Answer these questions and formulas. Ideal Gas Law Worksheet, solving problems
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Gas Laws Worksheet, CHEM1210, Spring 2019
Simple Gas Laws
The simple gas laws discover the relationship of pressure, temperature, volume and amount of gas. They
were derived by holding two of the gas properties constant, varying the 3rd and measuring the effect on
the 4th property. Boyle’s Law tells us that the volume of gas increases as the pressure decreases. Charles’
Law tells us that the volume of gas increases as the temperature increases. Avogadro’s Law tells us that
the volume of gas increases as the amount of gas increases. And Guy-Lassac’s Law tells us that the
pressure of gas increases as the temperature increases. The ideal gas law is the combination of the
simple gas laws.
Law Name
Law
Definition
Boyle’s Law
For a given amount of
gas at constant
temperature, the
volume of a gas varies
inversely with pressure
Constant
Properties
Law
Formula
n, T = const
” ” = % %
Charles’ Law
The volume of a fixed
amount of gas is
directly proportional
to its Kelvin
temperature if the
pressure is kept
constant.
n, P = const
Avogadro’s Law
The volume of a gas is
directly proportional
to the number of
moles of gas present
in the sample at
constant temperature
and pressure.
P, T = const
Guy-Lassac’s Law
The pressure of a
given amount of
gas is directly
proportional to the
Kelvin temperature
if the volume is
kept constant.
n, V = const
” %
=
” %
” %
=
” %
” %
=
” %
Example Problems:
Problem 1: A balloon contains 7.2 L of He. When the pressure is reduced to 2.00 atm the balloon
expands to occupy a volume of 25.1 L. What was the initial pressure exerted on the balloon?
Step 1: List the known and unknown variables: V1=7.2L, P1=?
V2=25.1L, P2=2.00atm
Step 2: Make sure that the variables are in the appropriate units.
Step 3: Identify the simple gas law that would be appropriate to solve the problem, given the
information.
Boyle’s law: ” ” = % %
Step 4: Solve:
” (7.2 ) = = (2.00 )(25.1 )
(2.00 )(25.1 )
” =
= 6.972 = 7.0
(7.2 )
Problem 2: The temperature inside my refrigerator is about 4o Celsius. If I place a balloon which is
initially at 22o C and a volume of 0.5 liters in my fridge, what will the volume of the balloon be, after
it is fully cooled by my refrigerator?
Step 1: List the known and unknown variables: T1=22o C, V1= 0.50L, T2 =4.0oC, V2=?
Step 2: Make sure that the variables are in the appropriate units
In this case, T needs to be converted to Kelvins
T1=22o C + 273.15K = 295.15K
T2 =4oC + 273.15K = 277.15K
Step 3: Identify the simple gas law that would be appropriate to solve the problem, given the
information.
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7
7
Charle’s law: 98 = 9:
8
Step 4: Solve:
:
0.50
%
=
295.15 277.15
%
0.5
=
(277.15 ) = 0.47
295.15
Problem 3: A 25.5 L balloon holding 3.50 moles of carbon dioxide leaks. If we are able to determine
that 1.90 moles of carbon dioxide escaped before the container could be sealed, what is the new
volume of the container?
Step 1: List the known and unknown variables: V1=25.5L, n1=3.50 mol, n2 = 3.50mol(initially) 1.90mol(leaked)=1.60 mol (remaining in balloon), V2=?
Step 2: Make sure that the variables are in the appropriate units.
Step 3: Identify the simple gas law that would be appropriate to solve the problem, given the
information.
Avogadro’s Law:
78
=8
7
= =:
:
Step 4: Solve:
25.5
%
25.5
(1.60 ) = 11.7
=
∴ % =
3.50 1.60
3.50
Problem 4: The pressure in an automobile tire is 1.88 atm at 25.0°C. What will be the pressure, if the
temperature warms up to 37.0°C
Step 1: List the known and unknown variables: P1=1.88 atm, T1=25oC, P2=?, T2=37.0°C
Step 2: Make sure that the variables are in the appropriate units
In this case, T needs to be converted to Kelvins
T1=25.0o C + 273.15K = 298.15K
T2 =37.0oC + 273.15K = 310.15K
Step 3: Identify the simple gas law that would be appropriate to solve the problem, given the
information
Guy-Lassac’s Law∶
C8
98
=
C:
9:
Step 4: Solve:
1.88
%
1.88
(310.15 ) = 1.96
=
∴ % =
298.15 310.15
298.15
Solve the following problems
1. A rigid plastic container holds 1.00 L methane gas at 0.9 atm pressure when the temperature is
22.0°C. What pressure would the gas exert if the temperature is raised to 44.6°C ?
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2. If 5.00 g of O2 gas has a volume of 7.20 L at a certain temperature and pressure, what volume
does 15.0 g of O2 have under the same conditions?
3. The gas in a 600 mL balloon has a pressure of 1.20 atm. If the temperature remains constant,
what will be the pressure of the gas in the balloon when it is compressed to 400 mL?
4. On hot days, you may have noticed that potato chip bags seem to “inflate”, even though they
have not been opened. If I have a 250 mL bag at a temperature of 19oC, and I leave it in my car
o
which has a temperature of 60 C, what will the new volume of the bag be?
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Ideal Gas Law
Ideal Gas Law Equation: =
The ideal gas law is an equation that relates the volume, temperature, pressure and amount of gas
particles to a constant. The ideal gas constant is abbreviated with the variable R and has the value of
0.08206 atm·L/mol·K. The ideal gas law can be used when three of the four gas variables are known.
When using this equation, it is important that the units for pressure are atmospheres (atm), volume is in
liters (L), and temperature is converted to kelvins (K). The amount of gas is measured in units called
moles (mol).
Example: The pressure exerted by 2.8 moles of argon gas at a temperature of 85oC is 420 torr. What is
the volume of this sample?
Step 1: List the known variables: n= 2.8 moles; T= 85oC; P = 420 torr.
Step 2: List the unknown variable: V=?
Step 3: Check that the known variables are expressed in the appropriate units. If not, convert them.
n= 2.8 moles ü
T= 85oC – need to convert to Kelvin. K=C+273.15=85oC+273.15=358.15K
P = 420 torr – need to convert to atmospheres using the relationship 1.00 atm = 760 torr.
” LMN
420 × OPQ MRSS = 0.553
Step 4: Substitute into the equation for volume and solve, using the units as guides and canceling them
out.
.
(2.8 ) V0.08206 . W (358.15 )
=
=
= 148.8 = 1.5 10% (2 )
0.553
Solve the following problems.
1. A scuba tank has a pressure of 190 atm at a temperature of 283K. The volume of the tank is 350
L. How many moles of air are in the tank?
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2. A helium-filled balloon has a volume of 20 L and it contains 2.00 moles of gas. If the pressure of
the balloon is 1.2 atm, determine the temperature.
3. A tank of oxygen has a volume of 1500 L. The temperature of the gas inside is 35oC. If there are
9000 moles of oxygen in the tank what is the pressure in atm?
4. A canister of acetylene has a volume of 42 L. The temperature of the acetylene is 305 K and the
pressure is 780 torr. Determine the amount (moles) of gas in the canister.
Mixtures of Gases
Dalton’s law of partial pressures states that the total pressure of a mixture of gases is equal to the sum
of the individual pressures. In other words, mixtures of gases behave the same as a single gas would. In
a mixture of gases each individual gas contributes its own pressure, known as the partial pressure, to
the total pressure. The pressure of each gas is determined by the number of moles of gas, its volume
and temperature (ideal gas law). The sum of each gas pressure equals to the total pressure. The
equation for this law is MRML] = ” + % + _ …
The composition of a gas mixture can be described by the mole fractions of the gases present. The mole
fraction (X) of any component of a mixture is the ratio of the number of moles of that component to the
NR]bc Rd ”
=8
total number of moles of all the species present in the mixture (ntot): ” = MRML] NR]bc = = e= e=
e⋯
8
:
f
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The mole fraction is a dimensionless quantity between 0 and 1. If X1=1.0, then the sample is pure gas 1,
not a mixture. If X1=0, then no gas 1 is present in the mixture. The sum of the mole fractions of all the
components present must equal 1.
We can use the mole fraction of a gas A in a mixture to calculate the partial pressure of gas A, given the
total pressure exerted by the gas mixture, using the following equation:
h = h MRML]
Model: A Mixture of Gases
= 0.1 mol of oxygen gas
Tank A
Row #
1
2
3
4
5
6
7
8
9
10
11
12
= 0.10 mole of nitrogen gas
Tank B
Volume (L)
Temperature (K)
Moles of O2 gas
Moles of N2 gas
Total moles of gas in tank
Pressure O2 (atm)
Pressure N2 (atm)
Total Pressure in tank (atm)
X (O2)
X (N2)
P(O2) (atm)
P(N2) (atm)
Tank C
Tank A
10.00L
298K
Tank B
10.00L
298K
–
–
Tank C
10.00L
298K
1) What do all three tanks have in common?
2) Determine the moles of O2 gas and N2 gas for each tank in the model and enter those
values in the table (rows 3,4,5)
3) Use the Ideal Gas Law to calculate the pressure of O2 (show work here) and enter the
answers in the table (row 6):
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4) Use the Ideal Gas Law to calculate the pressure of N2 (show work here) and enter the
answers in the table (row 7):
5) What is the total pressure in each tank? Show work here. Enter your answers in the table (row
8).
6) Determine the mole fractions (X) of O2 gas and N2 gas for each tank. Show work here. Enter the
values in the table (row 9, 10).
7) Calculate the partial pressures of O2 gas (P(O2)) and N2 gas (P(N2)) for tank C using the mole
fraction and the total pressure of each gas. Show work here. Enter the values in the table (rows
11,12).
8) What do you notice when comparing rows 11 and 12 with rows 6 and 7? Why?
Solve the following problems:
1. Three gases are originally present in three separate 1.00 L containers. The pressure of the CO2
container is 0.32atm, the N2 container is at 0.49atm, and the He container measures at
0.16atm. The three gasses are then transferred to a single 1.00 L container.
i.
What is the pressure of this mixture of gases?
ii.
What are the mole fractions of the gases in the above mixture?
2. A mixture containing 0.226 mol He, 0.342 mol Ne, and 0.128 mol Ar is confined in a 4.00- L
vessel at 25 °C.
i.
What is the total pressure of the gas mixture?
ii.
What are the mole fractions of all the gases in the mixture?
iii.
What is the partial pressure of each gas in the mixture?
3. A mixture of 2 mol H2 and 3 mol He exerts a total pressure of 3 atm. What is the partial pressure
of He?
…
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