Gases

 State the kinetic-molecular theory of matter, and describe how it explains certain properties of matter.  List the five assumptions of the kinetic- molecular theory of gases.  Define the terms ideal gas and real gas.  Describe each of the following characteristic properties of gases: expansion, density, fluidity, compressibility, diffusion, and effusion.  Describe the conditions under which a real gas deviates from “ideal” behavior.

 Break it down:  Kinetic:movement  Molecular: particles  Theory:tested ideas Tested ideas about the movement of particles! This theory is used to explain the energy and forces that cause the properties of solids, liquids, and gases.

 Ideal gas: hypothetical gas based on the following five assumptions… 1. Gases consist of large numbers of tiny particles that are far apart relative to their size.  Most of the volume is empty space 2. Collisions between gas particles and between particles and container walls are elastic collisions.  elastic collision when there is no net loss of total kinetic energy

3. Gas particles are in continuous, rapid, random motion. They therefore possess kinetic energy, which is energy of motion. 4. There are no forces of attraction between gas particles. 5. The temperature of a gas depends on the average kinetic energy of the particles of the gas.  The kinetic energy of any moving object is given by the following equation:

 KMT applies only to ideal gasses.  Most gasses behave ideally if pressure is not too high or temperature is not too low.  Which parts are not true for real gases?

 Define pressure, give units of pressure, and describe how pressure is measured.  State the standard conditions of temperature and pressure and convert units of pressure.  Use Dalton’s law of partial pressures to calculate partial pressures and total pressures.

Pressure (P): the force per unit area on a surface. What causes pressure?  collisions of the gas molecules with each other and with surfaces with which they come into contact.  depends on volume (mL or L), temperature ( o F, o C, K), and the number of molecules present (mol, mmol).

Pressure = Force Area where P = Pressure, F = Force & A = Area  The greater the force on a given area, the greater the pressure.  The smaller the area is on which a given force acts, the greater the pressure.

Measuring Pressure  barometer: device used to measure atmospheric pressure

 atm : atmosphere of pressure  mm Hg : millimeters of mercury  A pressure of 1 mm Hg is also called 1 torr in honor of Torricelli for his invention of the barometer.  torr  Pa : Pascal - SI Unit pressure exerted by a force of 1 N acting on an area of one square meter  (kPa) kiloPascal  Others…  psi : pounds per square inch  Bar 1 atm = kPa = 760 mmHg = 760 torr

The average atmospheric pressure in Denver, Colorado is atm. Express this pressure in: a. millimeters of mercury (mm Hg) and b. kilopascals (kPa) Given: atmospheric pressure = atm Unknown: a. pressure in mm Hg b. pressure in kPa

A) B)

 STP : Standard Temperature & Pressure  1.0 atm (or any of units of equal value)  0 o C  Used by scientists to compare volumes of gases

 The pressure of each gas in a mixture is called the partial pressure.  John Dalton discovered that the pressure exerted by each gas in a mixture is independent of that exerted by other gases present.  Dalton’s law of partial pressures: the total pressure of a gas mixture is the sum of the partial pressures of each gas.

 Dalton derived the following equation: P T = P 1 + P 2 + P 3 + … Total Pressure = sum of pressures of each individual gas

 Water molecules at the liquid surface evaporate and mix with the gas molecules. Water vapor, like other gases, exerts a pressure known as vapor pressure.  Gases produced in the laboratory are often collected over water. The gas produced by the reaction displaces the water in the reaction bottle.

 Step 1: Raise bottle until water level inside matches the water level outside. (P tot = P atm )  Step 2: Dalton’s Law of Partial Pressures states: P atm = P gas + P H2O To get P atm, record atmospheric pressure.  Step 3: look up the value of P H2O at the temperature of the experiment in a table, you can then calculate P gas.

KClO 3 decomposes and the oxygen gas 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? Given: P T = P atm = torr P H2O = 17.5 torr (vapor pressure of water at 20.0°C, from table A-8 in your book) P atm = P O2 + P H2O Unknown: P O2 in torr

 Solution: P atm = P O2 + P H2O P O2 = P atm - P H2O  substitute the given values of P atm and into the equation: P O2 =731.0 torr – 17.5 torr = torr

Mole fraction of a gas(X A ) = Moles of gas A (n A ) Total number of moles of a gas (n tot ) mole fraction: ratio of the number of moles of one component of a mixture to the total number of moles

P A = X A P T Partial pressures can be determined from mole fractions using the following equation:

 Use the kinetic-molecular theory to explain the relationships between gas volume, temperature and pressure.  Use Boyle’s law to calculate volume-pressure changes at constant temperature.  Use Charles’s law to calculate volume- temperature changes at constant pressure.  Use Gay-Lussac’s law to calculate pressure- temperature changes at constant volume.  Use the combined gas law to calculate volume- temperature-pressure changes.

Constant: temperature, amount of gas  If you decrease the volume, what happens to the pressure?  If you increase the volume, what happens the pressure?  Pressure and volume are _____________ related.

P 1 V 1 = P 2 V 2

A sample of oxygen gas has a volume of mL when its pressure is atm. What will the volume of the gas be at a pressure of atm if the temperature remains constant? P 1 = atmP 2 = atm V 1 = mLV 2 = ?

Constant: pressure, amount of gas  If you increase the temperature of a gas, what will happen to the volume?  If you decrease the temperature of gas, what will happen to the volume?  Volume and temperature are ______________ related.

 Units: Fahrenheit, Celsius, and Kelvin  absolute zero: when all motion stops O K = -273 o C  To Convert to Kelvin K = °C.

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? Temperature must be in KELVIN!!! V 1 = 752 mLV 2 = ? T 1 = 25°C T 2 = 50°C

Constant: volume, amount of gas  If you increase the temperature of a gas what will happen to the pressure?  If you decrease the temperature of gas what will happen to the pressure?  Pressure and temperature are _____________ related.

The gas in a container is at a pressure of 3.00 atm at 25°C. Directions on the container warn the user not to keep it in a place where the temperature exceeds 52°C. What would the gas pressure in the container be at 52°C? Temperature must be in KELVIN!!! P 1 = 3.00 atmP 2 = ? T 1 = 25°C T 2 = 52°C

P 2 = P 1 T 2 = (3.00 atm) (325 K) = 3.27 atm T K

Constant: amount of gas  combined gas law: used when pressure, temperature, and volume change within a system NOTE: P & V are directly related to T, while P is inversely related to V

A helium-filled balloon has a volume of 50.0 L at 25.0°C and 1.08 atm. What volume will it have at atm and 10.0°C? Temperature must be in KELVIN!! P 1 = 1.08 atmP 2 = atm V 1 = 50.0 LV 2 = ? T 1 = 25.0°C T 2 = 10.0°C

 State Avogadro’s law and explain its significance.  Define standard molar volume of a gas and use it to calculate gas masses and volumes.  State the ideal gas law.  Using the ideal gas law, calculate pressure, volume, temperature, or amount of gas when the other three quantities are known.

 Avogadro’s law: states that equal volumes of gases at constant temperature and pressure contain equal numbers of molecules.  According to Avogadro’s law, one mole of any gas will occupy the same volume as one mole of any other gas at the same conditions, despite mass differences.  standard molar volume of a gas: L (rounded to 22.4 L)

 Gay-Lussac’s law of combining volumes of gases and Avogadro’s law can be applied in calculating the stoichiometry of reactions involving gases.  The coefficients in chemical equations of gas reactions reflect not only molar ratios, but also volume ratios (assuming conditions remain the same).  example—reaction of carbon dioxide formation: 2CO(g) + O 2 (g) → 2CO 2 (g) 2 molecules1 molecule2 molecules 2 mole1 mole2 mol 2 volumes1 volume2 volumes

Number 1 on Practice Sheet  What volume of nitrogen at STP would be required to react with mol of hydrogen to produce ammonia? N H 2  2 NH 3

0.100 mol H 2 x 1 mol N 2 x 22.4 L N 2 3 mol H 2 1 mol N 2 = L N 2

Constant: pressure, temperature  If you increase the amount of moles, what happens to the volume?  If you decrease the amount of moles what happens to the volume?  Amount of moles and volume are ____________ related.

This equation is NOT in the book, it was calculated during the Gas Simulation Lab V 1 = V 2 n 1 n 2

Combining all the gas law equations you get: This combined equation is set equal to variable R, called the ideal gas constant.

 ideal gas constant (R):  Its value depends on the units chosen for pressure, volume, and temperature in the rest of the equation.  Measured values of P, V, T, and n for a gas at near-ideal conditions can be used to calculate R: What are the standard conditions for an ideal gas? P = n = V = T = Plug in values into the equation and calculate. What is the constant that you get? Usually rounded to (Latm/molK)

 ideal gas law: relates all variables – pressure, volume, moles, temperature PV = nRT

ALWAYS MATCH UP YOUR UNITS!!!!

 A sample of carbon dioxide with a mass of g was placed in a 350. mL container at 400 K. What is the pressure exerted by the gas? P = ? V = 350. mL = L n = g = ? mol T = 400 K

P = nRT = mol (.0821 Latm/molK) 400 K V.350 L = atm

Number 2 on Practice Sheet  What volume of nitrogen at 215 O C and 715 mmHg would be required to react with mol of hydrogen to produce ammonia? N H 2  2 NH 3 Note: This system is NOT at STP!!

0.100 mol H 2 x 1 mol N 2 = mol N 2 3 mol H 2 P = 715 mmHg V = ? n = mol N 2 R = 62.4 LmmHg/molK T = 25 O C = 488 K

 Describe the process of diffusion.  State Graham’s law of effusion.  State the relationship between the average molecular velocities of two gases and their molar masses.

REMEMBER:  DIFFUSION: the gradual mixing of two or more gases due to their spontaneous, random motion  EFFUSION: process when the molecules of a gas confined in a container randomly pass through a tiny opening in the container

Graham’s law of effusion: the rates of effusion of gases at the same temperature and pressure are inversely proportional to the square roots of their molar masses.