Temperature Temperature is a measure of how hot or cold an object is compared to another object. indicates that heat flows from the object with a higher temperature to the object with a lower temperature. is measured using a thermometer. 1
Temperature Scales Temperature Scales Kelvin Celsius Fahrenheit 2
Learning Check A. What is the temperature of freezing water? 1) 0 F 2) 0 C 3) 0 K B. What is the temperature of boiling water? 1) 100 F 2) 32 F 3) 373 K C. How many Celsius units are between the boiling and freezing points of water? 1) 100 2) 180 3) 273 3
Temperature conversions Celsius to Kelvin K = C + 273 Kelvin to Celsius C = K - 273 Celsius to Fahrenheit F = 9/5 ( C) + 32 Fahrenheit to Celsius C = 5/9 ( F - 32) Kelvin to Fahrenheit F = 9/5 (K - 273) + 32 Fahrenheit to Kelvin K = 5/9 ( F - 32) + 273
Temperatures TABLE 2.5 5
Characteristic of Gases
The Nature of Gases Gases expand to fill their containers Gases are fluid they flow Gases have low density 1/1000 the density of the equivalent liquid or solid Gases are compressible Gases effuse and diffuse
Gases Are Fluids Gases are considered fluids. The word fluid means any substance that can flow. Gas particles can flow because they are relatively far apart and therefore are able to move past each other easily.
Gases Have Low Density Gases have much lower densities than liquids and solids do - WHY? Because of the relatively large distances between gas particles, most of the volume occupied by a gas is empty space. The low density of gases also means that gas particles travel relatively long distances before colliding with each other.
Gases are Highly Compressible Suppose you completely fill a syringe with liquid and try to push the plunger in when the opening is plugged. You cannot make the space the liquid takes up become smaller. The space occupied by the gas particles is very small compared with the total volume of the gas. Applying a small pressure will move the gas particles closer together and will decrease the volume.
Gases Completely Fill a Container A solid has a certain shape and volume. A liquid has a certain volume but takes the shape of the lower part of its container. In contrast, a gas completely fills its container. Gas particles are constantly moving at high speeds and are far apart enough that they do not attract each other as much as particles of solids and liquids do. Therefore, a gas expands to fill the entire volume available.
Gas Pressure
Gas Pressure Earth s atmosphere, commonly known as air, is a mixture of gases: mainly nitrogen and oxygen. As gas molecules are pulled toward the surface of Earth, they collide with each other and with the surface of Earth more often. Collisions of gas molecules are what cause air pressure.
Measuring Pressure Pressure = Force Area Units of Pressure Newton (N) m 2, cm 2 1 atm = 760 torr = 101.3 kpa = 760 mmhg Standard Temperature Pressure (STP): 1 atm, 0 C, 22.4 L, 1 mole
1. Covert 1.00 atm to mmhg 1.00 atm 760 mmhg 1 atm = 7.60 x 10^2 mmhg 2. Covert 3.00 atm to kpa. 3.00atm 101.3 kpa 1 atm = 304 kpa 3. What is 100.0 KPa in atm? 100.0 kpa 1 atm 101.3 kpa = 0.9872 atm
Measuring Pressure Using Barometer Measures atmospheric pressure The atmosphere exerts pressure on the surface of mercury in the dish. This pressure goes through the fluid and up the column of mercury. The mercury settles at a point where the pressure exerted downward by its weight equals the pressure exerted by the atmosphere.
Gas Theory
Kinetic Molecular Theory Particles of matter are ALWAYS in motion Volume of individual particles is zero. Collisions of particles with container walls cause pressure Particles exert no forces on each other. The average kinetic energy of a gas particle is directly proportional to the temperature. An increase in temperature increases the speed in which the gas molecules move. All gases at a given temperature have the same average kinetic energy. Lighter gas molecules move faster than heavier molecules. Ideal gas- imaginary perfect gas fitting the theory
Checking for understanding List 5 characteristics of gases: 1. 2. 3. 4. 5. List 5 characteristics of gases according to the KMT: 1. 2. 3. 4. 5.
Gas Laws
Measurable Properties of Gases Gases are described by their measurable properties. P = pressure exerted by the gas V = total volume occupied by the gas T = temperature of the gas n = number of moles of the gas Units atm L K mol
**Gas Laws ABCGG LAWS** A vogadro s n is proportional to V @ constant T B oyles s P is inversely proportional to V @ constant T C G harles s ay- Lussac s V is proportional to T @ constant P P is proportional to T @ constant V G raham s Rate of effusion is inversely proportional to square root of gas s molar mass
Pressure-Volume Relationship : Boyle s Law Pressure and Volume are inversely proportional at constant temperature Pressure = Volume (when one increases the other one decreases) Volume = Pressure PV = k P 1 V 1 = P 2 V 2
For ALL calculations!!! 1. Circle the numbers, underline what you are looking for. 2. Make a list of number you circled using variables. 3. Write down the formula 4. Derive the formula to isolate the variable you are looking for. 5. Plug in the numbers 6. Answer according to significant figures
Boyle s Law Calculation A given sample of gas occupies 523mL at 1.00 atm. The pressure is increased to 1.97 atm while the temperature stays the same. What is the new volume of the gas? P 1 = 1.00 atm V 1 = 523 ml P 1 V 1 = P 2 V 2 P 2 = 1.97 atm V 2 =? ml V 2 = P 1V 1 P 2 = (1.00 atm) (523 ml) (1.97 atm) = 265 ml
1. A sample of oxygen gas has a volume of 150.0mL at a pressure of 0.947 atm. What will the volume of the gas be at a pressure of 1.00 atm if the temperature remains constant? P 1 = 0.947 atm V 1 = 150.0 ml P 2 = 1.00 atm V 2 =? ml P 1 V 1 = P 2 V 2 V 2 = P 1V 1 P 2 = (0.947atm) (150.0 ml) (1.00atm) = 142mL
2. If 2.5 L of a gas at 110.0 kpa is expanded to 4.0 L at constant temperature, what will be the new value of pressure? P 1 =110.0 kpa V 1 = 2.5 L P 2 =? kpa V 2 = 4.0 L P 1 V 1 = P 2 V 2 P 2 = P 1 V 1 V 2 = (110.0 kpa) ( 2.5 L) (4.0 L) = 69 kpa
Real World Application BOYLE S LAW Syringes and turkey basters are operated by Boyle's Law: pulling back on the plunger increases the volume inside the syringe, which decreases the pressure, which then corrects when liquid is drawn into the syringe, thereby shrinking the volume again. Spray cans, like spray paint and air freshener, are governed by Boyle's Law: intense pressure inside the can pushes outward on the liquid inside the can, trying to escape, and forces the liquid out when the cap makes an opening. You breathe because of Boyle's Law. Balloons work because of Boyle's Law. A car (combustion) engine works when the sudden increase in pressure from the combustion of the fuel expands the cylinder and pushes on the piston, causing the crankshaft to turn
Temeperature-Volume Relationship: Charle s Law Volume and temperature are proportional at constant pressure (when gases are heated, they expand) temperature = volume (K) temperature = Volume (K) KE of the gases, volume @ temperature V T = k V 1 T 1 = V 2 T 2
Charles's Law Calculation A balloon is inflated to 665 ml volume at 27 C. It is immersed in a dry-ice bath at 78.5 C. What is its volume, assuming the pressure remains constant? V 1 = 665 ml T 1 = 27 C + 273 K = 300 K V 2 =? ml T 2 = -78.5 C + 273 K = 194.5 K V V 1 T = 2 2 = T 1 V 1 T 1 = V 2 T 2 = (665 ml)( 194.5 K) (300 K) 4.3 x 10^2 ml
1. Helium gas in a balloon occupies 2.5 L at 300.0K. The balloon is dipped into liquid nitrogen that is at a temperature of 80.0K. What will be volume of the helium in the balloon at the lower temperature be? V 1 = 2.5 L T 1 = 300 K V 2 =? ml T 2 = 80.0 K V 1 T 1 = V 2 T 2 V 1 T 2 V 2 = = T 1 (2.5 L)( 80.0 K) = 0.67 L (300 K)
2. A helium filled balloon has a volume of 2.75 L at 20.0 C. The volume of the balloon changes to 2.46 L when placed outside on a cold day. What is the temperature outside in C? V 1 = 2.75 L V 2 = 2.46 L T 1 = 20 C + 273 K = 293 K T 2 =? C V 1 T 1 = V 2 T 2 V 2 T 2 = = V 1 T 1 (2.46 L)( 293 K ) (2.75 L) = 262.10 K = -10.89 C = -10.9 C
Real World Application CHARLE S LAW A balloon blown up inside a warm building will shrink when it is carried to a colder area, like the outdoors. Humans' lung capacity is reduced in colder weather; runners and other athletes may find it harder to perform in cold weather for this reason. Charles' Law, along with a couple other gas laws, is responsible for the rising of bread and other baked goods in the oven; tiny pockets of air from yeast or other ingredients are heated and expand, causing the dough to inflate, which ultimately results in a lighter finished baked good. Car (combustion) engines work by this principle; the heat from the combustion of the fuel causes the cylinder to expand, which pushes the piston and turns the crankshaft.
Temperature-Pressure Relationships: Gay-Lussac s Law Pressure and temperature are proportional at constant volume pressure = temperature (K) pressure = temperature (K) P T = k P 1 T 1 = P 2 T 2
Gay-Lussac s Law Calculation 1. An aerosol can containing gas at 101 kpa and 22 C is heated to 55 C. Calculate the pressure in the heated can. P 1 = 101 kpa T 1 = 22 C + 273 K = 295 K P 2 =? kpa T 2 = 55 C + 273K = 328 K P 1 T 1 = P 2 T 2 P 1 P 2 = = T 1 T 2 (101 kpa)( 328 K ) (295 K) = 110 kpa
2. A sample of helium gas is at 122 kpa and 22 C. Assuming constant volume. What will the temperature be when the pressure is 203 kpa? P 1 = 122 kpa T 1 = 22 C + 273 K = 295 K P 2 = 203 kpa T 2 =? K P 1 T 1 = P 2 T 2 T 2 = P 2 T 1 P 1 (203 kpa)(295k) = (122 kpa) = 490K or 220 C
Real World Application GAY-LUSSAC S LAW Bullets and cannons are based on these principles: gas superheated by the burning of gun powder is trapped behind the bullet and expands until the bullet leaves the barrel. Someone opening an oven may feel a quick flow of hot air; the air inside the oven is heated, therefore pressurized. The same is true when heating food in closed containers; often, a container will open to release the pressure. If it does not, opening the container will quickly release all the pent-up pressure, which can be very dangerous because the gases inside the hot container may be super-heated. This is why it is always best to open hot containers away from your body and face.
Volume-Molar Relationships: Avogadro s Law Volume and number of moles (n) are proportional at constant temperature and pressure volume = number of moles volume = number of moles 22.4 L for 1 mole of a gas @ STP V n = k V 1 n 1 = V 2 n 2
Avogadro s Law What volume of CO 2 contains the same number of molecules as 20.0mL of O 2 at the same conditions? 20 ml
Real World Application AVOGADRO S LAW Avogadro's Law, along with other gas laws, explains why bread and other baked goods rise. Yeast or other leavening agents in the dough break down the long carbohydrates from the flour or sugar and convert them into carbon dioxide gas and ethanol. The carbon dioxide forms bubbles, and, as the yeast continues to leaven the dough, the increase in the number of particles of carbon dioxide increase the volume of the bubbles, thereby puffing up the dough. Avogadro's Law explains projectiles, like cannons and guns; the rapid reaction of the gunpowder very suddenly creates a large amount of gas particles--mostly carbon dioxide and nitrogen gases--which increase the volume of the space behind the cannon or bullet until the projectile has enough speed to leave the barrel. A balloon inflates because of Avogadro's Law; the person blowing into the balloon is inputing a lot of gas particles, so the balloon increases in volume. We breathe because of Avogadro's Law, among others; the lungs expand, so more gas particles can enter the lungs from the outside air (inhaling). Then the lungs contract, so the waste gas particles are expelled (exhaling).
The Combined Gas Law
Combining the gas laws Robert Boyle Jacques Charles Joseph Louis Gay-Lussac P 1 V 1 = P 2 V 2 V 1 = V 2 T 1 T 2 These are all subsets of a more encompassing law: the combined gas law P 1 T 1 = P 2 T 2 P 1 V 1 P 2 V 2 = T 1 T 2
Gas Laws The ratio of the product of pressure and volume and the temperature of a gas is equal to a constant. Combined P V Gas Law 1 2 1 T 1 P V 2 T 2
Checking for understanding Boyle s Law State the law Explain the law in your own words Write the formula(s) Charle s Law Gay-Lussac s Law Avogadro s Law
Ideal Gas
Molecular Composition of Gases No gas perfectly obeys all four of these laws under all conditions. These assumptions work well for most gases and most conditions. One way to model a gas s behavior is to assume that the gas is an ideal gas that perfectly follows these laws. An ideal gas, unlike a real gas, does not condense to a liquid at low temperatures, does not have forces of attraction or repulsion between the particles, and is Is composed of particles that have no volume.
Ideal Gas Law The ideal gas law expresses the relationship between pressure, volume and temperature of a fixed amount of gas. PV = nrt P = pressure in atm V = volume in liters n = moles R = proportionality constant = 0.0821 L atm/ mol K T = temperature in Kelvins
Ideal Gas Law Calculation How many moles of gas are contained in 22.4 L liter at 100. atm and 283K? P = 100 atm V = 22.4 L n =? Moles R = 0.0821 L atm/mol K T = 283 K n = = PV RT PV = nrt (100 atm)(22.4l) (0.0821 L atm/mol K) ( 283 K) =96.4 moles
Calculate the pressure exerted by 43 mol of nitrogen in a 65L of cylinder at 5.0 C. P =? atm n = 43 mol V = 65 L T = 5 C + 273K = 278 K R = 0.0821 L atm/mol K P = = nrt V PV = nrt (43 mol)(0.0821 L atm/mol K) ( 278 K) (65 L) =15 atm
What will be the volume of 111 mol of nitrogen where the temperature is -57 C and pressure is 250 atm? P = 250 atm V =? L n = 111 mol R = 0.0821 L atm/mol K T = -57 C + 273K = 216 K V = P = nrt PV = nrt (111 mol)(0.0821 L atm/mol K) ( 216 K) (250 atm) =7.9 L
Real World Application IDEAL GAS LAW The Ideal Gas Law provides important information regarding reactions, like the combination of gases; stoichiometry, like the gas produced in a reaction; physical processes, like the mixing of gases; and thermodynamic processes, like the movement of matter toward disorder. The Ideal Gas Law is used in engineering to determine the capacity of storage containers. It is also helpful in determining the efficiency and standard operation of equipment.
Checking for understanding 1. Explain how is ideal gas different from a normal gas. 2. Write the formula for ideal gas 3. What variables can be determined by using the formula?
Gas Behavior Diffusion/Effusion Diffusion is the movement of particles from regions of higher density to regions of lower density. Effusion is the passage of gas particles through a small opening
Both effusion and diffusion depend on the molar mass of the particle, which determines the speed Effusion
Diffusion: describes the mixing of gases. The rate of diffusion is the rate of gas mixing. Molecules move from areas of high concentration to low concentration.
Effusion: a gas escapes through a tiny hole in its container -Think of a nail in your car tire Diffusion and effusion are explained by the next gas law: Graham s
Graham s Law Rate A Rate B = Mass B Mass A The rate of effusion and diffusion is inversely proportional to the square root of the molar mass of the molecules. Derived from: Kinetic energy = 1/2 mv 2 m = the molar mass, and v = the velocity.
Graham s Law Sample: compare rates of effusion of Helium with Nitrogen With effusion and diffusion, the type of particle is important: Gases of lower molar mass diffuse and effuse faster than gases of higher molar mass. Helium effuses and diffuses faster than nitrogen thus, helium escapes from a balloon quicker than many other gases!
Graham s Law The molecular speeds, v A and v B, of gases A and B can be compared according to Graham s law of diffusion shown below. r r A B M M B A Graham s law of diffusion states that the rate of diffusion of a gas is inversely proportional to the square root of the gas s molar mass. Particles of low molar mass travel faster than heavier particles.
Graham s Law Calculation At the same temperature, which molecule travels faster O 2 or H 2? r r H O 2 2 M M O H 2 2 O H 2 2 32.00 g = 3.98 2.02 g Hydrogen travels 3.98 times faster than oxygen.
Graham s Law Calculation Oxygen molecules have a rate of about 480 m/s at room temperature. At the same temperature, what is the rate of molecules of sulfur hexafluoride, SF 6? r O 2 = 480 m/s r SF 6=? m/s M O 2 = 32g M SF 6= 146g r r O 2 SF 6 M M SF O 2 6 480m/s r SF 6 146g 32g = 220 m/s
Comparing distance traveled You can compare the distanced traveled by 2 gases in the same amount of time using this equation also. Distance traveled by A = Distance traveled by B MassB MassA
Big Points to Remember: All gases at the same temperature have the same average kinetic energy. But, they do not have the same average velocity (or speed!) Speed depends on Molar Mass The heavier the gas, the slower it moves! The lighter the gas, the faster it moves!
Dalton s Law The pressure of each gas in a mixture is called the partial pressure. The total pressure of a mixture of gases is the sum of the partial pressures of the gases. This principle is known as Dalton s law of partial pressure. P total = P A + P B + P C
Dalton s Law Calculation What is the total pressure in a balloon filled with air (O 2 & N 2 ) if the pressure of the oxygen is 170 mm Hg and the pressure of nitrogen is 620 mm Hg? P total = P A + P B + P C.. P total = P Oxygen + P nitrogen = 170 mmhg + 620 mmhg = 790 mmhg
Real World Application DALTON S LAW Dalton's Law is especially important in atmospheric studies. The atmosphere is made up principally of nitrogen, oxygen, carbon dioxide, and water vapors; the total atmospheric pressure is the sum of the partial pressures of each gas. The different partial pressures account for a lot of the weather we experience. Dalton's Law plays a large role in medicine and other breathing areas. Different proportions of gas have different therapeutic effects, so it is important to know the partial pressures of each gas, in a gas line or gas tank, for example.
Checking for understanding Graham s Law Dalton s Law State the law Explain the law in your own words Write the formula(s)