the gas laws learning about the special behavior of gases objective #2, begins on pg. 5 of the note...

The Gas LawsThe Gas LawsThe Gas LawsThe Gas LawsLearning about the special behavior Learning about the special behavior

of gasesof gases

Objective #2, begins Objective #2, begins on pg. 5 of the Note on pg. 5 of the Note

packpack

Combined Gas Law:There really is no need to remember 3

different equationsA single expression , called the

combined gas lawcombined 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.

Example, to solve for V1…

(how to get V1 all by itself)

P1 V1 P2V2

T1 T2

Re-arranging the Combined Gas Law

Example, to solve for V1…

Move the P1, to the bottom…

P1 V1 P2V2

T1 T2

Re-arranging the Combined Gas Law

Example, to solve for V1…

Then move the T1, to the top…

V1 P2V2

T1 T2 P1

Re-arranging the Combined Gas Law

Example, to solve for V1…

V1 P2V2T1

T2 P1

Re-arranging the Combined Gas Law

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:

V1 = V2 =

T1 = T2 =

P1 = P2 =

P2V2T1

T2P1

P2V2T1

P1V1 P2V2T1

T2V1

P1V1T2

T1P2

P1V1T2

P2V2 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 4A 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 4A 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 4A 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 4A 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 4A 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 invertinvert 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

P1 V1

=

=

=

•Practice…•Practice…•Practice!!

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”