Now, a little more about
Gases!
Boyle’s Law
• The volume of a gas is inversely
related to the pressure at a
constant temperature.
P1V1 = P2V2
Equivalent Units of Pressure
• 1 atmosphere
• 760 mmHg (aka torr)
• 101.3 kPa (kilopascals)
• 14.7 psi (pounds per square inch)
Example -
• A sample of helium gas in a
balloon is compressed from
4.0L to 250mL at a constant
temperature. If the original
pressure of the gas is 210kPa,
what will be the pressure of the
compressed gas?
Charles’ Law
• The volume of a gas is directly
proportional to the temperature
at a constant pressure.
V1 = V 2
T1 T2
Units for Temperature
• Gas Law Equations require
temperature to be measured in
Kelvins.
K = °C + 273.15
Example…
• What is the volume of the air
in a balloon that occupies
0.620 L at 25°C if the
temperature is lowered to
0.0°C?
Gay-Lussac’s Law
• The pressure of a gas is directly
proportional to the temperature
(K) if the volume remains
constant.
• P1 = P 2
T1 T2
Example…
• The pressure in an automobile
tire is 1.88 atm at 25°C. What
will be the pressure in psi if the
temperature warms up to
37.0°C?
Combined Gas Law
V1P1 = V2P2
T1
T2
Example…
• An unopened, cold 2.00 L bottle of
soda contains 46.0 mL of gas
confined at a pressure of 131.96
kPa at a temperature of 5.0°C. If
the bottle is dropped into a lake
and sinks to a depth at which the
pressure is 154 kPa and a
temperature of 2.1°C, what will be
the new volume of the gas?
STP
• Standard Temperature
273 K
• Standard Pressure
1 atm or 760 mmHg
Example…
• A sample of gas has a
volume of 2050 mL at 0.95
atm and 36°C. What will be
the volume of the gas at
STP?
Dalton’s Law of Partial Pressure
• The total pressure of a mixture of
gases is equal to the sum of the
partial pressures of each
component gas.
• Pt = P1 + P2 + P3…
Examples…
• A scuba tank contains a mixture of
gases including 0.42 atm N2, 205 torr
O2 and 35.5 kPa CO2. What is the total
pressure inside the tank in
atmospheres?
• A sample of oxygen gas was collected
over water at 20.0°C and 731.0 mmHg.
What is the pressure of the dry gas?
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.
rateA = √MB
rateB √MA
What is effusion?
• When a gas is confined in a
container that has a very small
opening, the gas molecules will
randomly encounter the
opening and pass through it.
example
• Calculate the ratio of effusion
between ammonia, NH3, and
hydrogen chloride gas.
Avogadro’s Principle
• Equal volumes of gases at the
same temperature and pressure
contain equal numbers of particles!
• Molar Volume – the volume of 1.0
mol of any gas at STP.
1 molgas = 22.4 L (new)
= 6.02 x 1023 particles
= MM in grams
Examples…
• What size container do you need to
hold 0.0459 mol N2 gas at STP?
• How many grams of CO2 gas are in
a 2.5 L flask at STP?
• How many atoms of He are present
in a 1.75 L balloon?
Ideal Gas Law :
PV = nRT
Where P = pressure
V = volume in Liters
n = number of mols
R = ideal gas constant
T = temperature (Kelvin)
Calculate R, the Ideal Gas Constant…
• 1 mol of gas at STP and molar volume
• R = 0.0821 atm·L
mol·K
= 62.4 mmHg·L
mol·K
= 8.314 kPa·L
mol·K
Example…
• Calculate the number of moles of
gas contained in a 3.0L vessel at
33°C and a pressure of 1.50 atm.
• Determine the Celsius temperature
of 2.49 mols of gas contained in a
0.75L vessel at a pressure of 143
kPa.
Variations…
• n = m/M so…
PVM = mRT
• d= m/V so…
PM = dRT
Example…
• Calculate the grams of oxygen gas
present in a 2.50L sample kept at
1.66 atm pressure and a
temperature of 10.0°C.
• What is the molar mass of a gas
that has a density of 1.02g/L at
0.990 atm pressure and 37°C?
Examples…
• Calculate the grams of N2 present
in a 0.600L sample kept at
765 mmHg and a temperature of
22.0°C.
• What is the density of NH3 at
800 mmHg and 25°C?
Real Gases deviate from ideal behavior
under 2 circumstances…
To think of these, refer back to the five
assumptions of kinetic theory.
Under what conditions would some of
these assumptions not hold true?
Deviations of a real gas
1. Extremely high pressure
2. Extremely low temperature
Van der Waals Equation
• a and b are constants specific to each
gas. One corrects for the volume of the
molecules, the other corrects for
intermolecular forces of attraction.
Which is which?
• B corrects for molecular volume
• A corrects for attractive forces
Stoichiometry (revisited!)…
•
•
Objective: use known information
about part of a chemical equation to
determine quantities of another part
of the equation.
Three step problem:
1. Convert to mols
2. Mol to mol ratio
3. Convert out of mols
•
Conversions:
– g and mol, use Molar Mass
– L and mol, use 22.4L
•
Example –
– Given 25 L of oxygen gas,
A)How many grams of water can
be produced?
B)How many liters of hydrogen
will be required?
Gas Stoichiometry at non-STP
• Iron (III) chlorate decomposes with
heat into iron (III) chloride and oxygen
gas. If 37.6 liters of oxygen gas is
collected at 800 torr and 30ºC, how
many grams of iron (III) chlorate were
decomposed?
• (108 g)
• Hydrogen peroxide decomposes in the
presence of light into oxygen gas and liquid
water. The bottle of “peroxide” which you
buy at the drug store is really only 3.00%
hydrogen peroxide and 97.0% water. If you
poured a 1.00 pound bottle of 3.00% H2O2
into a dish and allowed it to decompose, what
would be the volume of just the oxygen gas if
it were collected at 10ºC and with a
combined pressure of 650 torr, assuming that
all of the hydrogen peroxide decomposed?
Hint:
• (remember that the oxygen is being
collected “over water” since it is
bubbling out of the 97% water in the
bottle). Vapor pressure of water at
10º C is 9.2 torr.
• (5.52 liters)
• 6.00 grams of solid magnesium react with
100 grams of hydrochloric acid which is 84%
water. How many liters of hydrogen gas can
be collected at 700 torr and 50oC? (Hint: the
hydrogen is being collected “over water”
since there is water in the hydrochloric acid
solution which the hydrogen gas bubbles
through as it is formed). The vapor pressure
of water at 50oC is 92.5 torr.
• (7.27 liters)
• Which reactant is left over and how much?
• (0.74 grams of magnesium)