At a given constant temperature and number of moles of gas, the
pressure and volume of a gas are inversely proportional. That is, the
higher the pressure, the smaller the volume; the lower the pressure, the
larger the volume. This relationship can be expressed in the equation:
P · V = constant
To find out how one of the quantities changes when you change the other,
use the following equation:
P1 · V1 = P2 · V2
1) An inflated balloon has a volume of 0.55 L at sea level (1 atm) and is
allowed to rise to a height of 6.5 km, where the pressure is about 0.40
atm. Assuming that the temperature remains constant, what is the final
volume of the balloon? Convert your answer to cubic meters (1
m3 = 1000 L). (Source: Chemistry, Raymond Chang)
2) A sample of chlorine gas occupies a volume of 946 mL at a pressure of
726 mmHg. Calculate the pressure of the gas (in mmHg) if the volume is
reduced at constant temperature to 154 mL. Convert your answer to atm (1
atm = 760 mmHg). (Source: Chemistry,
Raymond Chang)
3) At 46°C a sample of ammonia gas exerts a pressure of 5.3 atm.
What is the pressure when the volume of the gas is reduced to one-tenth
(0.10) of the original value at the same temperature? Convert your answer
to kPa (1 atm = 101.325 kPa) (Source: Chemistry, Raymond Chang)
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Charles’s Law (1787)
At a given constant pressure and number of moles of gas, the
volume and temperature of a gas are directly proportional. In other
words, the more you raise the temperature, the larger the volume of gas.
Temperature must be expressed in kelvins, not degrees Celsius (x°C =
x + 273 K). This relationship can be expressed in the equation:
V
— = constant
T
To find out how one of the quantities changes when you change the other,
use the following equation:
V1 V2
— = —
T1 T2
1) A 452 mL sample of fluorine gas is heated from 22°C to 187°C
at constant pressure. What is its final volume in liters? (Source: Chemistry, Raymond Chang)
2) A sample of carbon monoxide gas occupies 3.20 L at 125°C.
Calculate the temperature at which the gas will occupy 1.54 L if the
pressure remains constant. Be sure to express your answer in kelvins.
(Source: Chemistry, Raymond Chang)
3) Under constant pressure conditions 9.6 L of hydrogen gas initially at
88°C is cooled to -15°C. What is its volume after the cooling is
complete? (Source: Chemistry, Raymond
Chang)
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Avogadro’s Law (1811)
At a given constant temperature and constant pressure, the volume
and mass (i.e., the number of moles, n) of a gas are directly
proportional. This relationship can be expressed in the equation:
V
— = constant
n
To find out how volume changes when you change the number of moles, use
the following equation:
V1 V2
— = —
n1 n2
Note: you cannot change the number of moles just by changing the volume!
For that you have to add or subtract gas particles.
1) One mole of an ideal gas has a volume of 22.4 L at 1 atm and 273K.
(This set of conditions is known as STP: Standard Temperature and
Pressure). What is the volume of 0.50 mol of gas? Of 0.01 mol of gas?
Combined Gas Laws
The combined gas law brings all these relationships together into one
simple equation.
PV = nRT
The only complicating factor is the introduction of the gas constant (R =
0.0821 L·atm/K·mol or R = 8.314 L·kPa/K·mol).
This constant can be derived from the ideal gas law as follows:
PV
—— = R
nT
You can see now how the units of R work with pressure and volume in the
numerator and moles and temperature in the denominator. This same
expression can be used to follow changes in volume, pressure, and
temperature by realizing that no matter how you change these three
variables, they will always equal R. Assuming that there is no change in
the number of moles, use the following expression to take all three
variables into account during changes:
P1V1 P2V2
———— = ————
T1 T2
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1) A man filled his tires with air to a pressure of 32 lb/in2
when the temperature outside was -10°C. What pressure (in units of
atm) of air is in the tire once the weather finally warms up to a more
comfortable 20°C? (Hint: solve the equation for P). (Source: Chemistry, Raymond Chang)
2) Sulfur hexafluoride (SF6) is a colorless, odorless, very
unreactive gas. It is sometimes used in double-pane windows as a filler
gas because of its insulative properties. Calculate the pressure (in atm)
exerted by 1.82 moles of the gas in a steel vessel of volume 5.43 L at
69.5°C. (Hint: solve the equation for P). (Source: Chemistry, Raymond Chang)
3) Calculate the volume (in liters) occupied by 2.12 moles of nitric
oxide (NO) at 6.54 atm and 76°C. (Hint: solve the equation for V).
(Source: Chemistry, Raymond Chang)
4) An average pair of human lungs contains about 3.5 L of air after
inhalation and about 3.0 L after exhalation. Assuming that air in your
lungs is at 37°C (body temp.) and 1.0 atm, determine the number of
moles in a typical breath. (Hint: solve the equation for n). (Source:
PLTL Unit 5, USM Chemistry Department)
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5) Using your answer from the previous question, find the number of moles
of oxygen usually inhaled in a single breath. Oxygen is 20.948% by
volume of air. (Hint: use Avogadro’s Law to help answer this
question).
6) A gas is known to be one of the following nitrogen oxides: NO,
NO2, N2O4, or N2O. It has a
density of 1.96 g/L. If you have a 1.00 L sample at 273K, what is its
identity? (Source: PLTL Unit 5, USM Chemistry Department)
Stoichiometry with Gases
Stoichiometry is as important for gases as it is for solids, liquids and
solutions. To solve problems with gases you do exactly what you did for
reactants in other states of matter: convert to moles! You can use a
variety of ways to find the number of moles, depending on the information
you are given. Given grams, finding moles is easy. Given a volume,
temperature and pressure, finding moles means using n = PV/RT. Given a
density and a volume, find the mass and from there you can find the
number of moles. Remember to convert to the units required by the problem
once you have performed your calculation.
1) Aqueous lithium hydroxide solution is used to purify air in
spacecraft and submarines because it absorbs carbon dioxide according to
the equation:
2LiOH(aq) + CO2(g) →
LiCO2(aq) + H2O(l)
The pressure of carbon dioxide in a cabin having a volume of 2.4 ×
105 L is 7.9 × 10-3 atm at 312 K. A solution
of lithium hydroxide (LiOH) of negligible volume is introduced into the
cabin. Eventually the pressure of CO2 is reduced to 1.2
× 10-4 atm. How many grams of lithium carbonate are
formed in this process? (Source: Chemistry, Raymond Chang)
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2) Consider the following description of an automobile air bag:
“In a frontal impact of sufficient severity, the air bag sensing
system on the vehicle will detect that the vehicle is suddenly stopping
as a result of a crash. The sensing system completes an electrical
circuit, triggering a chemical reaction of the sodium azide sealed in the
inflators. the reaction produces nitrogen gas, which inflates the air
bag." (Source: 1995 Saturn Owner's Manual, p. 33)
The reaction is: 2NaN3(s) → 2Na(s) +
3N2(g)
How many grams of sodium azide are needed to produce 40.0 L of nitrogen
to fill an air bag at a pressure of 1.30 atm and a temperature of
28.0°C? (Source: PLTL Unit 5, USM Chemistry Department)