, which has the units of ________________.

The SI Unit for Force is the ________________, which has the units of ________________.

Despite a gradual change to SI units for pressure, many chemists still express pressure in _______ , _______ and _______

Unit Name

Pressure Unit

Pascal (Pa); Kilopascal (kPa)

1.01325 x 105 Pa; 101.325 kPa

Atmosphere (atm) 1 atm

Millimeters of mercury (mmHg) 760 mmHg

Torr 760 torr

Bar 1.01325 bar

Pounds per square inch (lb/in2 or psi) 14.7 lb/in2

Psi 14.696 psi

ForceArea Pressure =


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PRACTICE: UNITS OF PRESSURE

EXAMPLE: A geochemist heats a limestone (CaCO3) sample and collects the CO2 released in an evacuated flask. The CO2

pressure is 283.7 mmHg. Calculate the CO2 pressure in torrs and atmospheres.

PRACTICE: If the barometer in a laboratory reads 34.2 inHg what is the pressure in bars? (1 in = 2.54 cm)


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CONCEPT: MANOMETER A manometer is an instrument used to measure the pressure of a gas within a container.

• The pressure of the gas is determined by measuring the difference in height of the mercury within the manometer.

EXAMPLE: The pressure of a gas sample is recorded at sea level with an open-end U-tube manometer. If the height of the mercury solution within the barometer is 14.5 cm higher on the side open to the atmosphere, what is the pressure (in atm) of the gas? The barometric pressure at the time of recording was 786.9 torr.


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CONCEPT: PARTIAL PRESSURES OF GASES

_________________ Law states that in a container of unreacting gases, the total pressure of the container is the sum of the

partial pressures of the individual gases.

PTOTAL = PGas 1 + PGas 2 + PGas 3 + ……

The total pressure is due to the total number of moles.

• The partial pressure of each gas molecule is the total pressure multiplied by the mole fraction of each gas molecule.

PGas1 = XGas 1)( • PTotal( )

XGas1 =molesGas1)(TotalMoles)(

X = ___________________________ PGas1 = ___________________________

EXAMPLE: A container has 16.7 g O2, 8.1 g H2 and 35.2 g N2 and contains a total pressure of 0.83 atm. Calculate the mole

fraction of O2 and its partial pressure.

PRACTICE: A gas mixture with a total pressure of 812 mmHg contains the following gases at with their partial pressures:

Cl2 = 210 mmHg, H2 = 180 mmHg, CO2 = 215 mmHg. If argon gas is also present calculate its mole fraction.


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CONCEPT: SIMPLE GAS LAWS

_________________ Law states that at constant temperature, the volume occupied by a gas in a container is inversely

proportional to the external pressure.

V = 1P [T and n fixed]

_________________ Law states that at constant pressure, the volume occupied by a gas in a container is directly

proportional to its (absolute) Kelvin temperature.

V = T [P and n fixed]

_________________ Law states that at constant temperature and pressure, the volume of a gas is directly proportional to

the amount (mol) of gas

V = n [P and T fixed]

Each of the gas laws focuses on the effect that changes in one variable can have on the volume of a gas, and by combining

these individual effects into one relationship we gain the ______________________________.

PV = nRT

_________________ Law states that at constant volume and moles of gas, the pressure exerted by a gas is directly

proportional to the internal temperature of the container.

P = T [V and n fixed]


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PRACTICE: SIMPLE GAS LAWS

EXAMPLE 1: A sample of neon gas occupies 112 mL at 0.567atm. If the temperature remains constant, what is the volume

(in L) at 1165 mmHg?

EXAMPLE 2: An engineer pumps air at 0oC into a mechanized piston-cylinder engine. If the volume measures 7.18 cm3 what will the new temperature be at 12.3 mL?

PRACTICE 1: A large plastic container holds 47.1 g of water vapor at a pressure of 1.12 atm. What is the new pressure if

12.1 g of water vapor is removed at constant temperature?

PRACTICE 2: A steel tank has a volume of 592 L and is filled with 0.638 kg of hydrogen gas. Calculate the pressure of the

gas if the temperature is 82oC.


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CONCEPT: THE IDEAL GAS LAW & STOICHIOMETRY

In the previous chapters, we encountered reactions that involved gases as:

• Reactants (i.e, combustion with O2)

• Products (i.,e. a metal displacing H2 gas from acid).

EXAMPLE: Magnesium reacts with excess hydrochloric acid to form aqueous magnesium chloride and 26.7 mL of

hydrogen gas at 25oC and 723 mmHg.

Mg (s) + 2 HCl (aq) MgCl2 (aq) + H2 (g)

How many grams of magnesium reacted?

EXAMPLE: Acetylene (C2H2), an important fuel in wielding, is produced in the laboratory when calcium carbide (CaC2)

reacts with water:

CaC2 (s) + 2 H2O (l) C2H2 (g) + Ca(OH)2 (aq)

The pressure of acetylene collected over water is 729 torr while the volume was measured as 629 mL. If at 21oC the vapor

pressure of the water is 29 torr, how many grams of acetylene was produced?


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CONCEPT: GAS BEHAVIOR AT STANDARD CONDITIONS

To better understand the factors that direct gas interactions chemists often use a set of standard conditions called

_____________________________________.

0oC (273.15 K) and 1 atm

Under these conditions, the volume of 1 mole of an ideal gas is called the _______________________________________.

22.4141 L or 22.4 L (3 Sig Figs)

EXAMPLE: A sample of Freon-12 (CF2Cl2) occupies 20.7 L at 25oC and 947 torr. What is the volume under standard

conditions?

PRACTICE: What volume will 5.72 x 1025 atoms of argon gas occupy at STP?


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CONCEPT: FURTHER APPLICATIONS OF THE IDEAL GAS LAW

By rearranging the ideal gas law we can derive new equations to figure out the density and molar mass of any gas sample.

PRACTICE 1: What is the density of chlorine gas at STP?

PRACTICE 2: An unknown gas sample weighs 3.12 g. If it has a volume of 0.206 µL when the temperature is 45oC and the

pressure is 957 torr. What is its molar mass?

PV = nRT

M =mRTPV

Molar Mass of a Gas

Original Ideal Gas Law Equation

Density of a Gas

d = PMRT


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CONCEPT: RATES OF EFFUSIONS

________________ Law states that the rate of effusion of a gas is inversely proportional to the square root of its molar

mass.

Rate of effusion =1M

RateGas1)(RateGas2)(

=MGas2)(MGas1)(

EXAMPLE 1: Calculate the ratio of the effusion rates of helium and methane (CH4).

EXAMPLE 2: Rank the following in order of increasing rate of effusion:

O2 AlF5 CO2 Xe


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CONCEPT: KINETIC ENERGY OF GASES

In order to measure the average kinetic energy of a gas molecule we must employ the root mean square equation:

urms = 3RTM

R =

T =

M =

EXAMPLE: A 1.56 x 1013 pg gaseous particle travels at 6.21 ms . Determine its kinetic energy.

PRACTICE: Calculate the molar mass, in , of a gaseous compound with an average root mean velocity of 652 ms

at a

temperature of 30oC.

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CONCEPT: THE KINETIC-MOLECULAR THEORY

To better understand the behavior of a gas we use the kinetic-molecular theory.

• Under this theory, a gas is seen as a collection of molecules or individual atoms that are in constant motion.

An ideal gas has the following characteristics:

1. The size of the particle is ____________________________________ when compared to the volume of the container.

2. The average kinetic energy of a particle is directly proportional to the temperature of the container in ______________ .

3. The collision of a particle with another gas particle or with the walls of a container are completely _________________ .

EXAMPLE: Two identical 10.0 L flasks each containing equal masses of O2 and N2 gas are heated to the same

temperature. Which of the following statements is/are true?

a) The flask with the oxygen gas will have a greater overall pressure.

b) The nitrogen and oxygen gases will have the same average speed or velocity

c) The nitrogen and oxygen gases will have the same average kinetic energy.


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CONCEPT: VAN DER WAALS EQUATION

P+ n2aV2

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%& V− nb( ) = nRT

Pideal = Pobserved + an2

V2

Videal = VContainer − nb

a = __________________ coefficient b = __________________ coefficient

a can be _______ , _______ or _______ in sign b can be _______ or _______ in sign

Ideal gas ____________ forces a = _____ Ideal gas has no volume so b = _____

Polar gas ____________ forces a = _____ Real gas has volume so b = _____

Ionized gas ____________ forces a = _____


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PRACTICE: VAN DER WAALS EQUATION (CALCULATIONS 1) EXAMPLE 1: Using the Van der Waals equation, determine the pressure of 20.0 g oxygen gas in 250 mL graduated flask when the temperature is 50 oC.

EXAMPLE 2: Which conditions of P, T and n make for the most ideal gas?

a) High P, high T, high n

b) Low P, low T, low n

c) Low P, high T, low n

d) Low P, high T, high n

P+ n2aV2

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Van der Waals Constant


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PRACTICE: VAN DER WAALS EQUATION (CALCULATIONS 2)

EXAMPLE 1: If the Vander Waal constant a is found to be 0 for gas A, what is true regarding this gas?

I. Gas A does not behave ideally. II. Gas A behaves ideally. III. Gas A is Argon.

a) I only

b) II only c) II & III only

d) III only

EXAMPLE 2: Which of the following compounds will have the lowest mean free path?

a) Chlorine b) Water c) Neon d) Helium


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2. Answer each of the following questions:

For image A, the gas container is connected to an open-end U-tube manometer. The mercury in the manometer is 5.0 cm higher on the side open to the atmosphere. If the atmospheric pressure is 759 mmHg, what is the pressure of the gas in atm?


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For image B, the gas container is connected to an open-end U-tube manometer. The mercury in the manometer is 7.6 cm lower on the side open to the atmosphere. If the atmospheric pressure is 1080 mmHg, what is the pressure of the gas in atm?


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For image C, the gas container is connected to a closed end U-tube manometer. If the pressures of the gas and the atmosphere are initially 800 mmHg and 1200 mmHg respectively, what will be the pressure of the gas if mercury in the manometer is 5.0 cm higher on the side closer to the atmosphere?


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7. A sealed container with a moveable piston contains a gas with a pressure of 1380 torr, a volume of 820 mL and a temperature of 31oC. What would the volume be if the new pressure is now 2.83 atm, while the temperature decreased to 25oC?


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8. The pressure in a system is said to be 5.83 atm. What would be the new pressure if the number of moles of gas were quadrupled and the volume were tripled while maintaining constant temperature?


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9. The pressure in a system is said to be 6.11 atm. What would be the new pressure if the number of moles of gas were cut by a third and the volume was cut by a fourth while maintaining constant temperature?


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10. A bicycle tire is filled with air to a pressure of 4.25 atm at a temperature of 19oC. Riding the bike on a hot day increases the temperature of the tire to 52oC. The volume of the tire also increases by 5.0%. What is the new pressure in the bicycle tire?


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12. What is the volume, in mL, occupied by 132.7 g CO2 (MW: 44.01 g/mol) at STP?


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13. The volume of O2 gas collected at 24oC and an atmospheric pressure of 702 mmHg is 192 mL. Calculate the mass of the dry oxygen gas collected if the pressure of water vapor at 24oC is 22 mmHg.


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16. What is the density (in g/L) of phosphorus pentachloride at 1157.3 mmHg and 32oC?


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17. A gaseous compound of nitrogen and hydrogen is found to have a density of 0.977 g/L at 528 torr and 100oC. What is the molecular formula of the compound? a) N2H4 b) NH3 c) HN3 d) HN e) N4H8


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18. Consider two containers of gases at the same temperature. One has helium at a pressure of 1.00 atm. The other contains carbon dioxide with the same density as the helium gas. What is the pressure of the carbon dioxide gas sample? a) 0.023 atm b) 1.00 atm c) 0.091 atm d) 0.18 atm e) 2.12 atm


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19. Determine the molecular formula of a gaseous compound that is 49.48% carbon, 5.19% hydrogen, 28.85% nitrogen, and 16.48% oxygen. At 27oC, the density of the gas is 1.45 g/L and it exerts a pressure of 0.092 atm.


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22. Calculate the molar mass, in gmol

, of a gaseous compound with a velocity of 312 ms

at 35oC.


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25. How many times faster will H2 gas pass through a pin hole into an area of vacuum than O2 gas? a) 32 b) 2 c) 2.5 d) 4 e) 8


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26. Rank the following in order of increasing rate of effusion:

O2 AlF5 CO2 Xe


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29. Three identical flasks contain equal moles of three different gases all at standard temperature and pressure. Flask A contains C2H4, Flask B contains CO2 and Flask C contains Cl2. Answer each of the following questions:

a) Which flask will have the greatest overall pressure?

b) Which flask has the greatest average speed of velocity?

c) Which flask has the greatest average kinetic energy? a) Which flask has the greatest density?

b) Which flask has the most molecules?

c) Which flask contains the most number of atoms?

d) Which flask has the greatest momentum?


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32. Which of the following statements is TRUE? a) Particles of different masses have the same average speed at a given temperature.

b) The larger a molecule, the faster it will effuse.

c) At very high pressures, a gas will occupy a larger volume than predicted by the ideal gas law.

d) For a given gas, the lower the temperature, the faster it will effuse.

e) None of the above statements are true.


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33. Which conditions of P, T and n make for the most ideal gas? a) High P, high T, high n

b) Low P, low T, low n

c) Low P, high T, low n

d) Low P, high T, high n


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34. Two identical 10.0 L flasks each containing equal masses of O2 and N2 gas are heated to the same temperature. Which of the following statements is/are true?

a) The flask with the oxygen gas will have a greater overall pressure.

b) The nitrogen and oxygen gases will have the same average speed or velocity

c) The nitrogen and oxygen gases will have the same average kinetic energy.


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CHEMISTRY - OPENSTAX 2015E CH.9 - GASESlightcat-files.s3.amazonaws.com/packets/admin_chemistry...In order to measure the average kinetic energy of a gas molecule we must employ the