Unit 9: Gases Chapter 14 Chemistry 1K

Table of Contents Chapter 14: Gases –14.1: The Gas Laws –14.2: The Combined Gas Laws & Avogadro’s Principle –14.3: The Ideal Gas Law –14.4: Gas Stoichiometry

Defining Gas Pressure 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. Note: the pressure of a gas is directly proportional to its mass. Click box to view movie clip.14.1 The Gas Laws

14.1 Defining Gas Pressure 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.

14.1 The Gas Laws How are Temperature and 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. 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.

14.1 The Gas Laws 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. –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.

14.1 The Gas Laws 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. –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.

14.1 The Gas Laws 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 ( ). 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.

14.1 The Gas Laws 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. –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.

14.1 The Gas Laws 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.

14.1 The Gas Laws 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.

14.1 The Gas Laws Converting Barometric Pressure Units Notice that the units are arranged so that the unit mm will cancel properly and the answer will be in inches. 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 = kPa.

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.14.1 The Gas Laws

14.1 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. –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.

14.1 The Gas Laws Boyle’s Law: Pressure and Volume Robert Boyle ( ), 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. –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: Pressure and Volume By using inverse proportions, all four findings can be included in one statement called Boyle’s law. Boyle’s law states that the pressure and volume of a gas at constant temperature are inversely proportional. –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. Click box to view movie clip.14.1 The Gas Laws

14.1 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.

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 P 2, the new pressure, so solve the equation for P 2. Substitute known values and solve.14.1 The Gas Laws Applying Boyle’s Law

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.14.1 The Gas Laws Click box to view movie clip.

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. –Next, solve the Charles’s law equation for the new temperature, T The Gas Laws 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 = 50 o C14.1 The Gas Laws Applying Charles’s Law

14.1 The Gas Laws 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 in. Hg to psi Answer –29.4 psi

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.14.2 The Combined Gas Laws & Avogadro’s Principle 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. –Next, solve the combined gas law equation for the quantity to be determined, the new volume, V The Combined Gas Laws & Avogadro’s Principle Applying the Combined Gas Law

14.2 The Combined Gas Laws & Avogadro’s Principle Applying the Combined Gas Law Substitute the known quantities and compute V 2.

14.2 The Combined Gas Laws & Avogadro’s Principle 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 particles) of any gas at standard temperature and pressure (0°C and 1.00 atm pressure, STP) occupies a volume of 22.4 L. –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.

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. –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.14.2 The Combined Gas Laws & Avogadro’s Principle Applying Avogadro’s Principle

14.2 The Combined Gas Laws & Avogadro’s Principle Applying Avogadro’s Principle

14.2 The Combined Gas Laws & Avogadro’s Principle Question 1 A sample of SO 2 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

14.3 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, PV = nRT where n represents the number of moles. –The ideal gas constant, R, already contains the molar volume of a gas at STP along with the standard temperature and pressure conditions.

14.3 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 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.

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. –Next solve the ideal gas law equation for P. –Substitute the known quantities and calculate P.14.3 The Ideal Gas Law Applying the Ideal Gas Law

14.3 The Ideal Gas Law 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. –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.

14.3 The Ideal Gas Law 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. –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.

14.3 The Ideal Gas Law Determining Molar Mass Notice that the units cancel to leave grams per mole, the appropriate units for molar mass.

14.3 The Ideal Gas Law 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

14.4 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. Ammonium sulfate can be prepared by a reaction between ammonia gas and sulfuric acid as follows. What volume of NH 3 gas, measured at 78°C and a pressure of 1.66 atm, will be needed to produce 5.00 x 103 g of (NH 4 ) 2 SO 4 ?

14.4 Gas Stoichiometry Gas Stoichiometry Using Mass First, you need to compute the number of moles represented by 5.00 x 10 3 g of (NH 4 ) 2 SO 4. Using atomic mass values from the periodic table, you can compute the molar mass of (NH 4 ) 2 SO 4 to be g/mol. Next, determine the number of moles of NH 3 that must react to produce mol (NH 4 ) 2 SO 4.

14.4 Gas Stoichiometry Gas Stoichiometry Using Mass Finally, use the ideal gas law equation to calculate the volume of mol NH 3 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 (NH 4 ) 2 SO 4 and the number of moles of NH 3 have more than three significant figures, whereas the calculated volume has only three.

14.4 Gas Stoichiometry 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.

14.4 Gas Stoichiometry Question 1 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

End of Unit 9 Be Preapred for Unit 9 Test.