Dilution Problems
It is customary in commercial laboratories to have both "working" solutions and "stock" solutions of their most commonly used reagents.
For example, They might maintain a working solution of HCl which is about 0.5 M and a stock solution of say about 20 M HCl.
When you need some more working solution you can prepare it from the stock solution by diluting it.
If we take a volume, V, of a stock solution with molarity, M, it contains a number of mol = MV.
When we add water to this volume, V, the number of moles does not change, but the concentration does change.
If we add enough water to bring the final volume to V', then the new molarity will be M', with M'V' = the same number of moles of solute. Thus
or, simply,
Let's calculate how much stock solution of 20.0 M HCl solution it would take to make 10.0 L of 0.500 M HCl..
One more example of a dilution problem:
(Material for Exam 1 stops here.)
Start Chapter 6
Energy - the Energy of Chemistry
Our concept of energy comes from physics. In elementary physics we learn that energy is the capacity to do work.
Then they have to tell us what work is. Work has been performed whenever some object has moved some distance against a force. That is,
work = force ´ distance.
(If you have had calculus you would write dw = F dx and then you would integrate this from the initial position, say x1, to the final position, x2However, work can also produce energy of various kinds.where the F(x) takes account of the fact that the force may depend on how far you have moved your object. If you haven't had calculus, don't worry abut this.),
If we push an automobile (apply a force to it) to get it rolling we are giving the automobile energy of motion - called kinetic energy.So right away we see three forms of energy (four if we include work).If we push the car up a hill (against the force of gravity) we give the car energy of position - called potential energy.
If we let the car roll back down the hill the potential energy is converted into kinetic energy.
If we stop the car with the brakes the kinetic energy is converted into heat energy. The brakes get hot and the heat is dissipated into the surrounding air.
Potential energy = energy of positionThe various forms of energy can be converted into each other.(The increase in potential energy from raising an object of mass, m, by a height, h, in a gravitational field with acceleration due to gravity, g, is given by,Kinetic energy = energy of motionpotential energy = mgh.)(The kinetic energy of an object of mass, m, moving with velocity, v, is given by.Heat energy = ??kinetic energy = mv2/2.)
(Heat energy is mainly the kinetic and potential energies of the random motions of the atoms in the object.)Chemical Energy = ??
(Chemical energy is essentially stored energy, or potential energy. For example, you can release a lot of chemical energy as heat by burning propane in air.)
Heat can be converted into work (and kinetic energy and potential energy and work), but only with restrictions.
The First Law of Thermodynamics
The subject of thermodynamics begins with what we call "The First Law of Thermodynamics."
The first law of thermodynamics states that energy is conserved. That is, energy can be converted back and forth among its various forms, but it can't be created or destroyed.
A common way to state the first law is to say that it is impossible to create a perpetual motion machine of the first kind. A perpetual motion machine of the first kind is a machine that creates energy out of nothing. It does work, but it never uses up any fuel or other resource.
The first law is really a statement of repeated observation. No one has ever observed the creation of energy out of nothing and no one has ever observed the disappearance of energy into nothing.
(Where does nuclear energy fit into this?)
Energy Units
The SI unit of energy is the Joule. One Joule (1 J) is the kinetic energy of 2 kg moving at a speed of 1 m/s (exactly).
You may have heard of the energy (or heat) unit, the calorie. The calorie was originally defined as the heat energy required to raise the temperature of 1.00 g of water by 1.00oC (near 15oC.) The calorie is now defined as:
1 cal º 4.184 J (exactly).
This calorie is not the Calorie that we see in dietetics.
The Calorie used in describing the energy content of foods is the "large
Calorie," which is really a kcal and it is spelled with a capital "C."
Specific Heat and Heat Capacity
It is a common observation that most times when we add heat to a sample of material the temperature increases.
(There are some important exceptions to this observation.)
The amount of the temperature increase depends on four things. It depends on:
The amount of heat added,The amount of material in the sample,
The identity of the material in the sample, and
The initial temperature of the sample.
Let's do an experiment.
Take a sample which contains m grams of our substance and add an amount of heat, q J. Say we observe an increase in temperature DT. (We will always use the symbol, D , the capital Greek delta, to indicate "change in." That is, DT = Tfinal - Tinitial.)
Define the specific heat (or the specific heat capacity) of a sample as.
(In more advanced treatments we usually use the "molar heat capacity." The molar heat capacity is defined in the same way. An amount of heat, q, is added to n moles of our substance and the temperature is observed to increase by an amount, DT. The molar heat capacity, which we will call.
,
is defined as,
Note that the specific heat and the molar heat capacity are related through the formula weight,.
Suppose we take 20.0 g of liquid water, add 554 J of heat and observe that the temperature increases by 6.62 K. (Recall that Kelvin degrees are the same size as Celsius degrees.) What is the specific heat?.)
There is a table of specific heats of several substances on p 247 in your text. Specific heat has units J/g K.
It is not necessary to memorize specific heats. However, there is one substance whose specific heat you should know. Liquid water has a specific heat of 1.00 cal/g K. Since we know that the definition of the calorie is 1 cal = 4.184 J, that tells us that the specific heat of liquid water in SI units is 4.184 J/g K.
Specific heats are useful in many problems in science and engineering.
Suppose we have an iron crucible which weighs 1530 g. How much heat will it take to raise the temperature of this iron crucible from 25.0 oC to 100. oC? From the table we find that the specific heat of iron is 0.451 J/g K.
Rearrange
into
.
Sign conventions in Thermodynamics:
It is obvious that if DT
> 0 then the temperature increased and if D
T < 0 then the temperature decreased. We will also regard the heat,
q,
as a "signed quantity." That is if q > 0 we say that the object
gained heat - heat flowed into our sample. Likewise if q < 0
we say that our object lost heat, heat flowed out of our sample. Clearly
whenever DT > 0 then q > 0, and
vice versa.
Changes of State
If you have a glass of ice water (the glass contains both
ice and liquid water) and you add some heat to the ice water the temperature
does not change. The heat melts some the ice rather than changing the temperature
of the system.
The conversion of ice to water (at 0 oC) is
called a "phase change."
Likewise, if you added some heat to a beaker of water
at 100 oC (the normal boiling point of water) the temperature
of the water would not increase. You would just vaporize some of the water.
The conversion of liquid water to water vapor is another phase change.
There is no increase or decrease in temperature when heat
is added or withdrawn at a phase change.
