Chapter 5: Gases 5.1 Pressure

Gaseous State of Matter  has no distinct or __________ so fills any container  is easily compressed  completely with any other gas  exerts pressure on its surroundings

Measuring Pressure  barometer: measures atmospheric pressure measures atmospheric pressure invented by Torricelli, Italian scientist in 1643 invented by Torricelli, Italian scientist in 1643 glass tube filled with mercury is inverted in a dish glass tube filled with mercury is inverted in a dish mercury flows out of the tube until pressure of the Hg inside the tube is equal to the atmospheric pressure on the Hg in the dish mercury flows out of the tube until pressure of the Hg inside the tube is equal to the atmospheric pressure on the Hg in the dish

Measuring Pressure  pressure: results from mass of air being pulled toward the earth by gravity results from mass of air being pulled toward the earth by gravity varies with altitude and weather conditions varies with altitude and weather conditions

Measuring Pressure  manometer: measures pressure of gas in a container measures pressure of gas in a container gas has less pressure than atmosphere if the Hg is closer to chamber gas has less pressure than atmosphere if the Hg is closer to chamber gas has more pressure than atmosphere if the Hg is further from chamber gas has more pressure than atmosphere if the Hg is further from chamber gas pressure = gas pressure =

Units of Pressure  : most common since use Hg in manometers and barometers  : equal to mmHg  (atm)  (Pa): SI unit; equal to N/m 2 1atm = 760mmHg = 760torr = 101,325Pa = kPa

Chapter 5: Gases 5.2 Gas Laws

Boyle’s Law  Discovered by Irish chemist, Robert Boyle  Used a J-shaped tube to experiment with varying pressures in multistory home and effects on volume of enclosed gas  P and V are proportional  PV = k  holds precisely at very low pressures

Charles’ Law  discovered by French physicist, Jacques Charles in 1787  first person to fill balloon with hydrogen gas and make solo balloon flight  V and T are proportional  V = kT

Charles’ Law  for any gas, at °C, the volume is zero  since negative volumes cannot exist, there cannot be a temperature lower than absolute zero (-273.2°C or 0 K)  never actually been reached ( K has been)  Kelvin system has no negative values Example

Avogadro’s Law  Discovered by Italian chemistry, Avogadro in 1811  proposed that equal volumes of gases at the same temperature and pressure contain the same number of particles  V = kn  V and n are proportional Example

Gay-Lussac’s Law  discovered in 1802 by Joseph Gay- Lussac  P = kT  P and T are proportional proportional Example

Example: Pressure Conversions The pressure of a gas is measured as 49 torr. Represent this pressure in atmospheres, Pascals, and mmHg.

Try This!  The pressure of a gas is measured as 2.5 atm. Represent this pressure in Torr, Pascals, and mmHg Torr Pa 1900 mmHg

Example: Boyle’s Law Consider a 1.53-L sample of gaseous SO 2 at a pressure of 5.6 x 10 3 Pa. If the pressure is changed to 1.5 x 10 4 Pa at constant temperature, what will be the new volume of the gas?

Example: Charles’ Law & Temp. A sample of gas at 15°C and 1 atm has a volume of 2.58 L. What volume will this gas occupy at 38°C and 1 atm?

Example: Avogadro’s Law Suppose we have a 12.2-L sample of gas containing 0.50 mol O 2 at a pressure of 1 atm and temperature of 25°C. If all of this O 2 were converted to O 3 (ozone) at the same temperature and pressure, what would be the volume of O 3 ?

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

Ch. 5 Gases 5.3 Ideal Gas law

Combinations of Gas Laws  Combined Gas Law:  Ideal Gas Law  Universal Gas Constant (R) combined proportionality constant combined proportionality constant equals L*atm/mol*K equals L*atm/mol*K equals J/mol*K equals J/mol*K

Real Gases vs. Ideal Gases  an ideal gas is a hypothetical substance that obeys the ideal gas law  real gases approach this behavior closest at low pressure and high temperature

Ch. 5 Gases 5.4 Gas Stoichiometry

Molar Volume  L = 1 mol at STP  Standard Temperature and Pressure (STP):

Molar Mass and Density

Example 1 CaO is made from decomposition of CaCO 3. Find the volume of CO 2 at STP made from decomposition of 152 g CaCO 3.

Example 2 A sample of CH 4 gas having a volume of 2.80 L at 25°C and 1.65 atm was mixed with sample of O 2 gas having volume of 35.0 L at 31°C and 1.25 atm. The mixture formed CO 2 and H 2 O. Find the volume of CO 2 at 2.50 atm and 125°C.

Example 2  Find the limiting reactant:

Example 2  Find the amount of product produced:

Example 2  Find the volume of product produced:

Example 3 If the density of a sample of gas is 1.95 g/L at 1.50 atm and 27°C, find the molar mass of gas. What could the identity of the gas be?

Ch. 5 Gases 5.5 Dalton’s Law of Partial Pressures

Partial Pressure  for a mixture of gases, the total pressure is the sum of the pressures each gas would exert if it were alone  using the ideal gas law, can change to:

Partial Pressures

Example 1 47 L He and 12 L O 2 at 25°C and 1.0 atm were pumped into a tank with a volume of 5.0 L. Calculate the partial pressure of each gas and the total pressure in the tank.

Example 1  Find moles of each gas:

Example 1  Find the new P of each gas:  Find the total pressure of the gases:

Partial Pressure  shows that the identities of the gases do not matter, just the number of moles  so, for ideal gases: 1. size of gas molecule is not important 2. forces between molecules is not important  these are the things that would change with the identity of the gas

Mole Fraction  Mole Fraction: ratio of number of moles of a certain component of a mixture to number of moles total in mixture

Water Displacement  when gas is collected using water displacement, there is always a mixtures of gases  the pressure of water vapor varies with temperature and will be given in a problem

Ch. 5 Gases 5.6 Kinetic Molecular Theory

The Kinetic Molecular Theory  model of gas behavior so only an approximation 1. volume of particles is assumed to be zero 2. particles are in constant motion 3. particles exert no forces on each other (no attraction or repulsion) 4. kinetic energy is proportional to  Kelvin temperature

Boyle’s Law: P and V  decrease in volume means that particles will hit wall more often and that will cause P increase

Gay-Lussac’s Law: P and T  the speed of particles increases as T increases so they hit the wall more often and with greater force and P increases

Charles’ Law: V and T  increase in T causes and increase in particle speed so they hit the wall more often  to keep P constant, the V must increase

Avogadro’s’ Law: V and n  increase in number of gas molecules would cause increase in P if V were held constant  to keep P constant, V must increase

Dalton’s Law  Kinetic Molecular Theory assumes that all particles are independent of each other

Temperature  Kelvin temperature is a sign of the random motions of gas particles  higher T means greater motion

Ch. 5 Gases 5.7 Effusion and Diffusion

Effusion  passing of gas through a small hole into an evacuated chamber

Diffusion  mixing of gases

Graham’s Law of Effusion  effusion rates depend directly on the average velocity of the particles  the faster they are moving, the more likely they are are to go through the hole

Example Compare the effusion rates of hydrogen and oxygen gas. So H 2 effuses 4 times faster than O 2

Compare

Ch. 5 Gases 5.8 Real Gases

Ideal Gases

Real Gases