States of Matter & Gas Laws
States:
There are three common states of matter: solid, liquid and
gas. Each state has some general traits
which all types of matter in this state follow.
Phases
Characteristics:
|
|
Density |
Shape |
Thermal Expansion |
Compressible |
|
Solid |
High |
fixed |
Very Little |
Very Little |
|
Liquid |
Medium |
takes shape of the
container |
Very Little |
Very Little |
|
Gas |
VERY Low |
takes shape of the
container |
Lots |
Very Easily |
What determines a substance’s state of matter? There are three factors. The first to come to mind is probably
temperature. If you heat something
eventually it melts or boils. The next
is not so obvious, the pressure. For
example, with a change in atmospheric pressure water boils at a lower
temperature in
Phase Diagram:
The phase diagram is a graphical tool used to determine what
state of matter a substance will be in a given temperature and pressure.
The phase diagram is a series of lines generated from actual experimental
data. In other words, someone took a
substance and checked its state at many different combinations of temperature
and pressure. They checked the state
when the substance was at 5°C and at 760 mmHg, then at 5°C and 761 mmHg, then at 5°C and
762 mmHg and so on. As you can see it would take a while to check all the
temperature/pressure combinations there are for any given substance.
The lines on the phase diagram divide the three phases. If you cross a line, a physical process has
occurred.
Generally, heating a
solid will cause it to melt to a liquid (at the melting or freezing point).
Continued heating (to the boiling point) produces a gas. For most substances, at higher pressures, the
freezing and boiling points are higher.
There are two specific
areas of interest, the triple point and the critical temperature. The triple point occurs at a specific
temperature and pressure at which all three phases exist in equilibrium. When observing a substance at its triple
point it appears to be boiling freezing and melting all at the same time. Once above the critical temperature,
molecules are unable to liquefy. Meaning
no matter how much pressure you apply, the molecules will remain a gas and will
not reform a liquid until the temperature is dropped. The molecules are simply moving too fast.
Phase Diagram for Water:
The same diagram for water shows the characteristic negative slope on the
solid-liquid equilibrium line, which accounts for why water floats. The manner in which water forms its
crystalline structure causes it to expand.
Hence the liquid state is the most dense state. This causes ice to float.
Looking at the graph upward from the temperature axis one notices that
increasing the pressure on a solid will change it to a liquid, the opposite
effect of what occurs on the first figure.
When a hockey player steps on to the ice, they apply a pressure to the
ice and the ice melts. So, hockey
players are not actually skating on ice, but a thin layer of water they just
melted by standing on that ice.
Units of Gasses:
|
abbreviation |
name |
normal atmospheric pressure |
|
Torr |
Torricelli |
760 |
|
mmHg |
millimeters of mercury |
760 |
|
Psi |
pounds per square inch |
14.7 |
|
Atm |
atmospheres |
1 |
|
Bar |
Bar |
1.01 |
|
kPa |
kilopascal |
101.325 |
|
inHg |
inches of mercury |
29.9 |
|
ft H2O |
feet of water |
33 |
Nature of Gas Pressure:
The pressure of a gas is a measure of force applied over a given area. For example, pounds per square inch. The force being applied is due to the impact
of gas particles on some object.
Right
this second, as you read these notes, billions of gas particles – N2,
O2, CO2, Ar, H2O – are slamming into your
eyes. Yes, your eyes and all of the rest
of your body. The air is acting in the
same fashion that water does when you submerge yourself. You feel the water pressing you as you dive
deeper. You feel it on your eardrums. Just as you feel it when you come back down a
mountain,
Why do your ears hurt or
feel uncomfortable when traveling up and down mountains? There is air pressing on your eardrums, so
why are your eardrums not constantly hurting?
Because your body equalizes the pressure. Normal atmospheric pressure is 14.7 psi. This means that the air is pressing on
everything with a pressure of 14.7 psi.
Your eardrums are no exception.
Your body has countered this by applying a pressure of 14.7 psi in the
inside of your eardrums. This results in
no net pressure and your eardrum rests happily undisturbed. But when you drive up a mountain you get an
uncomfortable feeling, maybe even painful, why?
The pressure in your head is now greater than that outside your head and
your eardrum is pressing outward. This
stress to the drum is uncomfortable, for some it is even incapacitating. The "popping" of your ears is your
head equalizing the pressure, which as you travel up is some value less than
14.7 psi. As you travel back down the
mountain your drums will be pressed in until your head can re-equalize the
pressure.
Evangelista Torricelli's Barometer:
The barometer picture here was invented by Evangelista Torricelli. This was one of the first 
methods used to measure
atmospheric pressure, and it is still used today. Today, most instruments named barometers are
not this large and contain no mercury, they work on other principals of
physics. But the name has been applied
to all instruments used to measure atmospheric pressure.
The
apparatus is set up by taking a tube filled with Hg, placing your thumb over
the top, inverting the tube and submerging the open end in another container, a
dish, also filled with Hg. The Hg in the
tube falls, leaving a vacuum at the top of the tube. But not all of the Hg drains out of the
tube. What force is holding this dense
liquid up against gravity’s pull? Air
pressure. Normal atmospheric pressure
will hold a column of Hg 760 mm tall.
This is one of our units listed above for atmospheric pressure; it is
equivalent to the Torr, obviously named after Torricelli.
Gas Laws:
There are several laws used to describe the behavior of gasses. What follows are descriptions of the most
important. There about 8 laws we will
discuss. These laws we will be
discussing pressure, temperature, volume and moles or numbers of gas
particles.
When
doing these problems, keep in mind that there are only 4 parameters to
consider: P, T, V, and n. For many of
these problems you will be keeping two of the four parameters steady as you
modify one of these four and calculate that modification of the fourth
parameter.
Boyle's Law:
This law defines the relationship between pressure and volume if temperature
and amount of gas is held constant. If the volume of a container is
increased, the pressure decreases. If
the volume of a container is decreased, the pressure increases. The law is described by the following equation:
P1V1 = P2V2
Example:
A sample of gas is in a 2.00 L contain at a pressure of 740.0 mmHg. What is the new pressure of the sample if the
container’s volume is reduced to 1.25 L?
Answer:
This problem is solved by inserting values into the given equation:
(740.0 mmHg) (2.00 L)
=(X) (1.25 L)
Solving
for X will give you a new pressure of 1184 mmHg.
Charles's Law:
This law defines the relationship between volume and temperature if pressure
and amount of particles are held constant.
If the temperature of a gas is increased, the volume of the gas will
increase. If the temperature of a gas is
decreased, the volume of the gas will decrease.
This is a direct relationship.
One goes down, so does the other.
Picture
the gas particles flying around inside a balloon. If you were to put the balloon in the
freezer, the gas particles would slow down, therefore they would not hit the
balloon walls as hard and the balloon would shrink in size.
or V1T2 = V2T1
Example: A gas is collected and found to fill 2.85 L at 25.0°C. What will be
its volume at standard temperature?
Answer: Convert 25.0°C to Kelvin and you get 298 K. Standard temperature is
273 K. We plug into our equation like this:
Solving for the new volume gives a value of 2.61 liters. The volume has decreased as the temperature
has decrease.
Gay-Lussac's Law:
This law characterizes the relationship between pressure and
temperature when volume and amount are held constant. If the temperature of a container is
increased, the pressure increases. If
the temperature of a container is decreased, the pressure decreases. This is another example of a direct
relationship. One goes up, so does the
other.
Think about this law in this manner, if the gas particles
are moving faster, as happens when the temperature of a gas is increased, the
force of the impact will increase.
Therefore, increasing the temperature will increase the pressure exerted
by a gas.
Example: 10.0 L of a gas is found to exert 97.0 kPa at
25.0°C. What would be the required
temperature (in Celsius) to change the pressure to standard pressure?
Answer: Change 25.0°C to 298.0 K and remember that standard
pressure in kPa is 101.325. Insert values into the equation and get:
The answer is 311.3 K, but the question asks for Celsius, so
you subtract 273 to get the final answer of 38.3°C, but then you knew that.
Right?
Avogadro's Law:
This law gives the relationship between volume and number of
gas particles when pressure and temperature are held constant. Remember the number is measured in
moles. If the amount of gas in a
container is increased, the volume increases.
If the amount of gas in a container is decreased, the volume
decreases. Another direct relationship.
The volume of a container holding a gas will increase with
increasing numbers of gas particles because there are more particles impacting
the wall of the container.
Example: A 5.00 L sample of a gas is known to contain 0.965
mol. If the amount of gas in this
container is increased to 1.80 mol, what new volume will result (at an
unchanged temperature and pressure)?
Answer:
V1n2 = V2n1
(5.00 L) (1.80 mol) =
(x) (0.965 mol)
Combined Gas Law:
To derive the Combined Gas Law, follow these steps:
Step 1: Write Boyle's Law
P1V1
= P2V2
Step
2: Multiply by Charles’s Law
V1T2 = V2T1
P1V12 / T1
= P2V22 / T2
Step 3: Multiply by Gay-Lussac's Law
P1T2 = P2T1
P12V12
/ T12 = P22V22
/ T22
Step
4: Take the square root to get the combined gas law:
P1V1
/ T1 = P2V2 / T2
As
a side note:
If we include Avogadro’s Law the following equation is generated:
P1V1
/ n1T1 = P2V2 / n2T2
Example:
A 2.00 L sample of a gas is collected at 25.0°C and 745.0 mmHg. What is the volume at STP?
You
have to recognize that five values are given in the problem and the sixth is
the only unknown. Also, remember to
change the Celsius temperatures to Kelvin.
When
problems like this are solved it is very helpful to write out all the variables
in the equation as shown below:
Next
fill in the data given in the problem.
Here is the right-hand side filled in with the STP values:
You
can be pretty sure that the term "STP" will appear in these types of
problems. I recommend you memorize these
standard conditions.
Here
are all the given values:
Insert
the values in their proper places in the combined gas law equation:
P1V1
/ T1 = P2V2 / T2
and
solve for x.
PV = nRT: The Ideal
Gas Law:
The derivation of this law is a lot of math. So, I will just give you the equation and
examples of how to use it.
PV = nRT
The Numerical Value for R:
R's value can be determined many ways. This is just one way:
We will assume we have 1.000 mol of a gas at STP. The volume of this amount of gas under the
conditions of STP is known to a high degree of precision. We will use the value of 22.414 L.
By the way, 22.414 L at STP has a name. It is called molar volume. It is the volume of ANY ideal gas at standard
temperature and pressure. As far as you
are concerned, all the gasses we discuss will behave as ideal gasses. So, if you have a sample of gas containing
6.022 x 1023 gas particle, this sample of gas will have a volume of
22.414 L, or about 5 gallons. Think
about an object that is 5 gallons. I
picture an office water cooler bottle, or a one of those LARGE buckets of
paint.
Let's plug our numbers into the equation:
(1.000 atm) (22.414
L) = (1.000 mol) (R) (273.15 K)
Notice how atmospheres were used as well as the exact value
for standard temperature.
Solving for R gives 0.08206 L atm / mol K, when rounded to
four significant figures. This is
usually enough. Remember the value. You'll need it for problem solving.
Notice the weird unit on R. Say out loud "liter
atmospheres per mole Kelvin."
This is not the only value of R that can exist. It depends
on which units you select. Those of you
that take more chemistry or physics will most likely meet up with 8.3145 Joules
per mole Kelvin, but that's for another course. We will only use the 0.08206 value in
gas-related problems.
Example: A sample of
gas with a mass of 2.1025 grams is found to occupy a volume of 2.850 L at
22.0°C at a pressure of 740.0 mmHg. How
many moles of the gas are present?
Notice that the units for pressure MUST be in atm., so the
740.0 mm Hg must be converted first.
740.0 mm Hg ÷ 760.0 mm Hg/atm = 0.9737 atm
However, the unrounded-off value should be used in the
calculation just below.
Now, plug into the equation:
(0.9737 atm) (2.850 L) = (n) (0.08206 L atm / mol K) (295.0
K)
and solve for n = 0.115 mol
Example: Using the
problem above, what is the molar mass of the gas?
This is a very common use of this law and the odds are very
good you will see this type of question on a test.
The key is to remember the units on molar mass: grams per
mole. We know from the problem statement
that 2.1025 grams of the gas is involved and we also know how many moles that
is.
We know that from doing the calculation above and getting
0.1146 mol.
So all we have to do is divide the grams of gas by how many
moles it is:
2.1025 g ÷ 0.1146 mol = 18.34 g/mol
With a molar mass of 18.34 g per mol can you make an
educated guess as to what gas this might be?
Let's go over those steps for using the Ideal Gas Law to
calculate the molar mass of the gas:
1. You
have to know the grams of gas involved.
Usually the problem will just give you the value, but not always. You might have to calculate it.
2. You
are going to have to calculate the moles of gas. Use PV = nRT and solve for n. Make sure to use L, atm and K.
3. Divide
grams by moles and there's your answer.
For any pure gas (let's use helium) PV = nRT holds
true. Therefore, P is directly
proportional to n if V and T remain constant.
As n goes up, so would P. Or the
reverse.
Suppose you were to double the moles of helium gas present.
What would happen?
Answer: the gas pressure doubles.
However, suppose the new quantity of gas added was a
DIFFERENT gas. Suppose that, instead of helium, you added neon.
What would happen to the pressure?
Answer: the pressure doubles, same as before.
Written as an equation, it looks like this:
PHe + PNe
= Ptotal
Where
n is the total number of gases in the mixture.
The
only necessity is that the two gases do not interact in some chemical fashion,
such as reacting with each other.
The
pressure each gas exerts in mixture is called its partial pressure.
Example:
A container holds three gases: oxygen, carbon dioxide, and
helium. The partial pressures of the three gases are 2.00 atm, 3.00 atm, and
4.00 atm, respectively. What is the total pressure inside the container?
PT = PO2
+ PCO2 + PHe
PT
= 2 atm + 3 atm + 4 atm = 9 atm
Graham's Law:
Consider samples of two different gases at the same Kelvin temperature.
Since
temperature is proportional to the kinetic energy of the gas molecules, the
kinetic energy (KE) of the two gas samples is also the same.
In
equation form, we can write: KE1 = KE2
Since KE = (1/2) mv2, (m = mass and v = velocity)
we can write the following equation:
m1v12
= m2v22
Note
that the value of one-half cancels out.
The
equation above can be rearranged algebraically into the following:
The square root of (m1 / m2) = v2
/ v1
You
may wish to assure yourself of the correctness of this rearrangement.
Another
way you may see this written is:
Rate1 of gas 1
Rate2 of gas 2
MM1 molar mass of gas 1
MM2 molar mass of gas 2
This
last equation is the modern way of stating Graham's law.
This is a good way to determine the ratio of the speeds of the gasses.
This will tell you which gas will make it through a small
hole quicker, i.e. the small holes you find in a balloon. For example, which gas will leave the balloon
quicker?
Intermolecular Forces:
Intermolecular forces are the forces of attractions that exist between
molecules in a compound. These cause the
compound to exist in a certain state of matter, solid, liquid or gas, and
affect the melting and boiling points of compounds as well as the solubilities
of one substance in another.
The melting point of a compound is the temperature at which a compound turns
from a solid to a liquid or a liquid to a solid.
The boiling point of a compound is the temperature at which a compound turns
from a liquid to a gas or a gas to a liquid.
This temperature is a true measure of the forces of attractions between
molecules as molecules separate from one another when they turn from a liquid
to a gas.
The stronger the attractions between particles, the more difficult it will
be to separate the particles. When substances melt, the particles are still
close to one another but the forces of attraction that held the particles
rigidly together in the solid state have been sufficiently overcome to allow
the particles to move. When substances
boil, the particles are completely separated from one another and the
attractions between molecules are completely overcome and the particles float
away as a gas. The energy required to
cause substances to melt and to boil, and thus disrupt the forces of
attraction, comes from the environment surrounding the material. If you place a piece of ice in your hand, the
ice will melt more quickly than if it is placed on a cold counter top. The energy required to melt the ice comes
from your hand, your hand gets colder and the ice gets warmer.
Look at the table of melting points and boiling points for the halogens,
shown below.
|
Melting
Points and Boiling Points of Similar Substances with Increasing Formula
Weights |
||||
|
SUBSTANCE |
FW (g/mole) |
mp (oC) |
bp (oC) |
|
|
F2 |
38 |
-220 |
-188 |
|
|
Cl2 |
71 |
-100.98 |
-34.6 |
|
|
Br2 |
160 |
-7.2 |
58.78 |
|
|
I2 |
254 |
113.5 |
184.35 |
|
As the size of the halogens increases, the melting and boiling points
increase. The energy required to move
and separate the molecules from one another increases as the size of the
molecules increases. More massive
molecules have more inertia, which must first be overcome before the molecules
can be separated.
If it takes more energy to separate the molecules, the attractions between
molecules must be greater. The types of
intermolecular forces responsible for the increase in melting points and
boiling points of these non-polar covalent compounds are called dispersion
forces also named
Now look at the table below:
|
Melting
Points and Boiling Points of Substances with Similar Formula Weights |
||||
|
SUBSTANCE |
FW (g/mole) |
mp (oC) |
bp (oC) |
|
|
F2 |
38 |
-220 |
-188 |
|
|
NO |
30 |
-164 |
-152 |
|
|
CH3OH |
32 |
-94 |
65 |
|
|
Ca |
40 |
893 |
1484 |
|
|
NaF |
42 |
993 |
1695 |
|
All the substances in this table have similar formula masses, thus they have
similar dispersion forces. If the only
attractions between substances have to do with size, then they should have
similar melting points and boiling points.
They do not. Let’s look more
closely at the nature of the substance to see if we can relate the structure of
the material with its properties.
Fluorine and Nitrogen
Monoxide:
Fluorine and nitrogen monoxide are similar in size and therefore
have similar dispersion forces. Fluorine is a non-polar covalent
molecule while nitrogen monoxide is a polar covalent molecule; it has an
overall dipole. Since nitrogen monoxide
has the higher melting point and boiling point, it must have the stronger
intermolecular forces. Given the same
size, polar covalent molecules must have stronger forces of attraction than
non-polar covalent molecules. These
forces of attractions are called dipole-dipole
forces.
Nitrogen Monoxide and
Methanol:
Nitrogen monoxide and methanol are similar in size and thus
have similar dispersion forces. Nitrogen
monoxide and methanol are polar covalent molecules and thus have dipole-dipole
forces. Since methanol has the higher
melting point and boiling point, it must have the stronger intermolecular
forces. The difference in these
molecules is the presence of a certain extremely polar bond present in methanol
that is not present in nitrogen monoxide.
This is the hydrogen bond or H-bond, formed between the oxygen and
hydrogen.
Oxygen is more electronegative than hydrogen and pulls the
electrons to the oxygen, away from the hydrogen. The oxygen is now holding a partial negative
charge. The hydrogen is left with very
little electron density, and since hydrogen has no core electrons, a large
partial positive charge develops.
The lack of electrons around the hydrogen leaves the nucleus
relatively bare. As the nucleus is
positively charged it is attracted to the lone pairs of electrons on the
oxygen.
This interaction of a non-bonding pair with a hydrogen
attached to an electronegative element such as oxygen is called a hydrogen
bond. Other elements that may hydrogen
bond include nitrogen and the halogens.
Calcium and Sodium
Fluoride:
A large jump in melting points and boiling points is
observed when we turn from covalent compounds to metals and ionic
compounds. Both metals and ionic
compounds involve the interaction of particles with full charges.
- Metals:
Metal ions interact with the sea of electrons that surround them. This attraction must be very strong as
the melting point and boiling point of calcium is much higher than the
covalent compounds which share a similar formula mass.
- Ionic
Compounds: Substances which bear full charges, anions and cations, are
attracted very strongly as evidenced by the melting point and boiling
point of sodium fluoride. Full charges are much more difficult to separate
then partial charges.
The types of interactions responsible for the extremely high
melting and boiling points of metals and ionic compound are called
electrostatic forces and are the strongest of all the intermolecular forces.
Intermolecular Forces Overview:
- Ionic
Compounds and Metals:
Electrostatic forces - these forces occur between charged
species and are responsible for the extremely high melting and boiling points
of ionic compounds and metals.
- Covalent
Compounds:
Dispersion forces - all molecules have the capability to
form
Dipole-dipole forces - only polar covalent molecules have
the ability to form dipole-dipole attractions between molecules. Polar covalent
molecules act as little magnets; they have positive ends and negative ends
which attract each other.
Hydrogen bonding - these occur between polar covalent
molecules that possess a hydrogen bonded to an extremely electronegative
element, specifically - N, O and the halogens.
Vapor
Pressure/Evaporation:
Vapor
pressure is the pressure of the vapor over a liquid (and some solids, Vick’s
Vapor Rub) at equilibrium.
Now,
what does that definition mean? I'm going to go through some explanation steps
that, hopefully, give you a correct idea of vapor pressure.
1.
Imagine an air tank, like the one below, of several
liters in size. It has rigid walls and is totally empty of all substances.
2.
Now, I inject some liquid into the tank, but I do not
fill the tank with liquid. What will happen to the liquid?
3.
That's right. Some, maybe all, of the liquid will
evaporate into gas, filling the empty space. Now if all the liquid evaporates,
we just have a tank of gas. That's not what we want. So let's suppose that only
some of the liquid evaporated and that there are both the liquid state and the
gas state present in the tank.
The
gas that is above the liquid is called its vapor and it creates a pressure
called vapor pressure.
What
I mean is, suppose you attached a pressure gauge to the tank, would a gas
pressure be recorded? The answer is YES!
However,
here is a key point. The vapor must be in contact with the liquid at all times.
Remove the liquid and you just have a box of gas; you do not have vapor or
vapor pressure.
Let's
emphasize this point!!!! For vapor pressure to exist, the vapor (gas phase)
MUST be in physical contact with the liquid (or solid) it came from. You CAN'T
have vapor pressure without two phases being present and in contact!!!!!!
How
is vapor pressure created? Another way to put it - how do molecules of the
liquid become molecules of gas?
Each
molecule in the liquid has energy, but not the same amount. The energy is
distributed according to the Maxwell-Boltzmann distribution. Even if you don't
know what that is, the point is that some molecules have a fairly large amount
of energy compared to the average. Those are the ones we are interested in.
We
are ESPECIALLY interested if one of these high energy molecules happens to be
sitting right at the surface of the water. Now, all the molecules are in motion
because of their energy, but none have sufficient energy to break the mutual
attractive force molecules have for each other. Suppose that our surface
molecule was moving up away from the surface AND had enough energy to break
away from the attractive forces of the molecules around it.
Where
would that molecule go? It would continue to move away from the liquid surface
AND IT BECOMES A MOLECULE OF GAS. This is great because we are now making some
vapor pressure. It happens to another molecule and another and another.
But
wait! The vapor pressure stops going up and winds up staying at some fixed
value. What's going on? Here's the answer, I hope you can handle it!
As
more and more molecules LEAVE the surface, what do some start to do? That's
right, some RETURN to the surface and resume their former life as a liquid
molecule. Soon the number of molecules in the vapor phase is constant because
the rate of returning equals the rate of leaving and so the pressure stays
constant.
This
image is my attempt to summarize this process. I'll put it here without
comment:
Factors that will affect vapor pressure:
1. Temperature
of the substance
2. The
specific substance you are studying
1. If
you ®
the temperature you ↑ the kinetic energy of the gas particles ® ↑
speed at which these particles are moving, then the particle has a better
chance of breaking free of the liquid.
2. Different
substances have different intensities of self-attraction. The name for these
attraction forces are intermolecular forces.
Heating Diagram:
This diagram depicts the curve of temperature verses time of
a given substance. Starting with a solid
that is melted into a liquid that is boiled to a vapor. As heat is added this is the shape of the
curve generated. Flat lines are due to
intermolecular forces being broken, solid ice turning to liquid water, liquid
water being turned into steam. Once
boiling begins the temperature remains fixed at the boiling point until all of
the liquid is converted to gas. Thus, at
the boiling point liquid and gas coexist in equilibrium. Similarly, solid and liquid coexist in
equilibrium at the melting or boiling point.
The angled lines are where the temperature is rising in a
given phase. So, flat lines indicate a
phase change is occurring and angled lines indicate no phase change.
The first angled line is the rising of temperature of a
solid. Once the melting temperature has
been reached, the line becomes flat and a phase change begins. The energy needed for this to occur is called
the Heat of Fusion and is defined as that amount of heat needed to melt a
specific mass of a specific substance.
If this curve were a cooling curve the line would be called the Heat of
Solidification, defined as that amount of heat given off a specific mass of a
specific substance when it freezes. Yes,
freezing is exothermic. It usually gets
warmer right when it begins to snow.
The second angled line is the rising of temperature of a
liquid. Once the boiling or vaporization
has been reached, the line again becomes flat, indicating a phase change is
occurring. The energy needed for this to
occur, the Heat of Vaporization, is that amount of heat needed to vaporize a
specific mass of a specific substance.
If this curve were a cooling curve the line would be called the Heat of
Condensation, defined as that amount of heat given off a specific mass of a
specific substance when it condenses.
Yes, condensing is exothermic. It
usually gets warmer right when it begins to rain.
A Detailed Heating
Curve for Water:
The following equation is used to calculate the amount of
heat needed during a phase change of specific substance. The phase change can be melting or freezing
or it can be vaporization or condensation.
The amount of heat needed for melting is the same as that given off in
freezing. Likewise, the amount of heat
needed for vaporization is the same as that given off in condensation.
The equation will take the form of one of the following:
|
Q = m • Hvap |
heat = mass · heat of vaporization |
|
Q = m • Hcond |
heat = mass · heat of condensation |
|
Q = m • Hfus |
heat = mass · heat of fusion |
|
Q = m • Hsol |
heat = mass · heat of solidification |
Would it take more heat to melt 10 grams of solid water, ice
or vaporize 10 grams of liquid water?
Look at the lengths of the flat lines on the above plot.
It takes more heat to boil something than it does to melt
it. Think about water on the stovetop
and an ice cube on the counter. Plus,
look at the Heat of Vaporization & Heat of Fusion; the Heat of Fusion is 80
cal/gram and the Heat of Vaporization is 540 cal/g.
Example:
How much heat would it take to melt 25 grams of solid water?
Q = 25 grams · 80 cal/gram = 2000 cal
Example:
How much heat would it take to vaporize 25 grams of liquid
water?
Q = 25 grams · 540 cal/gram = 13500 cal
Longer Problem: Start from ice go to steam.
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