Chapter 14 The Behavior of Gases

# of particles related gas pressure The pressure of a gas : the force per unit area that the particles exert on the walls of their container. Pressure =

# of particles related to gas pressure Pump more air inside a ball more particles mass of air inside increases more collision (inner wall of ball) higher pressure (at a given temp) inside the ball

# of particles related to gas pressure pressure (of a gas) mass

Defining Gas According to the kinetic theory, all matter is composed of particles in constant motion, and pressure is caused by the force of (g) particles striking the walls of their container. The more often (g) particles collide with the walls of their container, the > the pressure.

# of particles related to gas pressure pressure # particles (mol) Doubling the # of gas particles in a basketball doubles the pressure

Quick write The pressure inside a balloon always = to the atm pressure. How does the balloon adjust the pressure inside when it is transferred to places of different temperatures?

Temperature Related to Pressure At higher temp the (g) particles possess more KE move faster collide with the walls of the container more often and with greater force, so the pressure rises. i.e. When temp increases, pressure also increases.

Temperature Related to Pressure At constant volume (of the container), pressure K temp. e.g. gas in a glass bottle. When temp increases, pressure increases. At constant pressure, volume of a gas K temp. e.g. gas in a balloon. When temp increases, → bigger.

Barometer The height of the Hg column measures the pressure exerted by the atm. We live at the bottom of an ocean of air. The highest pressures occur at the lowest altitudes. When going up a mountain, atm pressure decreases because the depth of air above you is less.

Barometer standard atmosphere (atm) the pressure that supports a 760-mm column of Hg.

Pressure Units Because the pascal is a small pressure unit, it is more convenient to use kilopascal (kPa) 1 std atm pressure is equivalent to 101 kPa.

1 atm = 760 mmHg = 760 Torrs = 14.7 psi = 101.3 kPa Pressure Units (3) Pounds per square inch (psi) continues to be widely used in engineering and almost all nonscientific applications in the U.S. Pressure inside car tires. e.g. 36 psi Equivalent Pressures 1 atm = 760 mmHg = 760 Torrs = 14.7 psi = 101.3 kPa

The Gas Laws ideal gases (kinetic theory) 5 statements. (1) particles do not attract or repel each other. (2) particles are much smaller than the spaces between them. (total volume of particles ≈ 0) Assumptions are not true when pressure is very high ; total volume of particles becomes significant.

The Gas Laws (3) (g) particles are in constant, random motion. (4) No KE is lost when (g) particles collide with each other or with the walls of their container.(perfectly elastic) (5) All (g) have the same KE at a given temp.

Boyle’s Law: Pressure and Volume Robert Boyle (1627-1691), (English).

Boyle’s Law: Pressure and Volume After performing many expts with (g) at constant temp, Boyle got 4 findings. (1) If the pressure of a (g) increases, its volume decreases proportionately. (2) If the pressure of a gas decreases, its volume increases proportionately. (3) If volume of a (g) increases, its pressure decreases proportionately. (4) If volume of a (g) decreases, its pressure increases proportionately.

Boyle’s Law: Pressure and Volume

Boyle’s Law: Pressure and Volume the pressure and volume of a (g) at constant temperature are inversely proportional.

Boyle’s Law: Pressure and Volume

Boyle’s Law At a constant temp, the pressure exerted by a (g) depends on the frequency of collisions between (g) particles and the container. the same # of particles is squeezed into a smaller space → the frequency of collisions increases →increasing the pressure.

Boyle’s Law In math terms, this law is expressed as follows. P1V1 = P2V2

Applying Boyle’s Law (1) Example 1 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?

Example 2 (Boyle’s Law) A high-altitude balloon contains 30.0 L of He (g) at 103 kPa. What is the volume when the balloon rises to an altitude where the pressure is only 25.0 kPa? (Assume that the temp remains constant.)

Charles’s Law When the temp of a sample of (g) is increased and the volume is free to change, the pressure does not change. (e.g. balloon) Instead, the volume of the (g) increases in proportion to the increase in K temp. Charles’s law : at constant pressure, the volume of a given mass of (g) is directly proportional to its K temp.

Example 3 A weather balloon contains 5.30 kL of He gas when the temp is 12°C. At what temp will the balloon’s volume have increased to 6.00 kL?

Answer 50°C

Applying Charles’s Law (2) New Temp = 323 – 273 = 50°C

Example 4 (Charles’s Law) A balloon inflated in a room at 24°C has a volume of 4.00 L. The balloon is then heated to a temp of 58°C. What is the new volume if the pressure remains constant?

Gay-Lussac Law Gay-Lussac’s law pressure of (g) is directly proportional to its K temp (volume constant) Pressure α temperature (K) P1 P2 = T1 T2

Example 5 (Gay-Lussac’s Law) The gas left in a used aerosol can is at a pressure of 103 kPa at 25°C. If it is thrown onto a fire, what is the pressure of the gas when its temp reaches 928°C?

Answer 415.1 kPa

The Combined Gas Law (1) combined gas law relating P, V, and T STP : 1 atm; 101 kPa; 0°C; 273K

Factors Affecting Gas Pressure (1) If the (g) pressure increases until it exceeds the strength of an enclosed, rigid container, the container will burst.

Factors Affecting Gas Pressure (2) Aerosol Spray Paint

Factors Affecting Gas Pressure (4) When the volume of the container is halved, the pressure the (g) exerts is doubled.

Factors Affecting Gas Pressure (6) When the K temp of the enclosed gas doubles, the pressure of the enclosed (g) doubles.

Avogadro’s Principle (1) Avogadro Law = vol of all (g) at the same conditions of T and P contain the same # of particles. one mole (6.02 x 1023 particles) of any (g) at std temp and P (0°C and 1.00 atm pressure, 101 kPa, STP) occupies a vol of 22.4 L.

Example 6 (combined gas law) A sample of nitrogen monoxide has a volume of 72.6 mL at a temp of 16°C and a pressure of 104.1 kPa. What volume will the sample occupy at 24°C and 99.3 kPa?

Answer 78.2 mL

Example 7 (combined gas law) The volume of a gas-filled balloon is 30.0L at 40°C and 153 kPa pressure. What volume will the balloon have at std temp and pressure (STP)?

CST problem 1 The volume of 400 mL of chlorine gas at 400 mm Hg is decreased to 200 mL at constant temperature. What is the new gas pressure? A 400 mm Hg B 300 mm Hg C 800 mm Hg D 650 mm Hg

CST problem 2 Standard temperature and pressure (STP) are defined as A 0°C and 1.0 atm pressure B 0°C and 273 mm Hg pressure C 0 K and 1.0 atm pressure D 0 K and 760 mm Hg pressure

CST problem 3 Under which of the following sets of conditions will a 0.50 mole sample of He occupy a volume of 11.2 L? A 298 K and 0.90 atm B 273 K and 1.10 atm C 373 K and 0.50 atm D 273 K and 1.00 atm

CST problem 4 What is the equivalent of 423 K in °C? A -223°C B -23°C C 150°C D 696°C

CST problem 5 Under what circumstance might a gas decrease in volume when heated? A The gas is held constant at STP. B The gas remains under uniform temperature. C The gas is placed under increasing pressure. D The gas undergoes a decrease in pressure.

CST problem 6 Theoretically, when an ideal gas in a closed container cools, the pressure will drop steadily until the pressure inside is essentially that of a vacuum. At what temperature should this occur? A 0 °C B -460 °C C -273 °C D 0 K

Factors Affecting Gas Pressure (3) Volume can raise the pressure exerted by a contained (g) by reducing its volume. The more a (g) is compressed, the > is the pressure that the (g) exerts inside the container.

CST problem 1 A scientist observed changes in the gas pressure of one mole of a gas in a sealed chamber with a fixed volume. To identify the source of the changes, the scientist should check for variations in the A air pressure outside the chamber B molecular formula of the gas C temperature of the chamber D isotopes of the gas

CST problem 2 A weather balloon with a 2-m diameter at ambient temperature holds 525 g of He. What type of electronic probe could be used to determine the pressure inside the balloon? A barometric B thermometric C calorimetric D spectrophotometric

The End

Question 4 What pressure will be needed to reduce the vol of 77.4 L of He at 98.0 kPa to a vol of 60.0 L?

Answer 126 kPa

PV = nRT The Ideal Gas Law (1) The pressure, vol, temp, and # moles of gas can be related as in the ideal gas law. PV = nRT

The Ideal Gas Law (2) The ideal gas constant, R, already contains the molar vol of a gas at STP along with the std temp and pressure conditions. R = 0.082 L atm K−1 mol−1 R = 8.31 L kPa K−1 mol−1 62.36 L Torr K−1   mol−1

Applying the Ideal Gas Law What pressure in atm will 18.6 mol of methane exert when it is compressed in a 12.00-L tank at a temp of 45°C? change the temp to K before doing anything else.

Question 3 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. Answer 40.0g/mol; argon

Question 4 When potassium chlorate is heated, it decomposes to produce potassium chloride and oxygen (g). Write a balanced eqn for this rxn, and calculate the mass of potassium chlorate needed to produce 5.00 x 102 mL of oxygen (g) at 1.108 atm and 39°C. Answer 2KClO3(s) → 2KCl(s) + 3O2 ; 1,77g

Factors Affecting Gas Pressure (5) Temperature An increase in the temperature of an enclosed (g) causes an increase in its pressure. As a (g) is heated, the average KE of the particles in the (g) increases. Faster-moving particles strike the walls of their container with more energy.