The Gas Laws
Pressure
 ______________ per unit ______________.
 Gas molecules ______________ container.
 Molecules move around and ______________ sides.
 ___________________ are the force.
 Container has the __________________.
 Measured with a ___________________________.
Barometer

The pressure of the __________________ at sea level will support
a column of mercury _______________________.
1 _____________ = _______________________

Manometer


Manometer
____________ of mercury used to measure __________________.
h is how much ______________ the gas pressure is than the
________________________ pressure.

h is how much __________________ the gas pressure is than the
______________________pressure.
Units of pressure
 1 atmosphere = ________________________
 1 mm Hg = _______________
 1 atm = _________________ Pascals = ________________________
 These standards can be used in converting between pressure units.
 What is 724 mm Hg in kPa?
 in torr?
 in atm?
The Gas Laws
 Boyle’s Law
 Pressure and volume are ____________________ related at constant temperature.
 PV= k (k is a constant)
 As one goes up, the other goes _____________.
 P1V1 = P2 V2
 The shape of the curve resulting from a graph of pressure vs. volume is a _________________.
Examples
 20.5 L of nitrogen at 25ºC and 742 torr are compressed to 9.8 atm at constant T. What is the
new volume?

30.6 mL of carbon dioxide at 740 torr is expanded at constant temperature to 750 mL. What is
the final pressure in kPa?
Charles’ Law
 Volume of a gas varies _____________with the absolute _________________ at constant
pressure.
 V = kT (if T is in Kelvin)
 V1 = V2
T1 = T2
 A shape of the curve resulting from a graph of temperature vs. volume is a _________________
Examples
 What would the final volume be if 247 mL of gas at 22ºC is heated to 98ºC , if the pressure is
held constant?

At what temperature would 40.5 L of gas at 23.4ºC have a volume of 81.0 L at constant
pressure?
Avogadro's Law
 Two samples of gas occupying the same volume at the same temperature and pressure must
contain the same ____________________________________.
 At Standard Temperature and Pressure (STP, 0ºC and 1 atm) 1 mole of gas occupies _________.
 At constant temperature and pressure, the volume of gas is _________ related to the number of
__________.
 V = k n (n is the number of moles)
 V1 = V2
n1 = n2
Gay- Lussac Law
 At constant volume, pressure and absolute temperature are _______________related.
 P=kT
 P1 = P2
T1 = T 2
Combined Gas Law
 If the __________of gas remain constant, use this formula and cancel out the variables that
don’t change.
 P1 V1 = P2 V2
T1
T2
Examples
 A deodorant can has a volume of 175 mL and a pressure of 3.8 atm at 22ºC. What would the
pressure be if the can was heated to 100.ºC?

What volume of gas could the can release at 22ºC and 743 torr?
Ideal Gas Law
 PV = nRT
 V = 22.41 L at 1 atm, 0ºC, n = 1 mole, what is R?
 R is the ______________________________.
 R = __________________ L atm/ mol K
 R = _________________ L Kpa/ mol K
 R = _______________ L torr/ mol K
 Tells you the properties of a gas _________________.
 The other laws tell you about a gas when it ____________________.
Ideal Gas Law
 An _______________________________.
 The state of the gas is its _________________ at a given time (does not depend on the
____________ it took to get there)
 Given 3 variables, you can determine the ______________.
 An ____________________ Equation - based on ______________ evidence.
Ideal Gas Law
 the ideal gas is a __________________ substance.
 Think of it as a ________________.
 Gases only approach ideal behavior at ________________ (< 1 atm) and ________ temperature.
 Use the laws anyway, unless told to do otherwise.
 They give good _________________.
Examples
 A 47.3 L container containing 1.62 mol of He is heated until the pressure reaches 1.85 atm.
What is the temperature?

Kr gas in a 18.5 L cylinder exerts a pressure of 8.61 atm at 24.8ºC What is the mass of Kr?

A sample of gas has a volume of 4.18 L at 29ºC and 732 torr. What would its volume be at
24.8ºC and 756 torr?
Gas Density and Molar Mass
 The ideal gas law can be used to calculate _________ and ___________________.
 D = m/V
 Let M stand for molar mass
 M = m/n
 n= PV/RT
 M= m
PV/RT
 M = mRT = m RT = DRT
PV
V P
P
Examples
 What is the density of ammonia at 23ºC and 735 torr?

A compound has the empirical formula CHCl. A 256 mL flask at 100.ºC and 750 torr contains .80
g of the gaseous compound. What is the molecular formula?
Dalton’s Law
 The total pressure in a container is the _________of the pressure _______________ would
exert if it were __________ in the container.
 The total pressure is the sum of the _________________ pressures.
 PTotal = P1 + P2 + P3 + P4 + P5 ...
 For each P = nRT/V
Dalton's Law
 PTotal = n1RT + n2RT + n3RT +...
V
V
V
 In the same container R, T and V are the same.
 PTotal = (n1+ n2 + n3+...)RT
V
 PTotal = (nTotal)RT
V
Examples
4.0 L CH4
1.50 L
2.70 atm
4.58 atm

N2
3.50 L O2
0.752 atm
When these valves are opened, what is each partial pressure and the total pressure?
The mole fraction
 Ratio of moles of the substance to the _________________.
 symbol is Greek letter chi Χ
 Χ 1 = n1 = P1
nTotal PTotal
Examples
 The partial pressure of nitrogen in air is 592 torr. Air pressure is 752 torr, what is the mole
fraction of nitrogen?

What is the partial pressure of nitrogen if the container holding the air is compressed to 5.25
atm?
Vapor Pressure
 Water evaporates!
 When that water evaporates, the ___________ has a _________________.
 Gases are often collected over water so the vapor pressure of water must be
______________from the total ________________.
 Vapor pressure must be ______________.
Example
 Oxygen was produced during a chemical reaction. The gas was collected by displacement of
water at 22oC at an atmospheric pressure of 754 torr. The volume of gas collected was 0.650 L,
and the vapor pressure of water at 22oC is 21 torr. Calculate the partial pressure of O2 in the gas
collected and the mass of O2 collected.
Kinetic Molecular Theory
 A theory attempts to explain _________things happen.
 In this case, the KMT attempts to explain why ___________________ behave the way they do.
 These are assumptions that simplify the theory, but they don’t hold up with _____________.
Kinetic Molecular Theory
1. The particles making up a gas are so small we can ignore their _______________. (gas particles
are _____________________)
2. The particles are in ____________________ and their _________________ cause pressure.
3. The particles do not affect each other, neither _____________ or __________________.
4. The average kinetic energy is _______________ to the ___________________ temperature.
 There is a _______________________ of the ideal gas law that is used with real gases.
 Using the equation for kinetic energy (KE = 1/2mv2) and the assumptions of the KMT, the
___________________ of gas particles can be calculated.
The meaning of temperature
 PV/n = RT = 2/3(KE)avg
 (KE)avg = 3/2RT
 The average velocity of the gas particles is a special kind of average. The symbol u2 means the
average of the _______________ of the particle velocities. The square root of u2 is called the
_____________________________ and is symbolized by urms.
 Urms = 3RT
M
R = 8.314, T is temp in Kelvin, M is the molar mass in kg. Velocity will be in m/s.
Example
 Calculate the root mean square velocity of carbon dioxide at 25ºC.

Calculate the root mean square velocity of hydrogen at 25ºC.

Calculate the root mean square velocity of chlorine at 25ºC.
Range of velocities
 The average distance a molecule travels before colliding with another is called the
__________________________ and is _______________ (near 10-7 m)
 Temperature is an ______________. There are molecules of many ____________in the average.
 Shown on a graph called a velocity _______________________
Velocity
 Average velocity _______________________ as temperature increases.
 The spread of velocities ___________________ as temperature increases.
Effusion
 ________________ of gas through a small hole, into a vacuum.
 The effusion rate measures how _____________ this happens.
 ______________________ Law= the rate of effusion is ________________ proportional to the
square root of the ____________ of its particles.
Rate of effusion for gas 1

Rate of effusion for gas 2
M2
M1
Diffusion
 The ________________ of a gas through a room.
 ___________ considering molecules move at 100’s of meters per second.
 ____________ with ______________________________ slow down diffusions.
 Best estimate is Graham’s Law.
Examples
 A compound effuses through a porous cylinder 3.20 time faster than helium. What is it’s molar
mass?

If 0.00251 mol of NH3 effuse through a hole in 2.47 min, how much HCl would effuse in the same
time?

A sample of N2 effuses through a hole in 38 seconds. what must be the molecular weight of gas
that effuses in 55 seconds under identical conditions?
Real Gases
 Real molecules _______________________ and _____________________ with each other
(especially ___________________ molecules).
 Need to add correction factors to the ideal gas law to account for these.
Volume Correction
 The actual volume free to move in is ___________ because of particle size.
 More molecules will have _____________ effect.
 Corrected volume V’ = V - nb
 b is a constant that differs for each gas.
 P’ = nRT
(V-nb)
Pressure correction
 Because the molecules are _________________ to each other, the pressure on the container
will be _____________ than ideal
 depends on the ________________ of molecules per liter.
 since two molecules interact, the effect must be _______________
Where does it come from
 a and b are determined by _________________________.
 Different for ____________ gas.
 Bigger molecules have _____________ b.
 a depends on both _________ and ___________________.
 once given, plug and chug.
Altogether
 Pobs= nRT - a n 2
V-nb
V
 Called the Van der Waal’s equation if rearranged

Corrected
Pressure
Corrected
Volume
Example
 Calculate the pressure exerted by 0.5000 mol Cl2 in a 1.000 L container at 25.0ºC
 Using the ideal gas law.
 Van der Waal’s equation
 a = 6.49 atm L2 /mol2
 b = 0.0562 L/mol
Gases and Stoichiometry
 Reactions happen in _____________
 At Standard Temperature and Pressure (STP, 0ºC and 1 atm) 1 mole of gas occuppies 22.42 L.
 If not at STP, use the ______________________to calculate moles of reactant or volume of
product.
Examples
 Mercury can be achieved by the following reaction
HgO  Hg + O2

What volume of oxygen gas can be produced from 4.10 g of mercury (II) oxide at STP?

At 400.ºC and 740 torr?
Examples
 Using the following reaction
NaHCO3 + HCl  NaCl + H2O + CO2

calculate the mass of sodium hydrogen carbonate necessary to produce 2.87 L of carbon dioxide
at 25ºC and 2.00 atm.

If 27 L of gas are produced at 26ºC and 745 torr when 2.6 L of HCl are added what is the
concentration of HCl?
Examples
 Consider the following reaction
NH3 + O2  NO + H2O
 What volume of NO at 1.0 atm and 1000ºC can be produced from 10.0 L of NH3 and excess O2 at
the same temperture and pressure?
 What volume of O2 measured at STP will be consumed when 10.0 kg NH3 is reacted?
The Same reaction
 What mass of H2O will be produced from 65.0 L of O2 and 75.0 L of NH3 both measured at STP?
 What volume Of NO would be produced?
 What mass of NO is produced from 500. L of NH3 at 250.0ºC and 3.00 atm?
Example
 N2O can be produced by the following reaction
NH4NO3  N2O + H2O
 what volume of N2O collected over water at a total pressure of 94 kPa and 22ºC can be
produced from 2.6 g of NH4NO3? ( the vapor pressure of water at 22ºC is 21 torr)