© 2012 pearson education, inc. chapter 10 gases. gases © 2012 pearson education, inc....

© 2012 Pearson Education, Inc.

Chapter 10

Gases

Gases


Characteristics of Gases

• Unlike liquids and solids, gases:– Expand to fill their containers.– Are highly compressible.– Have extremely low densities.

Gases


A. Small molecular weights

B. Large molecular weights

Gases


• Pressure is the amount of force applied to an area:

Pressure

• Atmospheric pressure is the weight of air per unit of area.

P =FA

Gases


A. 100 kPa/ 100 in.2

B. 1x 105 N x 100 in.2

C. 14.7 psi x 100 in.2

D. 14.7 psi/ 100 in.2

Gases


Units of Pressure

• Pascals– 1 Pa = 1 N/m2

• Bar– 1 bar = 105 Pa = 100 kPa

Gases


Units of Pressure

• mmHg or torr– These units are literally the difference in the heights measured in mm (h) of two connected columns of mercury.

• Atmosphere– 1.00 atm = 760 torr

Gases


A. IncreasesB. Decreases

Gases


Manometer

The manometer is used to measure the difference in pressure between atmospheric pressure and that of a gas in a vessel.

Gases


Standard Pressure

• Normal atmospheric pressure at sea level is referred to as standard pressure.

• It is equal to– 1.00 atm– 760 torr (760 mmHg)– 101.325 kPa

Gases


Sample Exercise 10.1 Converting Pressure Units

(a) Convert 0.357 atm to torr. (b) Convert 6.6 102 torr to atmospheres. (c) Convert 147.2 kPa to torr.

Practice Exercise(a) In countries that use the metric system, atmospheric pressure in weather reports is given in kilopascals. Convert a pressure of 745 torr to kilopascals. (b) The pressure at the center of Hurricane Katrina was 902 mbar (millibars). There are 1000 mbar in 1 bar; convert this pressure to atmospheres.

Gases


Sample Exercise 10.2 Using a Manometer to Measure Gas Pressure

On a certain day a laboratory barometer indicates that the atmospheric pressure is 764.7 torr. A sample of gas is placed in a flask attached to an open-end mercury manometer ( FIGURE 10.3), and a meter stick is used to measure the height of the mercury in the two arms of the U tube. The height of the mercury in the open-end arm is 136.4 mm, and the height in the arm in contact with the gas in the flask is 103.8 mm. What is the pressure of the gas in the flask (a) in atmospheres, (b) in kilopascals?

Practice ExerciseConvert a pressure of 0.975 atm into Pa and kPa.

Gases


A. IncreasesB. Decreases

Gases


Boyle’s LawThe volume of a fixed quantity of gas at constant temperature is inversely proportional to the pressure.

Gases


A. 0 torrB. 760 torrC. 1140 torrD. 1520 torr

Gases


P and V are Inversely Proportional

A plot of V versus P results in a curve.Since

V = k (1/P)This means a plot of V versus 1/P will be a straight line.

PV = k

Gases


B. Quadratic

C. Exponential

D. Linear

A. Polynomial curve of third order

Gases


A. Increases by doubling its original value.B. Increases by tripling its original value.C. Decreases to half of its original value.D. Decreases to a fourth of its original value.

Gases


Charles’s Law

• The volume of a fixed amount of gas at constant pressure is directly proportional to its absolute temperature.

Gases


Charles’s Law

• So,

• A plot of V versus T will be a straight line.

VT

= k

Gases


A. Yes, because the temperature decreases by half.

B. No, because the temperature in kelvin (K) does not decrease by half.

Gases


Avogadro’s Law• The volume of a gas at constant temperature

and pressure is directly proportional to the number of moles of the gas.

• Mathematically, this means V = kn

Gases


A. 0.5B. 1C. 1.5D. 2

Gases


Sample Exercise 10.3 Evaluating the Effects of Changes in P, V, n, and T on a Gas

Suppose we have a gas confined to a cylinder with a movable piston. (Sections 5.2, 5.3) Consider the following changes (assuming no leaks): (a) Heat the gas from 298 K to 360 K at constant pressure. (b) Reduce the volume from 1 L to 0.5 L at constant temperature. (c) Inject additional gas, keeping temperature and volume constant. Indicate how each change affects the average distance between molecules, the pressure of the gas, and the number of moles of gas in the cylinder.

Practice ExerciseRecall that density is mass per volume. (Section 1.4) What happens to the density of a gas as (a) the gas is heated in a constant-volume container; (b) the gas is compressed at constant temperature; (c) additional gas is added to a constant-volume container?

Gases


Ideal-Gas Equation

V 1/P (Boyle’s law)V T (Charles’s law)V n (Avogadro’s law)

• So far we’ve seen that

• Combining these, we get

V nTP

Gases


Ideal-Gas Equation

The relationship

Can be written as

nTP

V

nTP

V = R

or

PV = nRT

Gases


Ideal-Gas Equation

The constant of proportionality is known as R, the gas constant.

Gases


Ideal-Gas Equation

• But how is R determined?• At STP (0°C, 1 atm) the volume of 1

mol of a gas = 22.41L

KmolLatm

Kmol

LatmR 08206.0

)15.273)(1(

)41.22)(0.1(

nT

PV

Gases


A. 6.023 x 1023 molecules

B. 22.4 x 6.023 x 1023 molecules

C. x 6.023 x 1023 molecules

D. 3.012 x 1023 molecules

1

22.4

Gases


A. Helium is an inert gas.B. Helium is a member of the first period.C. Helium is a very small atom and inert.D. Helium possesses two valence electrons.

Gases


Sample Exercise 10.4 Using the Ideal-Gas Equation

Calcium carbonate, CaCO3(s), the principal compound in limestone, decomposes upon heating to CaO(s) and CO2(g). A sample of CaCO3 is decomposed, and the carbon dioxide is collected in a 250-mL flask.

After decomposition is complete, the gas has a pressure of 1.3 atm at a temperature of 31 C. How many moles of CO2 gas were generated?

Practice ExerciseTennis balls are usually filled with either air or N2 gas to a pressure above atmospheric pressure to increasetheir bounce. If a tennis ball has a volume of 144 cm3 and contains 0.33 g of N2 gas, what is the pressure inside the ball at 24 C?

Gases


Sample Exercise 10.5 Calculating the Effect of Temperature Changes on Pressure

The gas pressure in an aerosol can is 1.5 atm at 25 C. Assuming that the gas obeys the ideal-gas equation, what is the pressure when the can is heated to 450 C?

Practice ExerciseThe pressure in a natural-gas tank is maintained at 2.20 atm. On a day when the temperature is –15 C, thevolume of gas in the tank is 3.25 103 m3. What is the volume of the same quantity of gas on a day whenthe temperature is 31 C?

Gases


Sample Exercise 10.6 Calculating the Effect of Changing P and T on Gas Volume

An inflated balloon has a volume of 6.0 L at sea level (1.0 atm) and is allowed to ascend until the pressure is 0.45 atm. During ascent, the temperature of the gas falls from 22 C to 21 C. Calculate the volume of the balloon at its final altitude.

Practice ExerciseA 0.50-mol sample of oxygen gas is confined at 0 C and 1.0 atm in a cylinder with a movable piston. The piston compresses the gas so that the final volume is half the initial volume and the final pressure is 2.2 atm. What is the final temperature of the gas in degrees Celsius?

Gases


Gas Stoichiometry – ΔP Problems

• When a reaction occurs at constant volume, the change in the pressure can be used to number of moles reacted and/or formed.

V

RTnP

V

RTnP

)(

)(

Gases


A small amount of butane is mixed with air in a rigid container. The mixture, initially at 1.00 atm., is ignited:

2C4H10(g) + 13 O2(g) → 8 CO2(g) + 10 H2O(g)

After the sample is completely combusted, and cooled to the initial temperature, the pressure is now 1.12 atm. What is the initial pressure of the butane?

Gas Stoichiometry – ΔP Problems

Gases


Solution

Check your work with an ice chart!

atmatmatm

PPP initialfinal

12.000.112.1

3

2

gas moles

used moles

P

Pressure 104104

HCHC

atm 080.03

2)atm 12.0(

3

2 Pressure 104

PHC

Gases


Densities of Gases

If we divide both sides of the ideal-gas equation by V and by RT, we get

nV

PRT

=

Gases


• We know that– Moles molecular mass = mass

Densities of Gases

• So multiplying both sides by the molecular mass () gives

n = m

PRT

mV

=

Gases


Densities of Gases

• Mass volume = density

• So,

Note: One needs to know only the molecular mass, the pressure, and the temperature to calculate the density of a gas.

PRT

mV

=d =

Gases


Molecular Mass

We can manipulate the density equation to enable us to find the molecular mass of a gas:

becomes

PRT

d =

dRTP =

Gases


A. More dense

B. Less dense

Gases


Sample Exercise 10.7 Calculating Gas Density

What is the density of carbon tetrachloride vapor at 714 torr and 125 C?

Practice ExerciseThe mean molar mass of the atmosphere at the surface of Titan, Saturn’s largest moon, is 28.6 g/mo. The surface temperature is 95 K, and the pressure is 1.6 atm. Assuming ideal behavior, calculate the density of Titan’s atmosphere.

Gases


Sample Exercise 10.8 Calculating the Molar Mass of a Gas

A large evacuated flask initially has a mass of 134.567 g. When the flask is filled with a gas of unknown molar mass to a pressure of 735 torr at 31 C, its mass is 137.456 g. When the flask is evacuated again

and then filled with water at 31 C, its mass is 1067.9 g. (The density of water at this temperature is 0.997 g/mL.) Assuming the ideal-gas equation applies, calculate the molar mass of the gas.

Practice ExerciseCalculate the average molar mass of dry air if it has a density of 1.17 g/L at 21 C and 740.0 torr.

Gases


Sample Exercise 10.9 Relating a Gas Volume to the Amount of Another Substance in a Reaction

Automobile air bags are inflated by nitrogen gas generated by the rapid decomposition of sodium azide, NaN3:

2 NaN3(s) 2 Na(s) + 3 N2(g)

If an air bag has a volume of 36 L and is to be filled with nitrogen gas at 1.15 atm and 26.0 C, how many grams of NaN3 must be decomposed?

Practice ExerciseIn the first step in the industrial process for making nitric acid, ammonia reacts with oxygen in the presenceof a suitable catalyst to form nitric oxide and water vapor:

4 NH3(g) + 5 O2(g) 4 NO(g) + 6 H2O(g)How many liters of NH3(g) at 850 C and 5.00 atm are required to react with 1.00 mol of O2(g) in this reaction?

Gases


A. The pressure exerted by N2 gas does not change when O2 is

added to the container.

B. The pressure exerted by N2 gas changes only if an equal or

greater amount of O2 is added to the container.

C. The pressure exerted by N2 gas decreases when O2 is added

to the container.

D. The pressure exerted by N2 gas increases when O2 is added

to the container.

Gases


Dalton’s Law ofPartial Pressures

• The total pressure of a mixture of gases equals the sum of the pressures that each would exert if it were present alone.

• In other words,

Ptotal = P1 + P2 + P3 + …

Gases


Sample Exercise 10.10 Applying Dalton’s Law of Partial Pressures

A mixture of 6.00 g O2(g) and 9.00 g CH4(g) is placed in a 15.0-L vessel at 0 C. What is the partial pressureof each gas, and what is the total pressure in the vessel?

Practice ExerciseWhat is the total pressure exerted by a mixture of 2.00 g of H2(g) and 8.00 g of N2(g) at 273 K in a 10.0-L vessel?

Gases


Sample Exercise 10.11 Relating Mole Fractions and Partial Pressures

A study of the effects of certain gases on plant growth requires a synthetic atmosphere composed of 1.5 mol percent CO2, 18.0 mol percent O2, and 80.5 mol percent Ar. (a) Calculate the partial pressure of O2

in the mixture if the total pressure of the atmosphere is to be 745 torr. (b) If this atmosphere is to be held in a 121-L space at 295 K, how many moles of O2 are needed?

Practice ExerciseFrom data gathered by Voyager 1, scientists have estimated the composition of the atmosphere of Titan,Saturn’s largest moon. The pressure on the surface of Titan is 1220 torr. The atmosphere consists of 82 molpercent N2, 12 mol percent Ar, and 6.0 mol percent CH4. Calculate the partial pressure of each gas.

Gases


Partial Pressures

• When one collects a gas over water, there is water vapor mixed in with the gas.

• To find only the pressure of the desired gas, one must subtract the vapor pressure of water from the total pressure.

Gases


Sample Exercise 10.12 Calculating the Amount of Gas Collected over Water

When a sample of KClO3 is partially decomposed in the setup shown in Figure 10.15, the volume of gas collected is 0.250 L at 26 C and 765 torr total pressure. (a) How many moles of O2 are collected? (b) How many grams of KClO3 were decomposed?

Practice ExerciseAmmonium nitrite, NH4NO2, decomposes on heating to form N2 gas:

NH4NO2(s) N2(g) + 2 H2O(l)When a sample of NH4NO2 is decomposed in the apparatus of Figure 10.15, 511 mL of N2 gas is collected over water at 26 C and 745 torr total pressure. How many grams of NH4NO2 were decomposed?

Gases


Kinetic-Molecular Theory

This is a model that aids in our understanding of what happens to gas particles as environmental conditions change.

Gases


Main Tenets of Kinetic-Molecular Theory

Gases consist of large numbers of molecules that are in continuous, random motion.

The combined volume of all the molecules of the gas is negligible relative to the total volume in which the gas is contained.

Attractive and repulsive forces between gas molecules are negligible.

Gases



Energy can be transferred between molecules during collisions, but the average kinetic energy of the molecules does not change with time, as long as the temperature of the gas remains constant.

Gases



The average kinetic energy of the molecules is proportional to the absolute temperature.

Gases


A. 1/10B. 1/3C. 1/2D.2/3

Gases


A. Additional pressure information is needed to compare average speeds.

B. HCl < O2 < H2

C. HCl < H2 < O2

D. H2 < O2 < HCl

Gases


Sample Exercise 10.13 Applying the Kinetic-Molecular Theory

A sample of O2 gas initially at STP is compressed to a smaller volume at constant temperature. What effect does this change have on (a) the average kinetic energy of the molecules, (b) their average speed, (c) the number of collisions they make with the container walls per unit time, (d) the number of collisions they make with a unit area of container wall per unit time?

Practice ExerciseHow is the rms speed of N2 molecules in a gas sample changed by (a) an increase in temperature,(b) an increase in volume, (c) mixing with a sample of Ar at the same temperature.

Gases

© 2012 Pearson Education, Inc.58

The Meaning of Temperature

Kelvin temperature is an index of the random motions of gas particles (higher T means greater motion.)

(KE)32avg RT

Gases


Kinetic Molecular Theory • Root mean square speed is an average

molecular speed• For one mole of a gas KE = 3/2 RT• For one molecule • Therefore

22

1 umKE

molKJRwhere

RTuu

RTu

RTumN

rms

A

3145.83

3

2

2

232

21

Gases


A. At constant T, root-mean-square speeds increase with increasingmolar masses.

B. At constant T, root-mean-square speeds increase with decreasingmolar masses.

Gases


Sample Exercise 10.14 Calculating a Root-Mean-Square SpeedCalculate the rms speed of the molecules in a sample of N2 gas at 25 C.

Practice ExerciseWhat is the rms speed of an atom in a sample of He gas at 25 C?

Gases


Kinetic Molecular Theory • The most probable speed of a gas can also be

determined:

RTump

2

Gases


A. 2/3

B. 1

C. 3/2

D. 2

Gases


Graham's Law

1

2

2

1

2

1

2

1

3

3

M

M

MRT

MRT

r

r

rms

rms

Gases


Effusion

Effusion is the escape of gas molecules through a tiny hole into an evacuated space.

Gases


Effusion

The difference in the rates of effusion for helium and nitrogen, for example, explains why a helium balloon would deflate faster.

Gases


A. RB. n

Gases


Sample Exercise 10.15 Applying Graham’s LawAn unknown gas composed of homonuclear diatomic molecules effuses at a rate that is 0.355 times the rate at which O2 gas effuses at the same temperature. Calculate the molar mass of the unknown and identify it.

Practice ExerciseCalculate the ratio of the effusion rates of N2 gas and O2 gas.

Gases


Diffusion

Diffusion is the spread of one substance throughout a space or throughout a second substance.

Gases


Increasing P Increasing T

A. Increase Increase

B. Decrease No change

C. Increase Decrease

D. No change Decrease

Gases


Diffusion

When two cottons plugs soaked in ammonia and hydrochloric acid are simultaneously placed at the ends of a long tube, a white ring forms where the NH3 and HCl molecules meet.

The calculated ratio is actually greater than the ratio determined from careful experiments. Why?

Gases


Real Gases

In the real world, the behavior of gases only conforms to the ideal-gas equation at relatively high temperature and low pressure.

Gases


A. AlwaysB. NeverC. Mostly not

Gases


Real Gases

Even the same gas will show wildly different behavior under high pressure at different temperatures.

Gases


Gases


A. 100 K and 1 atm

B. 100 K and 5 atm

C. 300 K and 2 atm

Gases


Deviations from Ideal Behavior

The assumptions made in the kinetic-molecular model (negligible volume of gas molecules themselves, no attractive forces between gas molecules, etc.) break down at high pressure and/or low temperature.

Gases


A. IncreaseB. DecreaseC. No change

Gases


A. Gases deviate from ideal behavior if their molar mass exceeds that of H2O and temperature is lower than 298 K.

B. Gases deviate from ideal behavior if the pressure is below 1 am and temperature is lower than 298 K.

C. Gases deviate from ideal behavior because the molecules have finite sizes and there are some attractions between the molecules.

D. Gases deviate from ideal behavior if their normal boiling points are below room temperature and greater than the freezing point of H2O.

Gases


Corrections for Nonideal Behavior

• The ideal-gas equation can be adjusted to take these deviations from ideal behavior into account.

• The corrected ideal-gas equation is known as the van der Waals equation.

) (V − nb) = nRTn2aV2(P +

Gases


The van der Waals Equation

) (V − nb) = nRTn2aV2(P +

Gases


Sample Exercise 10.16 Using the van der Waals Equation

If 1.000 mol of an ideal gas were confined to 22.41 L at 0.0 C, it would exert a pressure of 1.000 atm. Use the van der Waals equation and Table 10.3 to estimate the pressure exerted by 1.000 mol of Cl2(g) in 22.41 L at 0.0 C.

Practice ExerciseA sample of 1.000 mol of CO2(g) is confined to a 3.000-L container at 0.000 C. Calculate thepressure of the gas using (a) the ideal-gas equation and (b) the van der Waals equation.

© 2012 pearson education, inc. chapter 10 gases. gases © 2012 pearson education, inc....

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