Gaseous State
Chapter 9
9.1 The Behavior of Gases
Characteristics of Gas• Gases consist of Particles that are
relatively far apart• Gas particles move very rapidly• Gas particles have little interaction
until they collide.• Gases expand to fill the available
space.
Description of Gases• Gases can be described in various physical
properties.– Pressure– Temperature– Density– Volume– Number of Particles
• Changing one physical parameter will change one or more others.
Pressure• Pressure (P) = Force/area• There are several units for Pressure.– Pounds/Sq. Inch (psi)– 1 Atmosphere (atm) = 760 mm Hg =
760 torr– 1 atm = 101,325 Pa (pascal)– 1 atm = 14.7 psi
EXAMPLE• Calculate the amount of pressure a 105
lbs. woman exerts by stepping down on a stiletto heel (1/16 sq inch)? Compare this to an Elephant (12,000 lbs., 16 sq. in. foot)?
PROBLEM• The depths of the ocean can exceed
380 atm of pressure. How many pascals is this? How many psi?
9.2 Factors That Affect the Properties of Gases
Boyle’s Law• For a given mass of gas at a constant
temperature, volume varies inversely with pressure.
Implications of Boyle’s Law
Therefore
Ideal Gases• Any gas that behaves according to
the predicted linear relationships.– Pressure/Volume– Volume/Temperature
PROBLEM• Given an ideal gas held at constant mass
and temperature, what would be the volume of the gas if it was originally 125 ml, and its pressure is dropped from 1.40 atm to 0.500 atm?
Charles’s Law• For a given mass of a gas at constant
pressure, volume is directly proportional to temperature on an absolute (Kelvin) scale.
Implications of Charles’s Law
Therefore
Kelvin Scale• So far we have measured
temperature in degrees Celsius, a relative scale.
• Absolute temperature is measure in Kelvin (K, note no degree sign is used), this scale is related to the absolute motion of atoms.
0 K = -273.15 °CTherefore Temp °C +273.15 = Temp K
PROBLEM• Calculate the following temperatures
in Kelvin.
– Boiling Point of Water
– Freezing Point of Water
PROBLEM• Given an ideal gas held at constant mass
and pressure, what would be the temperature of the gas if it was originally at 125 °C, and its volume is dropped from 1.00 L to 0.500 L?
Combined Gas Law• Combining Boyle’s and Charles’s Law
results in the following equation.
PROBLEM• A sample of Hydrogen gas occupies
1.25 L at 80.0 °C and 2.75 atm. What would its volume be at 185 °C and 5.00 atm?
Guy-Lussac and Avagadro• Guy-Lussac’s Law stated that
combined gases always reacted in small whole number ratios (sound familiar?)
• Avagadro hypothesized that the volume occupied by a gas is proportional to the number of gas particles and hence the moles of gas.
Avagadro’s Hypothesis• At a given pressure and temperature,
equal volumes of gas contain equal numbers of moles.
• Standard Temperature and Pressure (STP) are defined as 273.15 K and 1 atm, at which 1.00 mole of gas occupies 22.414 L, defined as molar volume
PROBLEM• What volume would 1.00 mole of gas
occupy at 37°C and 1.00 atm?
9.3 The Ideal Gas Law
Review of the Relationships• Boyle’s Law: (C is a constant)
at constant n, T
• Charles’s Law: at constant n, P
• Avagadro’s Hypothesis: at constant P, T
Combine the Equations• Assume the constants combined
equal another constant we will call the Ideal Gas Constant, R
• Rearrange this into the Ideal Gas Law
So What is the Value for R?• Assuming a standard gas you can
calculate the value of R becomes
For a Standard gas 1.000 mole at 273.15 K and 1.000 atm has a volume of 22.414 L
= 0.08206
PROBLEM• Calculate the Ideal Gas Constant if
pressure is measured in torr
PROBLEMThe volume of an oxygen cylinder is 2.025 L. At a temperature of 32 °C the cylinder has a pressure of 945 torr. How many moles of Oxygen gas are in the cylinder?
PROBLEM• Given the amount of oxygen in the
previous question, what is its mass?
• What is its density?
Partial Pressures• Dalton’s Law of Partial Pressure:
Gases in a mixture behave independently and exert they same pressure as they would alone.
+ +…
PROBLEMGiven a 2.500 L container at 45.00°C, what would be the total pressure in the container from a mixture of 2.100 moles gaseous sulfur dioxide and 1.800 moles hydrogen sulfide?
9.5 Gases and Chemical Reactions
The return of Stoichiometry• You can use the gas laws to solve
stoichiometry problems by converting values between states of matter.
Example• A sample of hydrogen gas has a volume of 8.00 L
at a pressure of 5.00 atm and a temperature of 25 °C. What volume of gaseous water is produced in the following reaction at 150.0 °C and 0.947 atm, if all the hydrogen gas reacts with copper (II) oxide
CuO(s) + H2(g) Cu(s) + H2O(g)ALGORITHM• mol of Hydrogen (PV=nRT)• mol of Water (formula)• V of Water (PV=nRT)
PROBLEMHow many grams of calcium carbonate is formed if 3.45 L of carbon dioxide, measured at 45.0 C and 1.37 atm, react with excess CaO?
CaO(s) + CO2(g) CaCO3(S)