Transcript The Gas Laws

The Gas Laws
Learning about the special behavior of
gases
Objective #2, begins on
pg. 5 of the Note pack
Combined Gas Law:
There really is no need to remember 3
different equations
A single expression , called the combined
gas law, combines the three gas laws,
only holding the amount of gas
constant..
Re-arranging the
Combined Gas Law
This is not in your notes, but perhaps it should be.
You will need to be able to solve for 1 variable,
when given the other 5. To do that, you will
need to re-arrange the formula.
Q: How do you isolate just 1 variable?
A: Criss-cross the other variables,
that are with it, to the other side
of the equation.
Re-arranging the
Combined Gas Law
Example, to solve for V1…
(how to get V1 all by itself)
P1 V 1
T1
P2V2
T2
Re-arranging the
Combined Gas Law
Example, to solve for V1…
Move the P1, to the bottom…
P1 V 1
T1
P2V2
T2
Re-arranging the
Combined Gas Law
Example, to solve for V1…
Then move the T1, to the top…
V1
T1
P2V2
T2 P1
Re-arranging the
Combined Gas Law
Example, to solve for V1…
V1
P2V2T1
T2 P1
Your turn…
With your neighbor, please write the
formula you would use to find each of
the following:
V1 =
V2 =
T1
=
T2 =
P1
=
P2 =
Your turn…
With your neighbor, please write the
formula you would use to find each of
the following:
PVT
P
V
T
V1 =
V2 =
2 2
1 1
1
T1P2
T2P1
T1
=
P1
=
P1V1T2
P2V2
P2V2T1
T2V1
2
T2 =
P2 =
P2V2T1
P1V1
P1V1T2
T1V2
We can not have 1/T1 as a legitimate
option, so the formula must be inverted.
Example 1
• The volume of a gas-filled balloon is 30.0 L at 40o C
and 153 kPa pressure. What volume will the balloon
have at standard temperature and pressure?
Example 1
• The volume of a gas-filled balloon is 30.0 L at 40o C
and 153 kPa pressure. What volume will the balloon
have at standard temperature and pressure?
First, determine what formula we’re going to use to find
what’s missing:
Example 1
• The volume of a gas-filled balloon is 30.0 L at 40o C
and 153 kPa pressure. What volume will the balloon
have at standard temperature and pressure?
First, determine what formula we’re going to use to find
what’s missing:
We’re finding V2 = V1 x P1 x T2
P2 x T1
Example 1
• The volume of a gas-filled balloon is 30.0 L at 40o C
and 153 kPa pressure. What volume will the balloon
have at standard temperature and pressure?
First, determine what formula we’re going to use to find
what’s missing:
We’re finding V2 = V1 x P1 x T2
P2 x T1
Now substitute, changing the temp to Kelvin:
Example 1
• The volume of a gas-filled balloon is 30.0 L at 40o C
and 153 kPa pressure. What volume will the balloon
have at standard temperature and pressure?
First, determine what formula we’re going to use to find
what’s missing:
We’re finding V2 = V1 x P1 x T2
P2 x T1
Now substitute, changing the temp to Kelvin:
V2 =(30 L)x(153 kPa)x(273K)
(101.3kPa)x(313K)
Example 1
• The volume of a gas-filled balloon is 30.0 L at 40o C
and 153 kPa pressure. What volume will the balloon
have at standard temperature and pressure?
First, determine what formula we’re going to use to find
what’s missing:
We’re finding V2 = V1 x P1 x T2
P2 x T1
Now substitute, changing the temp to Kelvin:
V2 =(30 L)x(153 kPa)x(273K)
(101.3kPa)x(313K)
V2 = 39.5 L
Example 2
• A gas at 155 kPa and 25o C occupies a container
with an initial volume of 1 L. By changing the
volume, the pressure of a gas increases to 605
kPa as the temperature is raised to 125o C.
What is the new volume?
Example 2
• A gas at 155 kPa and 25o C occupies a container
with an initial volume of 1 L. By changing the
volume, the pressure of a gas increases to 605
kPa as the temperature is raised to 125o C.
What is the new volume?
First, determine what formula we’re going to use to
find what’s missing:
Example 2
• A gas at 155 kPa and 25o C occupies a container
with an initial volume of 1 L. By changing the
volume, the pressure of a gas increases to 605
kPa as the temperature is raised to 125o C.
What is the new volume?
First, determine what formula we’re going to use to
find what’s missing:
We’re finding V2 = V1 x P1 x T2
P2 x T1
Example 2
• A gas at 155 kPa and 25o C occupies a container
with an initial volume of 1 L. By changing the
volume, the pressure of a gas increases to 605
kPa as the temperature is raised to 125o C.
What is the new volume?
First, determine what formula we’re going to use to
find what’s missing:
We’re finding V2 = V1 x P1 x T2
P2 x T1
Now substitute, changing the temp to Kelvin:
Example 2
• A gas at 155 kPa and 25o C occupies a container
with an initial volume of 1 L. By changing the
volume, the pressure of a gas increases to 605
kPa as the temperature is raised to 125o C.
What is the new volume?
First, determine what formula we’re going to use to
find what’s missing:
We’re finding V2 = V1 x P1 x T2
P2 x T1
Now substitute, changing the temp to Kelvin:
V2 =(1L)x(155kPa)x(398K)
(605kPa)x(298K)
Example 2
• A gas at 155 kPa and 25o C occupies a container
with an initial volume of 1 L. By changing the
volume, the pressure of a gas increases to 605
kPa as the temperature is raised to 125o C.
What is the new volume?
First, determine what formula we’re going to use to
find what’s missing:
We’re finding V2 = V1 x P1 x T2
P2 x T1
Now substitute, changing the temp to Kelvin:
V2 =(1L)x(155kPa)x(398K)
(605kPa)x(298K)
V2 = 0.342 L
Example 3
• A 5 L air sample at a temperature of – 50o C
has a pressure of 107 kPa. What will be the
new pressure if the temperature is raised to
102o C and the volume expands to 7 L?
Example 3
• A 5 L air sample at a temperature of – 50o C has a
pressure of 107 kPa. What will be the new pressure
if the temperature is raised to 102o C and the
volume expands to 7 L?
First, determine what formula we’re going to use to
find what’s missing:
Example 3
• A 5 L air sample at a temperature of – 50o C has a
pressure of 107 kPa. What will be the new pressure
if the temperature is raised to 102o C and the
volume expands to 7 L?
First, determine what formula we’re going to use to
find what’s missing:
We’re finding P2 = V1 x P1 x T2
V2 x T1
Example 3
• A 5 L air sample at a temperature of – 50o C has a
pressure of 107 kPa. What will be the new pressure
if the temperature is raised to 102o C and the
volume expands to 7 L?
First, determine what formula we’re going to use to
find what’s missing:
We’re finding P2 = V1 x P1 x T2
V2 x T1
Now substitute, changing the temp to Kelvin:
Example 3
• A 5 L air sample at a temperature of – 50o C has a
pressure of 107 kPa. What will be the new pressure
if the temperature is raised to 102o C and the
volume expands to 7 L?
First, determine what formula we’re going to use to
find what’s missing:
We’re finding P2 = V1 x P1 x T2
V2 x T1
Now substitute, changing the temp to Kelvin:
P2 =(5L)x(107kPa)x(375K)
(7L)x(223K)
Example 3
• A 5 L air sample at a temperature of – 50o C has a
pressure of 107 kPa. What will be the new pressure
if the temperature is raised to 102o C and the
volume expands to 7 L?
First, determine what formula we’re going to use to
find what’s missing:
We’re finding P2 = V1 x P1 x T2
V2 x T1
Now substitute, changing the temp to Kelvin:
P2 =(5L)x(107kPa)x(375K)
(7L)x(223K)
P2 = 128.52 kPa
Example 4
A given mass of air has a volume of 6 L at 101 kPa. What
volume will it occupy at 25 kPa if the temperature
does not change?
Example 4
A given mass of air has a volume of 6 L at 101 kPa. What
volume will it occupy at 25 kPa if the temperature
does not change?
First, determine what formula we’re going to use to find
what’s missing. Since temp doesn’t change, T1 and T2
cancel each other out:
Example 4
A given mass of air has a volume of 6 L at 101 kPa. What
volume will it occupy at 25 kPa if the temperature
does not change?
First, determine what formula we’re going to use to find
what’s missing. Since temp doesn’t change, T1 and T2
cancel each other out:
We’re finding V2 = V1 x P1 x T2
P2 x T1
Example 4
A given mass of air has a volume of 6 L at 101 kPa. What
volume will it occupy at 25 kPa if the temperature
does not change?
First, determine what formula we’re going to use to find
what’s missing. Since temp doesn’t change, T1 and T2
cancel each other out:
We’re finding V2 = V1 x P1 x T2
P2 x T1
Now substitute, changing the temp to Kelvin:
V2 = (6L)x(101kPa)
(25kPa)
Example 4
A given mass of air has a volume of 6 L at 101 kPa. What
volume will it occupy at 25 kPa if the temperature
does not change?
First, determine what formula we’re going to use to find
what’s missing. Since temp doesn’t change, T1 and T2
cancel each other out:
We’re finding V2 = V1 x P1 x T2
P2 x T1
Now substitute, changing the temp to Kelvin:
V2 = (6L)x(101kPa)
(25kPa)
V2 = 24.24L
A Word of Caution!!
When we’re trying to find an unknown
Temp., like T2…
P1 V1=
P2V2
T1
T2
A Word of Caution!!
When we’re trying to find an unknown
Temp., like T2…
P1 V1
P2V2
=
T1
T2
A Word of Caution!!
When we’re trying to find an unknown
Temp., like T2…
P1 V1
P2V2 So we have P1 V1 = 1
=
T1
T2
P2 V2 T1 T2
This doesn’t work, to have 1/T2
A Word of Caution!!
When we’re trying to find an unknown
Temp., like T2…
P1 V1
P2V2 So we have P1 V1
1
=
=
T1
T2
P2 V2 T1 T2
To fix this, we need to invert both sides:
A Word of Caution!!
When we’re trying to find an unknown
Temp., like T2…
P1 V1
P2V2 So we have P1 V1
1
T1 =
T2
P2 V2 T1= T2
To fix this, we need to invert both sides:
P2 V2 T1 = T2
P 1 V1
Now you know how to do
MOST of Objective #2
(we’ll do the rest a little later…)
Next part is “Collecting a gas over water”
•Practice…
•Practice…
•Practice!!