Chapter 10 Physical Characteristics of Gases

10-1 The Kinetic-Molecular Theory of Matter  Kinetic-molecular theory is based on the idea that particles of matter are in constant motion.  The theory can be used to explain the properties of solids, liquids and gases in terms of the energy of particles and the forces that act between them.

10-1 The Kinetic-Molecular Theory of Gases  KMT provides a model of an ideal gas.  An ideal gas is an imaginary gas that perfectly fits all the assumptions of KMT.

10-1 The Kinetic-Molecular Theory of Matter – Assumption 1  Gases consist of a large number of tiny particles that are far apart relative to their size. –Most of the volume is empty space. –Gases have low density. –Gases are easily compressed. –Gas particles are considered point masses (have mass but no volume).

10-1 The Kinetic-Molecular Theory of Matter – Assumption 2  Collisions between gas particles and between particles and container walls are elastic collisions. –No net loss of energy. –Kinetic energy is transferred, but total KE of 2 particles is constant as long as temperature is constant.

10-1 The Kinetic-Molecular Theory of Matter – Assumption 3  Gas particles are in continuous, rapid, random motion. –They possess kinetic energy. –Gas particles move in all directions. –Gas particles move in straight line trajectories until they collide and change directions.

10-1 The Kinetic-Molecular Theory of Matter – Assumption 4  There are no forces of attraction or repulsion between gas particles. –Gas particles are too far apart to experience intermolecular forces. –When they collide, their kinetic energy is sufficient to overcome any attractive forces (they bounce apart like billiard balls).

10-1 The Kinetic-Molecular Theory of Matter – Assumption 5  The average kinetic energy of gas particles depends on the temperature of the gas.  All particles in a gas sample have the same mass, so KE depends only on speed.  Average speeds increase with an increase in temperature and decrease with a decrease in temperature. velocity mass

Fraction of Particles v. Particle Speed at Various Temperatures Speed distribution for the same gas molecules at various temperatures.

Speed distribution for various gases with different masses at same temperature.

10-1 The Kinetic-Molecular Theory of Matter - Assumptions  The behavior of real gases can be modeled with KMT (ideal gas assumptions) except under special circumstances.  Assumptions of KMT are not valid at extremely low temperatures and/or extremely high pressures.

10-1 KMT and Gas Behavior: Expansion Gases move rapidly in all directions (assumption 3) without significant attractive or repulsive forces between them (assumption 4). In this way, they expand to fill the entire available volume.

10-1 KMT and Gas Behavior: Fluidity  Attractive forces are insignificant between particles of an ideal gas. (assumption 4) They easily glide past each other.  Liquids and gases flow, and are therefore referred to as fluids.

10-1 KMT and Gas Behavior: Low Density  Particles in the gaseous state are very far apart. (assumption 1)  A small number of gas particles can therefore occupy a large volume.  The ratio of mass to volume is very low, about 1/1000 the density of the same substance in liquid or solid form.

 Because gas particles are so far apart (assumption 1), it is possible to force them closer together, reducing the volume occupied by the gas KMT and Gas Behavior: Compressibility

10-1 KMT and Gas Behavior: Diffusion and Effusion  Diffusion – the spontaneous mixing of the particles of two substances caused by their random motion (assumption 3)  Effusion – a process by which gas particles pass through a tiny opening because of their rapid random motion (assumption 3)

10-1 Deviation of Real Gases from Ideal Behavior  A real gas is a gas that does not behave completely according to the assumptions of the kinetic- molecular theory.  In 1873, Johannes van der Waals accounted for these deviations by explaining that real gases occupy space and exert attractive forces on each other.  When gas particles are forced to be close together, particle volume and attractive forces are no longer negligible.  extremely high pressure  extremely low temperature

10-2 Pressure  Pressure is force per unit area. P = f/A 5 m 15 m 300 N

10-2 Pressure  Gas molecules exert pressure with any surface with which they are in contact.  Pressure is caused by collisions.  Pressure depends on volume, temperature and number of gas molecules present.

10-2 Pressure  Earth’s atmosphere is an envelope of air that exerts pressure on earth’s surface and all the objects on it.  Atmospheric pressure is the sum of the pressures exerted by all the gases that make up the atmosphere (nitrogen, oxygen, argon, carbon dioxide, etc.)  Earth’s atmosphere exerts a pressure of approximately 10.1 N/cm 2

How did this happen?

10-2 Measuring Pressure  A barometer is a device used to measure atmospheric pressure.  The first barometer was invented by Evangelista Torricelli in the 1600s.  The mercury falls until the pressure exerted by its weight is equal to the pressure exerted by the atmosphere.  The average atmospheric pressure at sea level is 760 mmHg.

10-2 Units of Pressure  millimeters of mercury (mmHg)  atmospheres (atm)  pascals (Pa) and kilopascals (kPa)  torr (torr) 760 mmHg = kPa = 760 torr = 1 atm

10-2 Units of Pressure  Convert 0.97 atm to kPa.  Convert 785 mmHg to atm.  Convert 120 kPa to mmHg.  Convert 430 mmHg to kPa.

10-2 STP  Standard Temperature and Pressure –0˚C –1 atm, kPa, 760 mmHg

10-3 Gas Laws!  Gas laws are simple mathematical relationships between the volume, temperature, pressure and amount of a gas.  Boyle’s Law relates pressure and volume.  Charles’s Law relates volume and temperature.  Gay-Lussac’s Law relates pressure and temperature.  The combined gas law relates pressure, temperature and volume.

10-3 Boyle’s Law: Pressure-Volume Relationship  Decreasing the volume of a gas causes the pressure to increase.  Increasing the volume of a gas causes the pressure to decrease.  Pressure is caused by gas molecules hitting the walls of the container.  Decreasing the volume means there will be more molecules per unit volume.  The number of collisions will increase and the pressure will increase.

10-3: Boyle’s Law  The volume of a fixed mass of gas varies inversely with the pressure at constant temperature.  Remember, two variables are inversely proportional if their product is a constant. PV = k

10-3: Boyle’s Law  Boyle’s law is most often used to compare changing conditions for a gas.  If temperature and number of molecules remains constant, then P 1 V 1 = k AND P 2 V 2 = k So, P 1 V 1 = P 2 V 2 If three of these values are known, you can solve for the fourth.

10-3: Boyle’s Law Sample Problem  A sample of oxygen gas has a volume of 150 mL when its pressure is atm. What will the volume of the gas be at a pressure of atm if the temperature remains constant?

10-3: Boyle’s Law Sample Problem  A gas has a pressure of 1.26 atm and occupies a volume of 7.40 L. If the gas is compressed to a volume of 2.93 L at a constant temperature, what will its pressure be?

10-3 Charles’ Law: Volume- Temperature Relationship  At constant pressure, gases expand when heated and contract when cooled.  At higher temperatures, gas molecules move faster and collide more often with their container and with greater force.  In a flexible container like a balloon, this forces the walls outward.  The increased volume means gas molecules must travel farther before colliding with their container.  The lower collision frequency is offset by the greater collision force and the pressure remains constant. Hot air balloons use Charles’s Law.

10-3: Charles’s Law  The volume of a fixed mass of gas at constant pressure varies directly with the Kelvin temperature.  Two variables are directly proportional if their quotient is a constant. V/T = k Why must the temperature be in degrees Kelvin?

10-3: Celsius to Kelvin Conversions K = °C + 273

10-3: Charles’s Law  Charles’s Law is most often used to compare changing conditions for a gas.  If pressure and number of moles are constant, then V 1 /T 1 = k AND V 2 /T 2 = k So, V 1 /T 1 = V 2 /T 2 If three of these values are known, you can solve for the fourth.

10-3: Charles’s Law Sample Problem  A sample of neon gas occupies a volume of 752 mL at 25°C. What volume will the gas occupy at 50°C if the pressure remains constant?

10-3: Charles’s Law Sample Problem  A helium-filled balloon has a volume of 2.75L at 20°C. The volume of the balloon decreases to 2.46L when it is placed outside on a cold day. What is the outside temperature in K? in °C?

10-3: Gay-Lussac’s Law  What is the relationship between temperature and pressure if volume and number of moles are held constant?  How can this observation be explained using kinetic molecular theory?

10-3: Gay-Lussac’s Law  How can the relationship between pressure and temperature be expressed mathematically?  What formula might you use to compare changing conditions of temperature and pressure for a gas at constant volume?

10-3: Gay-Lussac’s Law Sample Problem  A sample of helium gas exerts a pressure of 3.2 atm at 50°C. If the container is cooled to 25°C, what pressure will the gas exert?

10-3: Gay-Lussac’s Law Sample Problem  A gas canister is designed to withstand pressure up to 30 atm. The gas contained in the canister exerts a pressure of 7.2 atm at 25°C. At what temperature will the canister explode?

10-3: The Combined Gas Law  Boyle’s Law: P 1 V 1 = P 2 V 2  Charles’s Law: V 1 /T 1 = V 2 /T 2  Gay-Lussac’s Law: P 1 /T 1 = V 2 /T 2  The combined gas law combines these three laws.

10-3 Combined Gas Law  A sample of nitrogen gas exerts 1.5 atm of pressure and occupies a volume of 4.2 L at 25°C. What volume will it occupy at STP?

10-3: Dalton’s Law of Partial Pressures  John Dalton (Atomic Theory) discovered that in the absence of a chemical reaction, the pressure of a gas mixture is the sum of the individual pressures of each gas alone.

10-3: Dalton’s Law of Partial Pressures  The pressure of each gas in a mixture is called the partial pressure of that gas.  Dalton’s law of partial pressures states that the total pressure of a mixture of gases is equal to the sum of the partial pressures of the component gases. P T = P 1 + P 2 + P 3 + …

10-3: Dalton’s Law of Partial Pressures

10-3: Gases Collected by Water Displacement  Gases produced in the lab are often collected over water.  Hydrogen gas can be produced by reacting an acid with certain metals, like zinc.  One apparatus for collecting the hydrogen gas is shown.

10-3: Gases Collected by Water Displacement  A gas collected by water displacement is always mixed with water vapor. It is impossible to collect a pure sample of gas over water.  Water molecules at the surface evaporate and mix with the gas.

10-3: Gases Collected by Water Displacement  The vapor pressure of water varies with temperature.  As temperature increases, more water molecules have enough energy to break free of the surface and become vapor particles.  Water vapor pressure increases with temperature.

10-3: Gases Collected by Water Displacement  If you wanted to determine the pressure of the gas you collected over water, you would need to correct for the pressure exerted by the water vapor.  First, make sure the water level inside and outside the collection flask are equal. This means the pressure inside the flask and outside the flask are equal. P atm P gas + P H2O P atm = P gas + P H2O

10-3: Gases Collected by Water Displacement  Read the atmospheric pressure.  Then, determine the temperature and look up the vapor pressure of water at that temperature. (Table A-8 in the appendix)  Subtract the vapor pressure of water at the given temperature from the atmospheric pressure to determine the pressure of the dry gas.

10-3: Gases Collected by Water Displacement  Oxygen gas from the decomposition of potassium chlorate, KClO 3, was collected by water displacement. The barometric pressure and the temperature during the experiment were torr and 20.0˚C, respectively. What was the partial pressure of the oxygen collected?

10-3: Gases Collected by Water Displacement  Some hydrogen gas is collected over water at 20.0˚C. The levels of water inside and outside the gas collection bottle are the same. The partial pressure of hydrogen is torr. What is the barometric pressure at the time the gas is collected?

10-3: Gases Collected by Water Displacement  Helium gas is collected over water at 25˚C. What is the partial pressure of the helium, given that the barometric pressure is mmHg?