Kinetic Molecular Theory & Gas Laws

Kinetic Theory of Gases  Gases exert pressure because their particles frequently collide with the walls of their container. –These collisions must be perfectly elastic (no loss of energy) –Adding more particles of gas increases pressure  more particles = more collisions  more collisions = more force  more force on area of wall = more pressure

More Kinetic Theory  Increased temperature causes particles to move faster –As temperature increases, pressure increases –Explains why temperature affects pressure  faster movement = more collisions  more collisions = more force  more force on area of wall = more pressure –Also…  faster movement = more forceful collisions  more forceful collisions = more force on area of wall  more force on area of wall = more pressure

Four Variables for Gases  Amount of Gas (n) –Measured in moles  Volume (V) –Measured in Liters  space  Temperature (T) hot or cold –Measured in Kelvin  Pressure (P) Force/area –Measured in atmospheres, kilopascals, millimeters of mercury, torr, bar, etc… (whew!)

Temperature Conversions What is 22 degrees C in Kelvin? What is 398 K in degrees C?

Common Pressure Conversions 1000 Pa (pascal) = 1 kPa (kilopascal) atm (atmosphere) = mmHg (mm of Mercury) = kPa = Torr

Atmospheric Pressure  Atmospheric Pressure – The pressure exerted by the air in the atmosphere. –Atmospheric pressure varies with altitude because at different altitudes there are different amounts of air above the earth. Tool for Measurement  Barometer – measures atmospheric pressure  Invented by Torricelli

STP  S tandard T emperature and P ressure –Standard Pressure  1 atm = mmHg = kPa –Standard Temperature  0 o C = 273 K

Boyle’s Law Volume is inversely proportional to pressure. As volume decreases, pressure increases (with temperature and amount of gas held constant) P 1 V 1 = P 2 V 2

To do a Gas Law Problem  Each gas law problem will give initial values and will ask for values under different conditions  From the question, list all initial variables known and record their numerical value and unit  Next to these variables (not the numbers), write a 1 for their subscript  Re-write the SAME variables (without numbers) near the original ones and put a 2 for their subscript  Using the numbers and variables you are given, choose the gas law relationship that fits the situation –Initial values go with the 1’s, changed values go with the 2’s

Example Boyle’s Law Problem A gas at a pressure of 712 mmHg is held in a container with a volume of 56.2 L. If the volume of the container is decreased to 29.3 L, what will be the new pressure of the gas if the temperature is held constant. P 1 = 712 mmHg P 2 = ? V 1 = 56.2 L V 2 = 29.3 L P 1 V 1 = P 2 V 2

Charles’ Law Temperature is directly proportional to volume As temperature increases, volume increases (with pressure and amount of gas held constant)

Example Charles’ Law Problem  The volume occupied by an inflated ball during a cold winter day (T = -12 o C) is 21.3 L. What will its volume be when the temperature reaches 44 o C? Assume constant pressure. T 1 = -12 o C = 261 K T 2 = 44 o C = 317 K V 1 = 21.3 L V 2 = ? V 1 / T 1 = V 2 / T 2

Gay-Lussac’s Law Pressure is directly proportional to temperature  As pressure decreases, temperature decreases (with volume and amount of gas held constant) –What if we decrease pressure indefinitely?  The temperature will drop to the point where particles cease to move.  This temperature is known as absolute zero (0 K)

Example Gay-Lussac’s Law Problem A sample of a gas has a pressure of 1.0 atm at 27  C. What will the pressure be at 927  C ? P 1 / T 1 = P 2 / T 2

Ideal Gases, Partial Pressure, and Gas Stoichiometry

The Ideal Gas Law  What is an ideal gas?  An ideal gas is one that obeys the kinetic- molecular theory. –Gas particles not attracted to each other –Gas particles take up negligible space  Gases behave almost ideally most of the time. –They deviate from the kinetic theory at very high pressures and very low temperatures.

The Ideal Gas Equation  R  Ideal Gas Constant

What is “R”? Let’s consider speed. Speed = distance / time Miles per hour = miles / hour  works out! Also, distance = speed x time Miles = miles / hour x hours  works out!

More on “R”… P V = n R T If we take R out, we have the following units: atmospheres (P) x liters (V) = moles (n) x kelvin (T) BUT WAIT! atmospheres x liters ≠ moles x kelvin So, we fix the units Throw in R, which is

Ideal Gas Law – Example 1 If a container has 39.2 moles of gas at a pressure of 1.33 atm and a temperature of 301 K, what is the volume of the container?

Ideal Gas Law – Example 2 Identify this gas from the P.T given the following information: It has a mass of 41.9 grams. At 27 degrees Celsius it occupies 6.2 liters of space and exerts a pressure of 2.0 atm.

Gas Stoichiometry  The ideal gas equation can be used with any gas, as long as it acts ideally (almost all do)  If this is case, then any gas should take up the same volume of space (as long as n, T, and P stay the same) P V = n R T  use this to calculate the volume of a gas under STP

Gas Stoichiometry (cont.) One mole of gas, under STP, takes up

Adding that to our roadmap…

Example Problem #1: In the reaction: Mg + 2HCl  H 2 + MgCl 2 If 2 moles of magnesium are used, how many moles of hydrogen gas will be produced? How many liters of hydrogen gas is that at STP?

Example Problem #2: Mg + 2HCl  H 2 + MgCl 2 (same rxn) How many moles of magnesium are needed to produce 11.2 liters of hydrogen gas at STP? How many grams of magnesium is that?

Dalton’s Partial Pressure Law  Earth’s atmosphere is made of different gases –78% Nitrogen –21% Oxygen –~1% Carbon Dioxide, Water, Argon, Carbon Monoxide  At standard pressure, all of these combined gases have a pressure of 1 atm (or 760 torr) –Question: What would happen to the atmospheric pressure if nitrogen was taken out of the mix?

Partial Pressure  Answer: the atmospheric pressure would decrease  Why? –Each gas in a mixture of gases exerts a pressure –The combined pressure of each gas equals the total pressure  Partial pressure – the pressure that one gas contributes to the total pressure –Alternate definition: the pressure that one gas would exert as if it were alone in the container

Calculating Partial Pressure moles of gas 1 moles of gas 1 Mole ratio of gas 1= total moles of gas total moles of gas Mole ratio of gas 1 x total pressure = partial pressure of gas 1 (continue for all gases if needed) (continue for all gases if needed)

Collecting Gas  One of the most common ways scientists collect gas to study is by water displacement –“Collected over water”  Because water vaporizes, the gas that is collected has some water molecules in it  In order to study only the gas desired, you must account for the partial pressure due to water (subtracting it)

Collecting Gas

Sample Problem #1 A container holds 1.7 moles of oxygen, 2.3 moles of nitrogen, and 1.5 moles of carbon dioxide. What are the partial pressures of each gas if the total pressure is 2.5 atm? mole ratios: mole ratios: Oxygen Nitrogen Carbon dioxide = = =

Sample problem #1 (cont.) Mole fractions(s) x total pressure = P.P. Oxygen =.31 x 2.5 = 0.78 atm Nitrogen =.42 x 2.5 = 1.1 atm Carbon dioxide =.27 x 2.5 = 0.68 atm

Sample Problem #2 A sample of gas is collected over water at 25 o C at 850 torr of pressure. If the vapor pressure of water at 25 o C is 23.8 torr, what is the pressure of the dry gas alone?

Sample #2 (follow up) If the same dry gas was brought down to -10 o C, how much pressure would it exert? (hint: use a gas law)