CHAPTER 10: GASES AP Chemistry

Measurements of Gases A. Volume, V 1. Definition: The amount of space an object or substance occupies 2. Common units: mL, L, cm3, dm3  1 L = 1 dm3  1 ml = 1 cm3 B. Amount, moles (n) 1. Definition: the amount of matter that contains x 1023 species 2. One mole of an ideal gas has a volume of 22.4 L at STP (1.00 atm and 0 ⁰ C C. Temperature, T 1. Definition: The average kinetic energy of the particles in an object or substance 2. Units: K, ⁰ C, or ⁰ F 3. Absolute zero is 0 K or ⁰ C; so to convert from ⁰ C to K, add

Measurements of Gases D. Pressure, P 1. Definition: the force exerted per unit area 2. Units: mmHg, atm, Pa, kPa, torr, bar, psi 3. 1 atm = 760 mmHg = 760 torr = psi = kPa = bar Convert 0.95 atm to mmHg 0.95 atm 760 mm Hg = 720 mm Hg 1.00 atm Convert 95.9 kPa to atm 95.9 kPa 1.00 atm = atm kPa

Measurement of Gases E. “STP” 1. STP stands of Standard Temperature & Pressure 2. STP conditions: K (0 ⁰ C) & 1 atm F. Manometers

Ideal Gas Laws Background 1. Volume is directly proportional to absolute (K) temp.  As the temp of gas increases, volume increases  V 1 /V 2 = T 1 /T 2 2. Volume is inversely proportional to pressure  As the pressure of a gas increases, volume decreases  P 1 V 1 = P 2 V 2 3. Pressure is directly proportional to the absolute (K) temp  As the temperature of gas increases, pressure increases  T 1 /T 2 = P 1 /P 2 4. Volume is directly proportional to the amount (moles)  As the moles of gas increases, volume increases  V 1 /V 2 = n 1 /n 2

Combined Gas Law

A flask is filled with air at STP. The flask is sealed, then heated with a Bunsen burner. How hot can the flask get without exploding, if the maximum pressure the glass can withstand is 3.00 atm? Before After T = P =

A 10.0 L vessel filled with He at STP is moved to a room with a pressure of 765 mm Hg and a temp of 25 C. What is the new volume? BeforeAfter V = T= P=

Gas Mixtures, Pressures, Mole Fractions A. Dalton’s Law 1. Equation: P total = P 1 + P 2 + … P x 2. Examples a. The gases in a balloon contribute the following partial pressures: CO 2 = 0.15 atm; O 2 = 0.22 atm; N 2 = 0.74 atm. Assuming these are the only three gases in the balloon, what is the total pressure? (Add them!) P total = b. What is the pressure of dry hydrogen collected over water at 25 ⁰ C if the pressure of the wet gas is torr and the vapor pressure is 23.8 torr at that temperature?

A sample of oxygen gas has been collected over water and has a volume of ml at STP. What is the volume of the dry gas at 22.0 C and 775 torr? Use the table in the Appendix to look up vapor pressure of water. BeforeAfter V= T= P*= To get P1 for the dry gas, subtract the water vapor pressure from P 1

A sample of oxygen gas has been collected over water and has a volume of 45.0 ml at 22.0 C and 0.95 atm. What is the volume of the dry gas at STP? Use the appendix to look up vapor pressure of water. BeforeAfter V= T= P= Subtract the water vapor pressure from P 1

Partial Pressure and Mole Fraction

Ideal Gas Law PV = nRT Where R = atm L/mol K Calculations: 1. What is the volume of 1.25 moles of helium gas at STP? 2. If 8.00 g of oxygen has a volume of 3.23 L at 1.50 atm, what is the temperature? 3. What is the pressure of a g sample of CH 4 gas at 735 torr and 25 ⁰ C?

Calculation of Molar Mass and Density Use the Ideal Gas law in this form: d = MP/RT 1. What is the density of air at STP if the average molar mass of air is 29.0 g/mol? 2. If the density of an elemental gas is g/L, what is its identity?

Volumes of Gases Involved in Reactions The coefficients in a balanced chemical equation give the mole ratios of the reactants and products. This law allows us to extend this relationship to volumes of gases. (Also referred to a Avogadro’s Law) The law says that the volumes of different gases involved in a reaction, if measured at the same temp and pressure, are in the same ratio as the coefficients as the balanced equation.

1.00 L of hydrogen reacts with the equivalent of nitrogen to form ammonia gas, NH3. How much nitrogen is needed? N 2(g) + 3H 2(g) → 2NH 3(g) 1.00 L H 2 1 mol H 2 1 mol N L N 2 = L N L H 2 3 mol H 2 1 mol N 2 or more simply: 1.00 L H 2 1 L N 2 = L N 2 3 L H 2 How much ammonia is formed from one liter of hydrogen?

Kinetic Theory of Gases (Day 2) 1. Kinetic Theory 1. Gases consist of particles in continuous, random motion. 2. Collisions between gas particles are elastic 3. The volume occupied by the particles is negligibly small. 4. Attractive forces between particles have negligible effect on their behavior. 5. The average energy of translational motion of a gas particle is directly proportional to the temperature.

Comparison on Matter in Terms of Kinetic Energy State Volume (variable/ constant Shape Type of motion (vibration, rotation, or translation Degree of movement Strength of attractive forces compared to kinetic energy SolidConstant VibrationalLowKE<<AF LiquidConstantVariable Vibrational, Rotational Medium KE ≈ AF GasVariable Vibrational rotational translational HighKE>>AF What happens to a liquid when it boils? Attractive forces between molecules are broken but no chemical bonds are affected; aka, the molecule stays intact.

Translational Energy, E t Equation – root-mean-square speed (rms) E t = mv 2 /2 = cTv m is mass in kg, c is a constant, and T is in Kelvin (Remember, 1 J = 1 kg m 2 /s 2 ) Example: How much translational energy does an oxygen molecule have it is moving at 2.0 m/s Et =

Average Speeds of Gas Particles

Distribution of Molecular Speeds and Energies (Day 3) Maxwell distribution Notice that the higher the average temperature, the more variation there is in the kinetic energy.

Diffusion and Effusion; Graham’s Law 1. Definitions: 1. Diffusion – the movement of gas particles through space from an area of high concentration to an area of lower concentration 2. Effusion – the flow of gas through small spaces, holes, or pores 2. Equation/Explanation for Graham’s Law 1. At a given temp and pressure, the rate of effusion of a gas is inversely proportional to the square root of its molar mass; it follows that the heavier the gas, the slower it moves. r is the rate of effusion and M is the molar mass.

Which gas has the lowest average molecular speed? Which has the highest? Which has the lowest average kinetic energy?

Real Gases Theory Under ordinary conditions, gases behave ideally, but at extreme conditions they deviate from the Ideal Gas Law At high pressure and low temperature, the gas is closer to the liquid state. This causes it to deviate from the “ideal.” This change occurs because the ideal gas law neglects 2 postulates of kinetic theory: the finite volume of gas particles, and the attractive forces btw molecules. Attractive Forces As pressure is increased, so do the attractive forces between particles. This causes the volume to be smaller than anticipated. Particle Volume At high pressure the molar volume of gases will decrease from ideal of 22.4 L/mol.

The dotted line represents the answers you would get for n (number of moles) using the ideal gas law at different pressures; the colored lines represent the REAL values for 4 gases

The dotted line represents the answers you would get for n (number of moles) using the Ideal gas law at different pressures; the colored lines represent three different temperature conditions for the same gas.