Chapter 10 Gas Laws Objectives: Understand the characteristics of gases, real and Ideal. Understand the gas law

Physical characteristics of gases  The Kinetic-Molecular Theory of Gases  The Kinetic molecular theory is based on the idea that particles of matter are always in motion.

Ideal Vs. Real Gases  Ideal gases Vs. Real gases  An ideal gas is an imaginary gas that perfectly fits all the assumptions of the kinetic-molecular theory.  A real gas is will only have these characteristics at a certain (not to high) pressure and temperature (not to low) To better understand this concept think of an ideal energy efficient car, this car would be 100 % efficient, that would never really happen because it would always loss energy to heat and friction.

Ideal vs. Real  Most gases are real gases in that they do not behave completely according to the assumptions of the kinetic molecular theory.  Noble gases will behave most like ideal gases. Other diatomic gases will as well, due to the fact that these are nonpolar gases and tend to bond only to themselves.

Kinetic-Molecular Theory  Five assumptions of ideal gases:  1. gases consist of large number of tiny particles that are far apart relative to their size. (most of the volume of gases is empty space)  2. Collision between gas particles and between particles and container walls are elastic collisions. an elastic collision is one in which there is no net loss of kinetic energy.  3. Gas particles are in constant, rapid, random motion. They therefore possess kinetic energy, which is energy of motion.  4. THERE ARE NO FORCES OF ATTRACTION OR REPULSION BETWEEN GAS PARTICLES. (THEY COLLID BUT DO NOT STICK TOGETHER)  5. The average kinetic energy of gas particles depends on the temperature of the gas.

Kinetic Energy an Temperature  Assumption five, the average kinetic energy of gas particles depends on the temperature of the gas.  Equation: KE = ½ mv 2  M = mass, v = speed  Gas of the same sub will have the same mass, therefore their KE depends only of speed. (speed increases with temp increase)  All gases at the same temperature have the same KE. Therefore lighter gases have higher speeds.

Physical Properties of gases  Expansion : Completely fill the container.  (3/4) move in all directions and no attraction  Fluidity: Flow past one another (4)  Low density: (density in gas is 1/1000 that of the liquid state) (1 – the gaseous state is farther apart)  Compressibility: With pressure we can decrease the volume.  Diffusion and Effusion: gases spread out and mix with one another.

Diffusion and Effusion  Diffusion:  Spontaneous mixing of the particles of two substances caused by their random motion  Effusion:  Is a process by which gas particles under pressure pass through a tiny opening.

Combine Gas Law  Recall that only Ideal gases can be determined by the combined gas law.  P 1 V 1 = P 2 V 2 T 1 T 2 T 1 T 2 P = Pressure T = Temperature V = volume

Pressure  Pressure = force per unit area on a surface.  Pressure = Force / Area  SI Unit for force is a Newton, N.  A Newton is the fore that will increase the speed of a one kilogram mass by one meter per second each second it is applied.

Pressure  At Earth’s surface, each kilogram of mass exerts 9.8 N of force, due to gravity.  Lets look at the relationship of force and area = pressure.  If a ballerina has a force of 500 N and is standing flat on two feet (325cm 2 ) the force is 1.5N. If the same ballerina stands on her toes the area decreases to (13cm 2 ) the force increases to 38.5 N. If she sands on one toe it increases to 77N.  So we can see the if force is constant and area decrease the pressure will increase.

Units of Pressure Pascal Pa SI unit 1Pa = 1N/m 2 Millimeter mm HgAt sea level of mercury0C = 760mmHg Atmosphere atm 1atm=760mmHg = X 10 5 Pa = kPa Torr Torr1 torr = 1 mm Hg

Standard Temperature and Pressure  STP = 1 atm of pressure at 0C.

Pressure conversions  The average pressure in Denver Colorado is atm. Express this pressure in mmHg?  In kPa?

Practice:  Covert a pressure of 1.75 atm to kPa?  To mmHg?  Convert a pressure of 570. torr to atmospheres an to kPa?

Gas Laws Objective: Be able to define the gas laws and use the equation to solve gas law problems. Understand the combined gas laws is all of the gas laws together. Be able to determine the gas laws from the combined gas law.

Combined Gas Law  Recall that only Ideal gases can be determined by the combined gas law.  Expresses the relationship between pressure, volume and temperature of a fixed amount of gas.  P 1 V 1 = P 2 V 2 T 1 T 2 T 1 T 2 P = Pressure T = Temperature V = volume

Boyles Law: Pressure- Volume  Boyles Law – volume of a fixed mass of gas varies inversely with the pressure at constant temperature.  This means that when volume increases pressure decreases by the same amount.  Lets consider the kinetic-molecular theory, how can we explain this relationship.

Boyles Law  PV = k  K is the constant  P 1 V 1 = P 2 V 2  Use this equation when comparing changing conditions.  If given three of the four values, one can solve for what is missing.

Practice:  A sample of oxygen has a volume of 150 ml when its pressure is 0.97 atm. What will the volume of the gas be at a pressure of atm if the temperature remains constant?

Charles’s Law: Volume- Temperature Relationship  The Kelvin temperature scale is a scale that starts at a temperature corresponding to C. That temperature is the lowest possible. The temperature C is called absolute zero and is given the value of aeroin the Kelvin scale.  K= C

Charles Law  V 1 = V 2 T 1 T 2 T 1 T 2  If pressure is constant then the volume changes 1/273 for each degree Celsius. Charles’s Law states that the volume of a fixed mass of gas at constant pressure varies directly with the Kelvin temperature

Charles Law  A sample of neon gas occupies a volume of 752 mL at 25C, What volume will the gas occupy at 50C if the pressure remains constant?

Gay-Lussac’s Law  The pressure of a fixed mass of gas at constant volume varies directly with the Kelvin temperature.  Pressure is constant  Pressure and Temperature are directly proportional, this means as one doubles so does the other.

Gay-Lussac Law  P 1 = P 2 T 1 T 2 T 1 T 2 Temperature should be in Kelvin: C = K C = K

Gay Lussac’s Law  Practice  The gas in an aerosol can is at a pressure of 3.00 atm at 25C. Directions on the can warn the user not to keep the can in a place where the temperature exceeds 52C. What would the gas pressure in the can be at 52C?

Combined Gas Law  We use the combine gas law when the three variables must be dealt with all at once.  The Combine Gas Law expresses the relationship between pressure, volume, and temperature of a fixed amount of gas.

Combined Gas Law  P 1 V 1 = P 2 V 2 T 1 T 2 T 1 T 2 In this case nothing is constant! Pressure units must be the same Volume units must be the same Temperature must be in Kelvin

Practice:  A helium-filled balloon has a volume of 50.0 L at 25C and 1.08 atm. What volume will it have at atm and 10C?

Partial Pressure  Daltons law of partial pressure – the total pressure of a mixture of gases is equal to the sum of the partial pressure of the component gases.  P t = P 1 + P 2 ………..  The total Pressure of a mixture of gases is equal to the pressures of all the components combined.

Gases Collected over water  In lab most of the time gas is collected over water. Gas collected this way is not pure, but has water vapor mixed into it.  We can use atmospheric pressure to determine the p of the water or the gas.  P atm = Pgas + Pwater  If you want to find the partial pressure of a dry gas we can subtract the water pressure (which can be a standard found on a chart) from the P atm.

Practice:  Oxygen gas from decomposition of potassium chlorate, KClO 3, was collected by water displacement. The barometric pressure and the temperature during the experiment were Torr and 20C. What was the partial pressure of he oxygen collected? The vapor pressure of water at 20C, from table A-8, is 17.5 torr

Volume- Mass Relationship of Gases  Gay-Lussac’s law of combing volumes of gases – at constant temperature and pressure, the volume of gaseous reactants and products can be expressed as ratios of small whole numbers.  Hydrogen gas + chlorine gas  Hydrogen chloride 1L 1L2L 1L 1L2L 1 volume 1 volume 2 volume 1 volume 1 volume 2 volume 1 molecule 1 molecule 2 molecules 1 molecule 1 molecule 2 molecules 1 mole 1 mole 2 mole 1 mole 1 mole 2 mole Avagardro’s law states that equal volumes of gases at the same temperature and pressure contains equal numbers of molecules.

Molar Volume of Gases  Standard molar Volume of a gas is the volume occupied by one mole of a gas at STP.  1 mol/22.4L

Practice:  A chemical reaction produces mol of oxygen gas. What volume in liters is occupied by this gas sample at STP?  Use molar volume: 22.4L/mol

More Practice:  A chemical reaction produced 98.0 mL of sulfur dioxide gas, SO 2, at STP. What was the mass of the gas produced?