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Topic 13

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**Topic 13: Gases Basic Concepts Additional Concepts Topic 13**

Table of Contents Topic 13 Topic 13: Gases Basic Concepts Additional Concepts

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Gases: Basic Concepts Topic 13 Defining Gas Pressure—How are number of particles and gas pressure related? The pressure of a gas is the force per unit area that the particles in the gas exert on the walls of their container. As you would expect, more air particles inside the ball mean more mass inside. Click box to view movie clip.

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Gases: Basic Concepts Topic 13 Defining Gas Pressure—How are number of particles and gas pressure related? 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.

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Gases: Basic Concepts Topic 13 Defining Gas Pressure—How are number of particles and gas pressure related? 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.

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Gases: Basic Concepts Topic 13 Defining Gas Pressure—How are number of particles and gas pressure related? 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.

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**How are temperature and gas pressure related?**

Gases: Basic Concepts Topic 13 How are temperature and gas pressure related? At higher temperatures, the particles in a gas have greater kinetic energy. They move faster and collide with the walls of the container more often and with greater force, so the pressure rises.

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**How are temperature and gas pressure related?**

Gases: Basic Concepts Topic 13 How are temperature and gas pressure related? 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. The volume of a gas at constant pressure is directly proportional to the Kelvin temperature.

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**Devices to Measure Pressure—The Barometer**

Gases: Basic Concepts Topic 13 Devices to Measure Pressure—The Barometer One of the first instruments used to measure gas pressure was designed by the Italian scientist Evangelista Torricelli ( ). He invented the barometer, an instrument that measures the pressure exerted by the atmosphere.

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**Devices to Measure Pressure—The Barometer**

Gases: Basic Concepts Topic 13 Devices to Measure Pressure—The Barometer His barometer was so sensitive that it showed the difference in atmospheric pressure between the top and bottom of a flight of stairs.

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**Devices to Measure Pressure—The Barometer**

Gases: Basic Concepts Topic 13 Devices to Measure Pressure—The Barometer 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.

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**Devices to Measure Pressure—The Barometer**

Gases: Basic Concepts Topic 13 Devices to Measure Pressure—The Barometer 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.

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**Devices to Measure Pressure—The Barometer**

Gases: Basic Concepts Topic 13 Devices to Measure Pressure—The Barometer This definition can be represented by the following equation. Because atmospheric pressure is measured with a barometer, it is often called barometric pressure.

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**Devices to Measure Pressure—The Barometer**

Gases: Basic Concepts Topic 13 Devices to Measure Pressure—The Barometer A barometer measures absolute pressure; that is, the total pressures exerted by all gases, including the atmosphere.

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Gases: Basic Concepts Topic 13 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 ( ).

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**One standard atmosphere is equivalent to 101.3 kilopascals.**

Gases: Basic Concepts Topic 13 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 kilopascals.

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Gases: Basic Concepts Topic 13 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.

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

Gases: Basic Concepts Topic 13 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.

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**Suppose the gauge pressure is 44 psi.**

Gases: Basic Concepts Topic 13 Pressure Conversions Suppose the gauge pressure is 44 psi. 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.

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**Converting Barometric Pressure Units**

Gases: Basic Concepts Topic 13 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.

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**Converting Barometric Pressure Units **

Gases: Basic Concepts Topic 13 Converting Barometric Pressure Units 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.

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**Converting Barometric Pressure Units**

Gases: Basic Concepts Topic 13 Converting Barometric Pressure Units 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.

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**Converting Pressure Units**

Gases: Basic Concepts Topic 13 Converting Pressure Units The reading of a tire-pressure gauge is 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 = kPa.

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**Converting Pressure Units**

Gases: Basic Concepts Topic 13 Converting Pressure Units

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**Converting Pressure Units**

Gases: Basic Concepts Topic 13 Converting Pressure Units 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.

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**Gas particles do not attract or repel each other.**

Gases: Basic Concepts Topic 13 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.

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**Gas particles are in constant, random motion.**

Gases: Basic Concepts Topic 13 The Gas Laws Gas particles are in constant, random motion. 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.

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**Boyle’s Law: Pressure and Volume**

Gases: Basic Concepts Topic 13 Boyle’s Law: Pressure and Volume Robert Boyle ( ), an English scientist, used a simple apparatus pictured to compress gases.

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**Boyle’s Law: Pressure and Volume**

Gases: Basic Concepts Topic 13 Boyle’s Law: Pressure and Volume 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.

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**Boyle’s Law: Pressure and Volume**

Gases: Basic Concepts Topic 13 Boyle’s Law: Pressure and Volume c) If the volume of a gas increases, its pressure decreases proportionately. d) If the volume of a gas decreases, its pressure increases proportionately. By using inverse proportions, all four findings can be included in one statement called Boyle’s law.

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**Boyle’s Law: Pressure and Volume**

Gases: Basic Concepts Topic 13 Boyle’s Law: Pressure and Volume Boyle’s law states that the pressure and volume of a gas at constant temperature are inversely proportional. Click box to view movie clip.

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Gases: Basic Concepts Topic 13 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.

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

Gases: Basic Concepts Topic 13 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.

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Gases: Basic Concepts Topic 13 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.

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**Substitute known values and solve.**

Gases: Basic Concepts Topic 13 Applying Boyle’s Law Substitute known values and solve.

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Gases: Basic Concepts Topic 13 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.

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**Charles’s Law Topic 13 Gases: Basic Concepts**

Click box to view movie clip.

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**Applying Charles’s Law**

Gases: Basic Concepts Topic 13 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.

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**Applying Charles’s Law**

Gases: Basic Concepts Topic 13 Applying Charles’s Law Next, solve the Charles’s law equation for the new temperature, T2.

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**Applying Charles’s Law **

Gases: Basic Concepts Topic 13 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

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Gases: Basic Concepts Topic 13 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.

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**Applying the Combined Gas Law **

Gases: Basic Concepts Topic 13 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 kPa. What volume will the sample occupy at 24°C and 99.3 kPa? Start by converting the temperatures to kelvins.

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**Applying the Combined Gas Law**

Gases: Basic Concepts Topic 13 Applying the Combined Gas Law Next, solve the combined gas law equation for the quantity to be determined, the new volume, V2.

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**Applying the Combined Gas Law**

Gases: Basic Concepts Topic 13 Applying the Combined Gas Law Substitute the known quantities and compute V2.

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Gases: Basic Concepts Topic 13 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. needs a multiply sign instead of an “x”

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Gases: Basic Concepts Topic 13 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. needs a multiply sign instead of an “x”

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**Applying Avogadro’s Principle**

Gases: Basic Concepts Topic 13 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 amu. Therefore, the molar mass of neon is g. needs a multiply sign instead of an “x”

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**Applying Avogadro’s Principle**

Gases: Basic Concepts Topic 13 Applying Avogadro’s Principle Next, determine the volume at STP of 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. needs a multiply sign instead of an “x”

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**Applying Avogadro’s Principle**

Gases: Basic Concepts Topic 13 Applying Avogadro’s Principle needs a multiply sign instead of an “x”

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Gases: Basic Concepts Topic 13 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.

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**Basic Assessment Questions**

Topic 13 Question 1 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

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**Basic Assessment Questions**

Topic 13 Answer 1 29.4 psi

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**Basic Assessment Questions**

Topic 13 Question 2 Use the table and the equation 1.00 in. = 25.4 mm to convert the following measurements. Round answers to the nearest tenth. 7.35 psi to mm Hg

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**Basic Assessment Questions**

Topic 13 Answer 2 380 mm Hg

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**Basic Assessment Questions**

Topic 13 Question 3 Use the table and the equation 1.00 in. = 25.4 mm to convert the following measurements. Round answers to the nearest tenth. 1140 mm Hg to kPa

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**Basic Assessment Questions**

Topic 13 Answer 3 kPa

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**Basic Assessment Questions**

Topic 13 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?

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**Basic Assessment Questions**

Topic 13 Answer 126 kPa

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**Basic Assessment Questions**

Topic 13 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?

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**Basic Assessment Questions**

Topic 13 Answer 46°C or 31.9 K

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**Gases: Additional Concepts**

Topic 13 Additional Concepts

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**Gases: Additional Concepts**

Topic 13 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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**Gases: Additional Concepts**

Topic 13 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.

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

Gases: Additional Concepts Topic 13 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.

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**Gases: Additional Concepts**

Topic 13 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.

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**Applying the Ideal Gas Law**

Gases: Additional Concepts Topic 13 Applying the Ideal Gas Law What pressure in atmospheres will 18.6 mol of methane exert when it is compressed in a L tank at a temperature of 45°C? As always, change the temperature to kelvins before doing anything else.

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**Applying the Ideal Gas Law **

Gases: Additional Concepts Topic 13 Applying the Ideal Gas Law Next solve the ideal gas law equation for P. Substitute the known quantities and calculate P.

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**Using Mass with the Ideal Gas Law**

Gases: Additional Concepts Topic 13 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.

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**Using Mass with the Ideal Gas Law **

Gases: Additional Concepts Topic 13 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.

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**Determining Molar Mass**

Gases: Additional Concepts Topic 13 Determining Molar Mass Determine the molar mass of an unknown gas if a sample has a mass of g and occupies a volume of 148 mL at 13°C and a pressure of kPa. First, convert the temperature to kelvins.

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**Determining Molar Mass **

Gases: Additional Concepts Topic 13 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.

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**Determining Molar Mass**

Gases: Additional Concepts Topic 13 Determining Molar Mass Notice that the units cancel to leave grams per mole, the appropriate units for molar mass.

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**Gases: Additional Concepts**

Topic 13 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.

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**Gas Stoichiometry Using Mass**

Gases: Additional Concepts Topic 13 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?

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**Gas Stoichiometry Using Mass**

Gases: Additional Concepts Topic 13 Gas Stoichiometry Using Mass 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 g/mol.

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**Gas Stoichiometry Using Mass**

Gases: Additional Concepts Topic 13 Gas Stoichiometry Using Mass Next, determine the number of moles of NH3 that must react to produce mol (NH4)2SO4.

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**Gas Stoichiometry Using Mass **

Gases: Additional Concepts Topic 13 Gas Stoichiometry Using Mass Finally, use the ideal gas law equation to calculate the volume of 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.

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**Gas Stoichiometry Using Mass**

Gases: Additional Concepts Topic 13 Gas Stoichiometry Using Mass 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.

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**Gas Stoichiometry Using Mass**

Gases: Additional Concepts Topic 13 Gas Stoichiometry Using Mass 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.

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**Additional Assessment Questions**

Topic 13 Question 1 What is the pressure in atmospheres of 10.5 mol of acetylene in a 55.0-L cylinder at 37°C? Answer 4.86 atm

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**Additional Assessment Questions**

Topic 13 Question 2 What volume does mol of H2 gas occupy at 25°C and 1.11 atm pressure? Answer 1.2L

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**Additional Assessment Questions**

Topic 13 Question 3 A mL sample of a noble gas collected at 88.1 kPa and 7°C has a mass of g. What is the molar mass of the gas? Identify the sample. Answer 40.0g/mol; argon

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**Additional Assessment Questions**

Topic 13 Question 4 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 atm and 39°C. Answer

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