Gas Laws GPS 17

Phases of Matter SOLID Definite Shape Definite Volume LIQUID Shape varies depending on container Definite Volume GAS Takes on the shape and volume of the container ENERGY INCREASES Simulation PLASMA A gas heated to extremely high temp. Atoms ionize to result in electrons and Ions

Kinetic Molecular Theory (KMT) Assumptions* 1.Gas particles are in constant, random motion 2.Collisions are elastic 3.The volume of the gas particles are negligible* 4.There are no interactions between particles* (attraction or repulsion) 5.The kinetic energy of the particles is ONLY dependent on temperature

Elastic Collisions Elastic collisionInelastic collision

Average Kinetic Energy and Temperature ↑T, ↑KE ave

Some Properties of Gases Fill their container completely Easy to compress Diffuse rapidly Exert pressure Pressure is defined as the force of particle collisions per unit area of the container

Gases Exert Pressure Pressure Force of particle collisions per unit area of container P = Force / Area

Gases Exert Pressure More gas particles present, more frequent collisions with container, greater pressure

Measuring Pressure Manometer used to measure the pressure exerted by a gas

Manometer Which gas is exerting more pressure? A B

Boyle’s Law (↓V, ↑P) When all other variables are constant, pressure and volume of a gas are inversely related P 1 V 1 = P 2 V 2

Boyle’s Law (↓V, ↑P) If volume is halved, pressure doubles V 1 = 1 LV 2 = 0.5 L P 1 = 1 atm P 2 = 2 atm

Notice that since the temperature is constant, that the particles still have the same average kinetic energy and are still moving with the same average speed (same size vector arrows in diagrams). Boyle’s Law (↓V, ↑P)

Charles’ Law (↑T, ↑V) When all other variables are constant, temperature and volume of a gas are directly related V 1 / T 1 = V 2 / T 2 or V 1 T 2 = V 2 T 1

Charles’ Law (↑T, ↑V) If temperature is doubled, volume doubles

Increasing temperature gives the particles of gas more average kinetic energy and greater average speed (heat ‘em up, speed ‘em up) Charles’ Law (↑T, ↑V)

Gay-Lussac’s Law (↑T, ↑P) When all other variables are constant, temperature (Kelvin) and pressure of a gas are directly related P 1 / T 1 = P 2 / T 2 or P 1 T 2 = P 2 T 1

Gay-Lussac’s Law (↑T, ↑P) If Kelvin temperature is doubled, pressure doubles T 1 = 273 KT 2 = 373 K P 1 = 1.00 atm P 2 = 1.37 atm

Gay-Lussac’s Law (↑T, ↑P) Increasing temperature gives the particles of gas more average kinetic energy and greater average speed (heat ‘em up, speed ‘em up)

V 1 / n 1 = V 2 / n 2 or V 1 n 2 = V 2 n 1 Avogadro’s Law (↑n, ↑V) When all other variables are constant, moles of gas and volume of a gas are directly related

If moles of gas is doubled, volume doubles Avogadro’s Law (↑n, ↑V) 2 moles 20 Liters 4 moles 40 Liters

Avogadro’s hypothesis: Equal volumes of gases under the same conditions of temperature and pressure contain equal numbers of molecules.

Combined Gas Law P 1 V 1 = P 2 V 2 T 1 T 2 P = pressure V = volume T = temperature in Kelvin (K) When moles (n) of gas constant

Ideal Gas Law Describes an ideal gas (recall KMT assumptions) Real gases behave most like ideal gases at higher temperatures and at lower pressures PV = nRT P is pressure V is volume n is number of moles of gas in mol R is the gas constant = atmL/molK T is the temperature in K Used when variables are NOT changing

Variables on the SAME side: INVERSELY related (↓V, ↑P) Variables on OPPOSITE sides: DIRECTLY related (↑T, ↑P) (↑T, ↑V) (↑n, ↑V) (↑n, ↑P)

Boyle’s Law from the Ideal Gas Law If only pressure and volume are changing and all other variables are constant: Variables that are constant cancel out: P 1 V 1 = n 1 RT 1 P 2 V 2 = n 2 RT 2 P 1 V 1 = 1 P 1 V 1 = P 2 V 2 P 2 V 2

Charles’ Law from the Ideal Gas Law If only temperature and volume are changing and all other variables are constant: Variables that are constant cancel out: P 1 V 1 = n 1 RT 1 P 2 V 2 = n 2 RT 2 V 1 = T 1 V 1 T 2 = V 2 T 1 V 2 T 2

Gay-Lussac’s Law from the Ideal Gas Law If only temperature and pressure are changing and all other variables are constant: Variables that are constant cancel out: P 1 V 1 = n 1 RT 1 P 2 V 2 = n 2 RT 2 P 1 = T 1 P 1 T 2 = P 2 T 1 P 2 T 2

Avogadro’s Law from the Ideal Gas Law If only moles and volume are changing and all other variables are constant: Variables that are constant cancel out: P 1 V 1 = n 1 RT 1 P 2 V 2 = n 2 RT 2 V 1 = n 1 V 1 n 2 = V 2 n 1 V 2 n 2

Combined Gas Law from the Ideal Gas Law If only pressure, temperature, and volume are changing and all other variables are constant: Variables that are constant cancel out: P 1 V 1 = n 1 RT 1 P 2 V 2 = n 2 RT 2 P 1 V 1 = T 1 P 1 V 1 = P 2 V 2 P 2 V 2 T 2 T 1 T 2

Gas Laws A gas in a cylinder with a movable piston occupies 1.2 liters at 1.5 atmospheres of pressure. The piston is moved and the gas now occupies 0.70 liters. Assuming temperature is constant, what will the pressure (in atm) now be in the cylinder? 2.6 atm

Pressure Units Pressure may be measured in: atmospheres (atm) millimeters of mercury (mmHg) kiloPascals (kPa) Equivalencies for converting between units: 760 mmHg = 1 atm kPa = 1 atm

Gas Laws A gas in a cylinder with a movable piston occupies 4.98 liters at 152 kPa of pressure. The piston is moved and the gas now occupies 5.23 liters. Assuming temperature is constant, what will the pressure (in atm) now be in the cylinder? 1.43 atm

Gas Laws A hot air balloon is filled with 1551 liters of hot air on a morning in which the temperature is 295 K. What would the volume (in liters) of the hot air balloon be if the temperature dropped to 285 K? 1498 L

Temperature in Kelvin Temperature must be in Kelvin for gas laws ˚C = K Example: Convert 25 ˚C into Kelvin

Gas Laws A hot air balloon is filled with 1551 liters of hot air on a morning in which the temperature is 55 ˚C. What would the volume (in liters) of the hot air balloon be if the temperature dropped to 15 ˚C? 1362 L

Gas Laws A sample of oxygen gas occupies 5.2 liters at 29ºC and 1.5 atm. What would be the volume (in liters) at 35ºC and 0.97 atm? 8.2 L

Gas Laws How many moles of helium are present in a 35.2 L tank at 45˚C at a pressure of 1635 kPa? (R = atmL/molK) 21.8 moles

Gas Laws How many liters of hydrogen are present if 3.52 moles of hydrogen are kept at 299K at a pressure of 1635 kPa? (R = 8.31 kPaL/molK) 5.35 liters

Gas Stoichiometry Solid MgO decomposes under intense heat as the reaction shows below. The O 2 gas produced exerts a pressure of 2.5 atm in the reaction container. Calculate the volume of O 2 at 185˚C produced from the decomposition of 15 g MgO. 2MgO(s) → 2Mg(s) + O 2 (g)

Gas Stoichiometry Water vapor, H 2 O(g), can be produced from the combustion of H 2 (g) and O 2 (g) as shown in the reaction below. The volume and pressure of the water vapor produced were measured to be 0.85 L and 1.55 atm at 37˚C. Determine the grams of oxygen gas that reacted. 2H 2 (g) + O 2 (g) → 2H 2 O(g)

Dalton’s Law of Partial Pressures The sum of the partial pressures (p a + p b + …) of all gases in a mixture of gases is equal to the total pressure of the gas mixture (P T ) P Total = p a + p b + … =+ P total = P neon + P helium

Dalton’s Law of Partial Pressures A mixture of carbon dioxide and oxygen gases is contained at 25˚C and mmHg. The carbon dioxide gas exerts 34.6 mmHg pressure. What is the partial pressure (in mmHg) of the oxygen gas? mmHg

Dalton’s Law of Partial Pressures Carbon dioxide exerts a pressure of 0.15 atm in a container. In the same container, helium gas exerts a pressure of 0.22 atm and oxygen gas exerts a pressure of 0.39 atm. What is the total pressure (in atm) of the mixture of gases in the container? 0.76 atm

Particle Speed: Effect of Mass At constant temperature: More massive particles move more slowly. Lighter particles move more quickly. Longer vector arrows show smaller particles moving at faster speed. Shorter vector arrows show larger particles moving at slower speed.

Maxwell-Boltzmann Distribution Speed (m/s), at 298 K Number of Particles Larger mass, slower average speed Smaller mass, faster average speed

Particle Speed: Effect of Temperature For a sample of gas having constant mass: Particles move more slowly at lower temperatures. Particles move more quickly at higher temperatures. Lower Temperature Slower average speed Higher Temperature Faster average speed

Maxwell-Boltzmann Distribution Lower temperature, slower average speed Higher temperature, faster average speed

Maxwell-Boltzmann Distribution Speed (m/s), at 280 K Number of Particles The graph shows three gas samples: Br 2, He and O 2, all at 280 K. Determine which of the curves represents each of the gas samples. A __________ B __________ C __________ A B C

Maxwell-Boltzmann Distribution Speed (m/s) Number of Particles The graph shows a single sample of gas at three different temperatures: 295 K, 400 K, 220 K Determine which of the curves represents each of the temperatures. A __________ B __________ C __________ A B C

Effusion of Gases Describes the passage of gas through a small hole Smaller particles of gas effuse more quickly Estimate size of particles by comparing their masses

After 48 hours, He balloon is smaller because the smaller He atoms effused faster than the larger N 2 molecules N2N2 He N2N2

Effusion Suppose you have four balloons, each filled with an equal volume of a different gas. The first balloon contains CO 2, the second Ne, the third O 2, and the fourth H 2. Each balloon was punctured with a needle at the same time, making a hole of exactly the same size in each of the four balloons. After the gases are allowed to escape from the balloons through the pinhole for one minute: Which balloon will be the smallest in size? Which balloon will be the largest in size?

Diffusion of Gases Describes the migration or mixing of gases due to random particle movement Larger mass of gas, slower diffusion rate

Diffusion

Diffusion The experimental apparatus represented above is used to demonstrate the rates at which gases diffuse. When the cotton balls are placed in the ends of a tube at the same time, the gases diffuse from each end and meet somewhere in between, where they react to form a solid. If one cotton ball is soaked with NH 3 (aq) and the other is soaked with HC 2 H 3 O 2 (aq), determine if the solid produced will form nearest the acid end, the base end, or the center of the tube.

Real Gases Gases behave ideally at lower pressures and higher temperatures KMT assumes no particle volume and no interactions (attraction/repulsion) between particles. In reality, these assumptions are NOT true. Pressure and volume corrections are added to the ideal gas law to get van der Waal’s Equation van der Waal’s Equation

Real Gases Gases deviate the most from ideal behavior if they are polar and have larger masses. These properties have relatively significant effects on the volume and pressure of the gas. Ex: Which deviates the most from ideal behavior, NH 3 or CH 4 ? Answer: NH 3 because it is polar, whereas CH 4 is nonpolar

Real Gases Which deviates the most from ideal behavior, H 2 or CH 4 ?

References

SOLs covered CH 4 c, d