Chapter 14 – Gases

Kinetic Molecular Theory (KMT) Defn – describes the behavior of gases in terms of particle motion Defn – describes the behavior of gases in terms of particle motion Makes assumptions of size, motion, & energy of gas particles Makes assumptions of size, motion, & energy of gas particles

KMT and Gases Ideal Gases – imaginary gas that conforms to assumptions of KMT Ideal Gases – imaginary gas that conforms to assumptions of KMT

Assumptions of KMT A) gas particles do not attract or repel each other A) gas particles do not attract or repel each other no intermolecular forces occurring. gases are free to move in their containers without interference from other particles

Assumptions of KMT B) gas particles have NO volume B) gas particles have NO volume almost all of the volume of a gas is empty space. The particles are insignificant in size compared to all the space

Assumptions of KMT C) gas particles are in constant motion C) gas particles are in constant motion they move in straight lines until they collide with each other or the walls of container

Assumptions of KMT D) no kinetic energy is lost when gas particles collide with each other or walls D) no kinetic energy is lost when gas particles collide with each other or walls aka elastic collision. There is no loss in speed of the particles

Assumptions of KMT E) ALL gases have same average kinetic energy at a given temperature E) ALL gases have same average kinetic energy at a given temperature as temperature increases, more energy. As temp decreases, less energy

Assumptions of KMT ***KEEP IN MIND IDEAL GASES DO NOT EXIST!!!!!!!*** ***KEEP IN MIND IDEAL GASES DO NOT EXIST!!!!!!!*** APPLIES AT ALL TEMPERATURES AND ALL PRESSURE APPLIES AT ALL TEMPERATURES AND ALL PRESSURE

Real Gases Defn – do not behave according to assumptions of KMT Defn – do not behave according to assumptions of KMT Characteristics Characteristics i) real gas particles have volume i) real gas particles have volume ii) real gas particles exert attractive forces on each other ii) real gas particles exert attractive forces on each other

Real Gases When do real gases act like ideal gases? When do real gases act like ideal gases? at very low pressure and very high temp -at low P, molecules far from each other - at high temp, molecules move too fast to have intermolecular interactions

Characteristics of Gases 1) expansion 2)fluidity 3) low density 4) compressibility 5) diffusion

4 measurable variables of gases Pressure Temperature Volume Amount

Pressure Defn – force/area; pressure caused by collisions of molecules Defn – force/area; pressure caused by collisions of molecules Units: atmosphere (atm), millimeter of mercury (mm Hg), torr, kiloPascal (kPa) Units: atmosphere (atm), millimeter of mercury (mm Hg), torr, kiloPascal (kPa) Conversions: Conversions: 1 atm = 760 mm Hg = 760 torr = kPa

Sample problem #1 Convert 2.3 atm to torr Convert 2.3 atm to torr 2.3 atm 1 atm 760 torr = 1748 torr

Sample problem #2 Convert 450 mm Hg to kPa Convert 450 mm Hg to kPa 450 mmHg 760 mm Hg kPa = 60 kPa

Measuring air pressure What device is used to measure air pressure????? What device is used to measure air pressure?????BAROMETER

Standard Temp and Pressure (STP) P = 1 atm P = 1 atm T = 0°C T = 0°C

Temperature Unit K Kelvin (K) Kelvin = °C + 273

Temperature Convert 45°C to Kelvin Convert 45°C to Kelvin 45°C °C = 318 K

Temperature Absolute zero – 0 K Absolute zero – 0 K Molecules stop moving Molecules stop moving Question: what is absolute zero temperature in Celsius? Question: what is absolute zero temperature in Celsius?-273°C

Volume Units: Units: mL mL L

Amount Units Units grams grams moles moles

Gas Laws Each gas law relates the 4 variables: Each gas law relates the 4 variables: Pressure Pressure Temperature Temperature Volume Volume Amount Amount For the next 4 gas laws, amount is not a factor We will only pay attention to P, T, & V We will only pay attention to P, T, & V

Boyles’ Law: P/V relationship Defn – at constant T, volume of a fixed amount of gas varies inversely with pressure Defn – at constant T, volume of a fixed amount of gas varies inversely with pressure inversely – as one variable increases, other variable decreases inversely – as one variable increases, other variable decreases P V

Boyle’s Law Formula Formula P 1 V 1 = P 2 V 2 P 1 & V 1 are initial conditions P 2 & V 2 are final conditions

Boyle’s Law A balloon filled with helium gas has a volume of 500 mL at 1.00 atm. When it rises to a higher altitude, the pressure is reduced to 0.50 atm. If the temperature is constant, what is the volume of the balloon? A balloon filled with helium gas has a volume of 500 mL at 1.00 atm. When it rises to a higher altitude, the pressure is reduced to 0.50 atm. If the temperature is constant, what is the volume of the balloon? 1000 mL

Charles’ Law: V/T relationship Defn – at constant P, volume of fixed amt of gas varies directly with Kelvin temp Defn – at constant P, volume of fixed amt of gas varies directly with Kelvin temp Directly – as one variable increase, the other increases Directly – as one variable increase, the other increases V T

Charles’ Law Formula Formula V 1 & T 1 are initial conditions V 1 & T 1 are initial conditions V 2 & T 2 are final conditions V 2 & T 2 are final conditions

Charles’ Law A helium balloon has a volume of 2.75 L at 20°C. On a cold day, the balloon is placed outside where it shrinks to 2.46 L. What is the temperature outside? A helium balloon has a volume of 2.75 L at 20°C. On a cold day, the balloon is placed outside where it shrinks to 2.46 L. What is the temperature outside? 262 K

Gay-Lussac’s Law: P/T relationship Defn – at constant V, pressure of fixed amt of gas varies directly with Kelvin temp Defn – at constant V, pressure of fixed amt of gas varies directly with Kelvin temp Directly – as one variable increase, the other increases Directly – as one variable increase, the other increases P T

Gay-Lussac’s Law Formula Formula P 1 & T 1 are initial conditions P 1 & T 1 are initial conditions P 2 & T 2 are final conditions P 2 & T 2 are final conditions

Gay-Lussac’s Law Before a trip from Sugar Land to South Padre, the pressure in an automobile tire reads 2.1 atm at 27°C. Upon arriving in Padre, the gauge reads 2.3 atm. What is the temperature in South Padre? Before a trip from Sugar Land to South Padre, the pressure in an automobile tire reads 2.1 atm at 27°C. Upon arriving in Padre, the gauge reads 2.3 atm. What is the temperature in South Padre? 329 K

Combined Gas Law: P/T/V Defn – relationship between P,V, & T of fixed amount of gas Defn – relationship between P,V, & T of fixed amount of gas Formula Formula

Combined Gas Law The volume of a gas is 27.5 mL at 22.0°C and 740 mm Hg. What will be its volume at 15°C and 755 mm Hg? The volume of a gas is 27.5 mL at 22.0°C and 740 mm Hg. What will be its volume at 15°C and 755 mm Hg? 26 mL

Avogadro’s Principle Defn – equal volumes of gases at same temp and pressure contain equal number of molecules Defn – equal volumes of gases at same temp and pressure contain equal number of molecules - the size of the molecule does not influence the volume a gas occupies - for example, 1000 relatively large Kr gas molecules occupies the same volume as 1000 smaller He gas molecules

Molar Volume of a Gas Molar Volume – volume that one mole of a gas occupies at STP (0°C, 1 atm) Molar Volume – volume that one mole of a gas occupies at STP (0°C, 1 atm) 1 mole = 22.4 L

Molar Volume of a Gas Ex prob #1: calculate the volume mol H2 will occupy at STP mol H mol H2 x 22.4 L H2 1 mol H2 = 19.7 L H2

What is the mass of L of oxygen gas at STP? What is the mass of L of oxygen gas at STP? L O L O 2 x 1 mol O L O L O L O 2 x 1 mol O 2 x 32 g O L O 2 1 mol O L O 2 1 mol O 2 = g O 2

Ideal Gas Law Defn – relationship between P,V,T and # of moles, n Defn – relationship between P,V,T and # of moles, n Formula Formula PV = nRT ideal gas constant

Ideal Gas Constant 3 different R constants 3 different R constants R = L·atm mol·K mol·K = 62.4 L· mm Hg = 62.4 L· mm Hg mol·K mol·K = L·kPa = L·kPa mol·K mol·K pay attention to what unit of pressure is given in problem then use the appropriate R pay attention to what unit of pressure is given in problem then use the appropriate R

Ideal Gas Law Ex prob 1: what is the volume of moles of oxygen gas at 20°C and 740 mm Hg? Ex prob 1: what is the volume of moles of oxygen gas at 20°C and 740 mm Hg? which R do we use? 6.18 L O 2

Ideal Gas Law Ex prob 2: calculate the pressure, in atm, of 4.75 L NO 2 containing 0.86 mol at 27°C. Ex prob 2: calculate the pressure, in atm, of 4.75 L NO 2 containing 0.86 mol at 27°C atm

Ideal Gas Law Ex prob 3: calculate the grams of N 2 present in a L sample kept at 1.0 atm and 22°C. Ex prob 3: calculate the grams of N 2 present in a L sample kept at 1.0 atm and 22°C. first determine # of moles mol N 2 convert to grams 0.70 g N 2

4 gas laws vs. ideal gas law The differences between ideal gas law and the other 4 are: The differences between ideal gas law and the other 4 are: 1) Ideal gas law utilizes an amount (moles), other 4 don’t 2) The 4 gas laws have a change in condition; ideal gas law does not