topic 13 topic 13 topic 13: gases table of contents topic 13 topic 13 basic concepts additional...

Topic 13Topic 13

Topic 13: Gases

Table of ContentsTable of ContentsTopic 13Topic 13

Basic Concepts

Additional Concepts

• The pressure of a gas is the force per unit area that the particles in the gas exert on the walls of their container.

Defining Gas Pressure—How are number of particles and gas pressure related?

Gases: Basic ConceptsGases: Basic Concepts Gases: Basic ConceptsGases: Basic Concepts

• As you would expect, more air particles inside the ball mean more mass inside.

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• From similar observations and measurements, scientists from as long ago as the 18th century learned that the pressure of a gas is directly proportional to its mass.


Gases: Basic ConceptsGases: Basic Concepts Gases: Basic ConceptsGases: Basic Concepts Topic 13Topic 13

• According to the kinetic theory, all matter is composed of particles in constant motion, and pressure is caused by the force of gas particles striking the walls of their container.


• The more often gas particles collide with the walls of their container, the greater the pressure.


• Therefore the pressure is directly proportional to the number of particles.


• For example, doubling the number of gas particles in a basketball doubles the pressure.


• At higher temperatures, the particles in a gas have greater kinetic energy.

How are temperature and gas pressure related?

• They move faster and collide with the walls of the container more often and with greater force, so the pressure rises.


• If the volume of the container and the number of particles of gas are not changed, the pressure of a gas increases in direct proportion to the Kelvin temperature.

How are temperature and gas pressure related?

• The volume of a gas at constant pressure is directly proportional to the Kelvin temperature.


• One of the first instruments used to measure gas pressure was designed by the Italian scientist Evangelista Torricelli (1608-1647).

Devices to Measure Pressure—The Barometer

• He invented the barometer, an instrument that measures the pressure exerted by the atmosphere.



• His barometer was so sensitive that it showed the difference in atmospheric pressure between the top and bottom of a flight of stairs.



• The height of the mercury column measures the pressure exerted by the atmosphere.

• We live at the bottom of an ocean of air. • The highest pressures occur at the lowest

altitudes. • If you go up a mountain, atmospheric

pressure decreases because the depth of air above you is less.



• One unit used to measure pressure is defined by using Torricelli’s barometer.

• The standard atmosphere (atm) is defined as the pressure that supports a 760-mm column of mercury.



• This definition can be represented by the following equation.

• Because atmospheric pressure is measured with a barometer, it is often called barometric pressure.



• A barometer measures absolute pressure; that is, the total pressures exerted by all gases, including the atmosphere.


Pressure Units

• Atmospheric pressure is the force per unit area that the gases in the atmosphere exert on the surface of Earth.

• The SI unit for measuring pressure is the pascal (Pa), named after the French physicist Blaise Pascal (1623-1662).


Pressure Units

• Because the pascal is a small pressure unit, it is more convenient to use the kilopascal. 1 kilopascal (kPa) is equivalent to 1000 pascals.

• One standard atmosphere is equivalent to 101.3 kilopascals.


Pressure Units• Because there are so many different

pressure units, the international community of scientists recommends that all pressure measurements be made using SI units, but pounds per square inch continues to be widely used in engineering and almost all nonscientific applications in the United States.


Pressure Conversions

• You can use the table to convert pressure measurements to other units.

• For example, you can now find the absolute pressure of the air in a bicycle tire.


Pressure Conversions

• To find the absolute pressure, add the atmospheric pressure to the gauge pressure.

• Because the gauge pressure is given in pounds per square inch, use the value of the standard atmosphere that is expressed in pounds per square inch.

• One standard atmosphere equals 14.7 psi.

• Suppose the gauge pressure is 44 psi.


Converting Barometric Pressure Units

• In weather reports, barometric pressure is often expressed in inches of mercury.

• What is one standard atmosphere expressed in inches of mercury?

• You know that one standard atmosphere is equivalent to 760 mm of Hg. What is that height expressed in inches?

• A length of 1.00 inch measures 25.4 mm on a meterstick.



• Select the appropriate equivalent values and units given.

• Multiply 760 mm by the number of inches in each millimeter to express the measurement in inches.



• The factor on the right of the expression above is the conversion factor.

• Notice that the units are arranged so that the unit mm will cancel properly and the answer will be in inches.


Converting Pressure Units

• The reading of a tire-pressure gauge is 35 psi. What is the equivalent pressure in kilopascals?

• The given unit is pounds per square inch (psi), and the desired unit is kilopascals (kPa).

• The relationship between these two units is 14.7 = 101.3 kPa.



• Multiply and divide the values and units.

• Notice that the given units (psi) will cancel properly and the quantity will be expressed in the desired unit (kPa) in the answer.


The Gas Laws

• The gas laws apply to ideal gases, which are described by the kinetic theory in the following five statements.

• Gas particles do not attract or repel each other.

• Gas particles are much smaller than the spaces between them.


The Gas Laws

• No kinetic energy is lost when gas particles collide with each other or with the walls of their container.

• All gases have the same kinetic energy at a given temperature.

• Gas particles are in constant, random motion.


Boyle’s Law: Pressure and Volume

• Robert Boyle (1627-1691), an English scientist, used a simple apparatus pictured to compress gases.



• After performing many experiments with gases at constant temperatures, Boyle had four findings.

a) If the pressure of a gas increases, its volume decreases proportionately.

b) If the pressure of a gas decreases, its volume increases proportionately.



• By using inverse proportions, all four findings can be included in one statement called Boyle’s law.


c) If the volume of a gas increases, its pressure decreases proportionately.

d) If the volume of a gas decreases, its pressure increases proportionately.


• Boyle’s law states that the pressure and volume of a gas at constant temperature are inversely proportional.



Boyle’s Law

• At a constant temperature, the pressure exerted by a gas depends on the frequency of collisions between gas particles and the container.

• If the same number of particles is squeezed into a smaller space, the frequency of collisions increases, thereby increasing the pressure.


Boyle’s Law

• Thus, Boyle’s law states that at constant temperature, the pressure and volume of a gas are inversely related.

• In mathematical terms, this law is expressed as follows.


Applying Boyle’s Law• A sample of compressed methane has a

volume of 648 mL at a pressure of 503 kPa.

• To what pressure would the methane have to be compressed in order to have a volume of 216 mL?

• Examine the Boyle’s law equation. You need to find P2, the new pressure, so solve the equation for P2.


Applying Boyle’s Law

• Substitute known values and solve.


Charles’s Law

• When the temperature of a sample of gas is increased and the volume is free to change, the pressure of the gas does not increase. Instead, the volume of the gas increases in proportion to the increase in Kelvin temperature. This observation is Charles’s law, which can be stated mathematically as follows.


Charles’s Law



Applying Charles’s Law

• A weather balloon contains 5.30 kL of helium gas when the temperature is 12°C.

• At what temperature will the balloon’s volume have increased to 6.00 kL?

• Start by converting the given temperature to kelvins.


Applying Charles’s Law

• Next, solve the Charles’s law equation for the new temperature, T2.


Applying Charles’s Law• Then, substitute the known values and

compute the result.

• Finally, convert the Kelvin temperature back to Celsius.

New Temperature = 323 – 273 = 50oC


The Combined Gas Law

• The gas laws may be combined into a single law, called the combined gas law, that relates two sets of conditions of pressure, volume, and temperature by the following equation.

• With this equation, you can find the value of any one of the variables if you know the other five.


Applying the Combined Gas Law• A sample of nitrogen monoxide has a volume

of 72.6 mL at a temperature of 16°C and a pressure of 104.1 kPa.

• What volume will the sample occupy at 24°C and 99.3 kPa?

• Start by converting the temperatures to kelvins.


Applying the Combined Gas Law

• Next, solve the combined gas law equation for the quantity to be determined, the new volume, V2.


Applying the Combined Gas Law

• Substitute the known quantities and compute V2.


Avogadro’s Principle • In the early nineteenth century, Avogadro

proposed the idea that equal volumes of all gases at the same conditions of temperature and pressure contain the same number of particles.

• An extension of Avogadro’s principle is that one mole (6.02 x 1023 particles) of any gas at standard temperature and pressure (0°C and 1.00 atm pressure, STP) occupies a volume of 22.4 L.


Avogadro’s Principle

• Given that the mass of a mole of any gas is the molecular mass of the gas expressed in grams, Avogadro’s principle allows you to interrelate mass, moles, pressure, volume, and temperature for any sample of gas.


Applying Avogadro’s Principle

• What is the volume of 7.17 g of neon gas at 24°C and 1.05 atm?

• Start by converting the mass of neon to moles.

• The periodic table tells you that the atomic mass of neon is 20.18 amu. Therefore, the molar mass of neon is 20.18 g.



• Next, determine the volume at STP of 0.355 mol Ne.

• If you needed only the volume at STP, you could stop here.

• Finally, use the combined gas law equation to determine the volume of the neon at 24°C and 1.05 atm pressure.


Question 1 – 3

Use the table and the equation 1.00 in. = 25.4 mm to convert the following measurements. Round answers to the nearest tenth.


59.8 in. Hg to psi

Question 1

Basic Assessment QuestionsBasic Assessment Questions


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29.4 psi

Answer 1

Basic Assessment QuestionsBasic Assessment QuestionsTopic 13Topic 13

7.35 psi to mm Hg

Question 2



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380 mm Hg

Answer 2


1140 mm Hg to kPa

Question 3



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151.95 kPa

Answer 3


Question 4

What pressure will be needed to reduce the volume of 77.4 L of helium at 98.0 kPa to a volume of 60.0 L?


Answer

126 kPa


Question 5

A sample of SO2 gas has a volume of 1.16 L at a temperature of 23°C. At what temperature will the gas have a volume of 1.25 L?


Answer

46°C or 31.9 K


Gases: Additional ConceptsGases: Additional Concepts Gases: Additional ConceptsGases: Additional Concepts Topic 13Topic 13

Additional Concepts

Gases: Additional ConceptsGases: Additional Concepts Gases: Additional ConceptsGases: Additional Concepts

The Ideal Gas Law

• The pressure, volume, temperature, and number of moles of gas can be related in a simpler, more convenient way by using the ideal gas law.

• The following is the law’s mathematical expression, where n represents the number of moles.

PV = nRT

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The Ideal Gas Law

• The ideal gas constant, R, already contains the molar volume of a gas at STP along with the standard temperature and pressure conditions.


The Ideal Gas Law

• The constant R does the job of correcting conditions to STP.

• You do not have to correct STP in a separate step.


The Ideal Gas Law

• The Value of R depends on the units in which the pressure of the gas is measured, as shown below.

• These values are all equivalent. Use the one that matches the pressure units you are using.


Applying the Ideal Gas Law

• What pressure in atmospheres will 18.6 mol of methane exert when it is compressed in a 12.00-L tank at a temperature of 45°C?

• As always, change the temperature to kelvins before doing anything else.


Applying the Ideal Gas Law

• Next solve the ideal gas law equation for P.

• Substitute the known quantities and calculate P.


Using Mass with the Ideal Gas Law

• Recall that it is possible to calculate the number of moles of a sample of a substance when you know the mass of the sample and the formula of the substance.


Using Mass with the Ideal Gas Law • You can substitute this expression into

the ideal gas law equation in place of n.

• Notice that this equation enables you to determine the molar mass of a substance if you know the values of the other four variables.


Determining Molar Mass

• Determine the molar mass of an unknown gas if a sample has a mass of 0.290 g and occupies a volume of 148 mL at 13°C and a pressure of 107.0 kPa.

• First, convert the temperature to kelvins.


Determining Molar Mass• Next, solve the ideal gas law equation for M,

the molar mass.

• Finally, substitute values and calculate the value of M.

• Notice that you must use the value of R that uses kilopascals as pressure units and express the volume in liters.


Determining Molar Mass

• Notice that the units cancel to leave grams per mole, the appropriate units for molar mass.


Gas Stoichiometry

• Now that you know how to relate volumes, masses, and moles for a gas, you can do stoichiometric calculations for reactions involving gases.


Gas Stoichiometry Using Mass

• Ammonium sulfate can be prepared by a reaction between ammonia gas and sulfuric acid as follows.

• What volume of NH3 gas, measured at 78°C and a pressure of 1.66 atm, will be needed to produce 5.00 x 103 g of (NH4)2SO4?



• First, you need to compute the number of moles represented by 5.00 x 103 g of (NH4)2SO4.

• Using atomic mass values from the periodic table, you can compute the molar mass of (NH4)2SO4 to be 132.14 g/mol.



• Next, determine the number of moles of NH3 that must react to produce 37.84 mol (NH4)2SO4.


Gas Stoichiometry Using Mass• Finally, use the ideal gas law equation to

calculate the volume of 75.68 mol NH3 under the stated conditions.

• Solve the equation for V, the volume to be calculated.

• Convert the temperature to kelvins, substitute known quantities into the equation, and compute the volume.



• Notice that the values for the molar mass of (NH4)2SO4 and the number of moles of NH3 have more than three significant figures, whereas the calculated volume has only three.



• When you do a problem in a stepwise way, you should maintain at least one extra significant figure in the intermediate values you calculate.

• Then, round off values only at the end of the problem.


Additional Assessment QuestionsAdditional Assessment Questions

What is the pressure in atmospheres of 10.5 mol of acetylene in a 55.0-L cylinder at 37°C?

Question 1

4.86 atm

Answer

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What volume does 0.056 mol of H2 gas occupy at 25°C and 1.11 atm pressure?

Question 2

1.2L

Answer

Additional Assessment QuestionsAdditional Assessment QuestionsTopic 13Topic 13

A 250.0-mL sample of a noble gas collected at 88.1 kPa and 7°C has a mass of 0.378 g. What is the molar mass of the gas? Identify the sample.

Question 3

Answer

40.0g/mol; argon


When potassium chlorate is heated, it decomposes to produce potassium chloride and oxygen gas. Write a balanced equation for this reaction, and calculate the mass of potassium chlorate needed to produce 5.00 x 102 mL of oxygen gas at 1.108 atm and 39°C.

Question 4

Answer


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