If you like the ChemWiki, please "like" us on facebook, "share" us on Google+, or "tweet" about the project.

GeoWiki.png
ChemWiki: The Dynamic Chemistry E-textbook > Wikitexts > ChemTutor > Chemical Reactions

Chemical Reactions

CHEMTUTOR

A chemical reaction is material changing from a beginning mass to a resulting substance. The hallmark of a chemical reaction is that new material or materials are made, along with the disappearance of the mass that changed to make the new. This does not mean that new elements have been made. In order to make new elements, the nuclear contents must change. There are magnitudes of difference in the amounts of energy in ordinary chemical reactions compared to nuclear reactions. The energy of rearrangement of the nuclei of atoms to change to new elements is enormous compared to the smaller energies of chemical changes. The alchemists, in their efforts to change less expensive metals to gold, did not have the fundamental understanding of what they were attempting to do to appreciate the difference.

Introduction

A chemical equation is a way to describe what goes on in a chemical reaction, the actual change in a material. Chemical equations are written with the symbols of materials to include elements, ionic or covalent compounds, aqueous solutions, ions, or particles. There is an arrow pointing to the right that indicates the action of the reaction. The materials to the left of the arrow are the reactants, or materials that are going to react. The materials to the right of the arrow are the products, or materials that have been produced by the reaction. The Law of Conservation of Mass states that in a chemical reaction no mass is lost or gained. The Law of Conservation of Mass applies to individual types of atom. One could say that for any element, there is no loss or gain of that element in a chemical reaction. There are such things as reversible reactions, reactions in which the products reassemble to become the original products. Reversible reactions are symbolized in chemical equations by a double-headed arrow, but the standard remains to call the materials on the left the reactants and the materials on the right the products.

EXAMPLES OF CHEMICAL CHANGES

Chemical reactions, also called chemical changes, are not limited to happening in a chemistry lab. Here are some examples of chemical reactions with the corresponding chemical equations:

A silver spoon tarnishes. The silver reacts with sulfur in the air to make silver sulfide, the black material we call tarnish.

2 Ag + S Ag2S

An iron bar rusts. The iron reacts with oxygen in the air to make rust.
4 Fe + 3 O2 2 Fe2O3

Methane burns. Methane combines with oxygen in the air to make carbon dioxide and water vapor.
CH4 + 2 O2 CO2 + 2 H2O

An antacid (calcium hydroxide) neutralizes stomach acid (hydrochloric acid).
Ca(OH)2 + 2 HCl CaCl2 + 2 H2O

Glucose (simple sugar) ferments to ethyl alcohol and carbon dioxide. The sugar in grapes or from grain ferments with yeast to make the alcohol and carbon dioxide. The carbon dioxide is the gas that bubbles out of beer or champaign.
C6H12O6 (glucose) 2 C2H5OH (ethyl alcohol) + 2 CO2

Alcohol plus oxygen becomes vinegar and a molecule of water. As in the fermentation of glucose, this is a more complex reaction than it appears here because it is a biochemical reaction.
C2H5OH + O2 HC2H3O2 + H2O

As a general rule, biochemical happenings make poor examples of basic chemical reactions for a first chemistry course because the actual reaction is carried on within living things and under enzyme control.

EXAMPLES OF PHYSICAL CHANGES

Here are some examples of changes that are NOT chemical reactions. In each case, the original material or materials may be reclaimed by physical processes.

  • Water boils out of a kettle or condenses on a cold glass.
  • An aluminum pot is put on a burner and gets hot.
  • Dry ice goes from a solid to a gaseous form of carbon dioxide (sublimation).
  • Gold melts or solidifies.
  • Sand is mixed in with salt.
  • A piece of chalk is ground to dust.
  • Glass breaks.
  • An iron rod gets magnetized.
  • A lump of sugar dissolves in water.

GRAY AREAS BETWEEN CHEMICAL AND PHYSICAL CHANGES

Even more telling are the gray areas. Are these changes chemical or physical? Why? (Punch the * discussion link after each one for a discussion on why that example is a gray area.)

  • Table salt dissolves in water. *
  • A hydrated crystal, such as blue vitriol, is dried with heat. *
  • Lightning makes ozone (O3) from oxygen (O2). The ozone then reverts to oxygen. *
  • Carbon dioxide dissolves in water. *
  • Ammonia gas dissolves in water. *
  • With pressure and heat graphite becomes diamond. *
  • An egg is cooked.*
  • A tree dies. *

CHEMICAL EQUATIONS OF CHEMICAL REACTIONS

In order to write the chemical equations, you must first know the formulas for the materials involved. The formulas must be written on the proper side of the arrow - - reactants ("before") on the left and products ("after") on the right. The order in which the reactants and products are written does not matter, just as long as every material is on the proper side. Once the materials involved in the reaction are written correctly, DON’T TOUCH THEM. If you need to draw a box around each participant in the reaction to keep your grubby paws off the materials, do it.

Very often you will see the descriptions of the materials in the reaction in parentheses after the material. A gas is shown by (g). A solid material is shown by (s). A liquid is shown by (l). A material dissolved in water (an aqueous solution) is shown by (aq). An upwards pointing arrow () indicates a gas being produced, and a downwards pointing arrow indicates a solid precipitate being produced.

BALANCING EQUATIONS

Now comes the fun part, balancing the reaction. The Law of Conservation of Mass states that in a chemical reaction there is no loss of mass. Each type of element will have the same amount before the reaction and after the reaction, or as reactant and product. But you can’t change the materials that participate in the reaction, so you must write an integer coefficient in front of (to the left of) each material in the reaction to make sure every type of atom has the same number on each side of the reaction. Let’s start with the reaction of the Haber process:

Nitrogen gas plus hydrogen gas under pressure and at high temperature turn into ammonia. First write the materials correctly. Nitrogen and hydrogen are diatomic gases. Ammonia is a binary covalent memory item. The nitrogen and hydrogen are the reactants, and the ammonia is the product. Leave room for the coefficients in front of the materials.

_ N2(g) + _ H2(g) _ NH3(g)

You can begin with either the nitrogen or the hydrogen. There are two nitrogen atoms on the left and only one on the right. In order to balance the nitrogen atoms, place a ‘2’ in front of the ammonia.

_ N2 + _ H2 2 NH3

There are two hydrogens on the left and six on the right. We balance the hydrogens by placing a ‘3’ in front of the hydrogen gas.

 _ N2 + 3 H2 2 NH3

Now go back and check to make sure everything is balanced. There are two nitrogen and six hydrogens on both sides of the reaction. It is balanced. There is no coefficient shown in front of the nitrogen. There is no need to write ones as coefficients. The reaction equation is:

N2 + 3 H2 2 NH3

 

BALANCING IONIC EQUATIONS WITH POLYATOMIC IONS

Silver nitrate and calcium chloride solutions combined produce a precipitate of silver chloride and leave a solution of calcium nitrate. This time we have ionic compounds in the reaction. Until you are sure of the compounds, you might want to write the ionic materials as the ions, as demonstrated here.

 _ Ag+(NO3)-(aq) + _ Ca2+ Cl(aq)  _ Ag+Cl- +  _ Ca2+ (NO3)-2 (aq)

Notice that from one side to the other there is no change in the nitrate ion. In this case you can count the nitrate ion as a whole rather than splitting it up into nitrogen and oxygen. Your thoughts might go this way: How many silvers on the right? One. How many silvers on the left? One. They are the same. How many nitrates on the left? One. How many nitrates on the left? One. How many nitrates on the right? Two. We need to put a coefficient of two in front of the silver nitrate.

2 AgNO3 + _ CaCl2 _ AgCl + _ Ca (NO3)2

This changes the balance of silvers, so we have to put a two in front of the silver chloride.

2 AgNO3 + _ CaCl2 2 AgCl + _ Ca (NO3)2

Now let’s check again. Two silvers on each side. Two nitrates on each side. One calcium on each side and two chlorides on both sides. The balanced reaction is:

2 AgNO3 + CaCl2 2 AgCl + Ca (NO3)2

 

BALANCING EQUATIONS WITH WATER AS A PRODUCT

Sulfuric acid and potassium hydroxide neutralize each other to make water and potassium sulfate. Here is an acid-base neutralization. These make a salt (Not necessarily common table salt.) and water. (Notice the ionic materials are written with the ion notation so they are sure to be right. Water and sulfuric acid are memory items and should not need to be written in ion form, though you could write the ions to make sure they are right.)

_ H2SO4(aq) + _ K+(OH)-(aq) _ K+2(SO4)2+(aq)+ _ H2O(l)

The water is made from the hydrogen ion of the acid and the hydroxide ion of the base. Notice that it is a lot easier to understand how to balance the reaction if you write the water as if it were an ionic compound.

_ H2(SO4)+ _ K+(OH)- _ K+2(SO4)2+ + _ H+(OH)-

This is easier now because the hydrogen in the acid does not get confused with the hydrogen in the hydroxide of the base. Two hydrogens on each side. One sulfate on both sides. Two potassiums and two hydroxides on each side.

H2(SO4)+ 2 K(OH) K2(SO4) + 2 H(OH)

The reaction is now balanced.

Next is an example of having to go around the equation again. Phosphoric acid and calcium hydroxide react to make water and calcium phosphate.

_ H3PO4(aq) + _ Ca2+(OH)-2 _ H+(OH)-(l)+ _ Ca2+3(PO4)3-2

First put a three on the water to balance the hydrogen in the phosphoric acid.

_ H3PO4 + _ Ca(OH)2 3 H(OH)+ _ Ca3(PO4)2

Now put a two on the phosphoric acid to balance the phosphate from the calcium phosphate.

2 H3PO4 + _ Ca(OH)2 3 H(OH)+ Ca3(PO4)2

We have changed the amount of hydrogen ion, so we will have to change it on the right again.

2 H3PO4 + _ Ca(OH)2 6 H(OH)+ Ca3(PO4)2

 And change the coefficient in front of the Ca(OH)2 to match the calcium on the right side.

2 H3PO4 + 3 Ca(OH)2 6 H(OH)+ Ca3(PO4)2

Only now does the rest of the equation balance with six hydrogens, six hydroxides, two phosphates, and three calciums on each side.

BALANCING BURNING REACTIONS

Most burning reactions are the oxidation of a fuel material with oxygen gas. Complete burning produces carbon dioxide from all the carbon in the fuel, water from the hydrogen in the fuel, and sulfur dioxide from any sulfur in the fuel. Methane gas (CH4) burns in air (using the oxygen) to make carbon dioxide and water (water vapor).

_ CH4(g) + _ O2(g) _ H2O(g) + _ CO2(g)

Easy. Put a two in front of the water to take care of all the hydrogens and a two in front of the oxygen. Anything you have to gather (any atom that comes from two or more sources in the reactants or gets distributed to two or more products) should be considered last.

CH4 + _ O2 2 H2O + CO2

CH4 + 2 O2 2 H2O + CO2

What if the oxygen does not come out right? Let’s consider the equation for the burning of butane, C4H10.

_ C4H10 + _ O2 _ CO2 + _ H2O

Insert the coefficients for carbon dioxide and water.

_ C4H10 + _ O2 4 CO2 + 5 H2O

We now have two oxygens on the left and thirteen oxygens on the right. The real problem is that we must write the oxygen as a diatomic gas. The chemical equation is not any different from an algebraic equation in that you can multiply both sides by the same thing and not change the equation. Multiply both sides by two to get the following.

2 C4H10 + _ O2 8 CO2 + 10 H2O

Now the oxygens are easy to balance. There are twenty-six oxygens on the right, so the coefficient for the oxygen gas on the left must be thirteen.

2 C4H10 + 13 O2 8 CO2 + 10 H2O

Now it is correctly balanced. What if you finally balanced the same equation with:

4 C4H10 + 26 O2 16 CO2 + 20 H2O

or

6 C4H10 + 39 O2 24 CO2 + 30 H2O

Either equation is balanced, but not to the lowest integer. Algebraically you can divide these equations by two or three to get the lowest integer coefficients in front of all of the materials in the equation.

Now that we are complete pyromaniacs, let’s try burning isopropyl alcohol, C3H7OH.

  _ C3H7OH(l) + _ O2(g) _ CO2(g) + _ H2O(g)

First take care of the carbon and hydrogen.

  _ C3H7OH + _ O2 3 CO2 + 4 H2O

But again we come up with an oxygen problem. The same process works here. Multiply the whole equation (except oxygen) by two.

2 C3H7OH + _ O2 6 CO2 + 8 H2O

Now the number nine fits in the oxygen coefficient. (Do you understand why?) The equation is balanced with six carbons, sixteen hydrogens, and twenty oxygens on each side.

2 C3H7OH + 9 O2 6 CO2 + 8 H2O

 

BALANCING BY OVERVIEW

Some equations are just mean, nasty, and rotten and defy your efforts to balance them. For some of these equations, a process I call overview is useful. Take as an example the smelting of magnetite, an iron ore.

_ Fe3O4(s) + _ CO(g) _ CO2(g) + _ Fe(l)

Unless you just happen to hit it right, you are unlikely to balance this equation with the trial method. (Go ahead and try it before you read further.)

An overview of the reaction shows that for each oxygen that the magnetite has, one carbon monoxide must turn to carbon dioxide. The carbon monoxide and carbon dioxide must have a coefficient that is four times the coefficient of the magnetite. Leave the magnetite coefficient and put a '4' in front of the carbon monoxide and carbon dioxide.

  _ Fe3O4 + 4 CO 4 CO2 + _ Fe

The carbon and oxygen is balanced, leaving only the iron to be balanced.

Fe3O4 + 4 CO 4 CO2 + 3 Fe

BALANCING REDOX EQUATIONS

The balancing of equations involving a reduction and oxidation will be considered in the chapter on redox (reduction and oxidation reactions).

TYPES OF COMMON IONIC REACTION

SYNTHESIS REACTIONS

ALSO CALLED COMBINATION, CONSTRUCTION, OR COMPOSITION REACTIONS

The title of this section contains four names for the same type of reaction. Your text may use any of these. Chemtutor prefers the first of the names and will use “synthesis” where your text may use one of the other words. The hallmark of a synthesis reaction is a single product. A synthesis reaction might be symbolized by:

A + B AB

Two materials, elements or compounds, come together to make a single product. Some examples of synthesis reactions are: Hydrogen gas and oxygen gas burn to produce water.

2 H2(g) + O2(g) 2 H2O(g)and

sulfur trioxide reacts with water to make sulfuric acid.

H2O(g) + SO3(g) H2SO4(g)

What would you see in a ‘test tube’ if you were witness to a synthesis reaction? You would see two different materials combine. A single new material appears.

 

DECOMPOSITION REACTIONS

ALSO CALLED DESYNTHESIS, DECOMBINATION, OR DECONSTRUCTION

Of the names for this type of reaction, Chemtutor again prefers the first. Mozart composed until age 35. After that, he decomposed. Yes, a decomposition is a coming apart. A single reactant comes apart into two or more products, symbolized by:

XZ X + Z

Some examples of decomposition reactions are: potassium chlorate when heated comes apart into oxygen gas and potassium chloride

2 KClO3(s) 2 KCl(s) + 3 O2(g)

and heating sodium bicarbonate releases water and carbon dioxide and sodium carbonate.

6 NaHCO3(s) 3 Na2CO3(s) + 3 H2O(g) + 3 CO2(g)

In a “test tube” you would see a single material coming apart into more than one new material.

 

SINGLE REPLACEMENT REACTIONS

ALSO CALLED SINGLE DISPLACEMENT, SINGLE SUBSTITUTION, OR ACTIVITY REPLACEMENT

Here is an example of a single replacement reaction: silver nitrate solution has a piece of copper placed into it. The solution begins to turn blue and the copper seems to disappear. Instead, a silvery-white material appears.

2 AgNO3(aq) + Cu(s) Cu(NO3)2(aq) + 2 Ag

A solution of an ionic compound has available an element. The element replaces one of the ions in the solution and a new element appears from the ion in solution. This type of reaction is called a replacement because a free element replaces one of the ions in a compound. There are two types of single replacement reactions, anionic and cationic. A cationic single replacement is what happened in the case of the silver being replaced by the copper in the above reaction because both the silver and the copper are only likely to make cations. An anionic single replacement is also possible. Into a potassium iodide solution chlorine gas is bubbled. The chlorine is used up and the solution turns purple-brown from the iodine. This is an example of an anionic single replacement reaction.

2 KI(aq) + Cl2(g) 2 KCl(aq) + I2(g)

Could you start with copper II nitrate and silver metal and get silver nitrate and copper metal, or could you start with potassium chloride and iodine and get potassium iodide and chlorine? No. The reactions don’t work that way. You can arrange cations or anions in a list of which ion will replace the next. This type of list is an activity series. The activity series of cation elements (metals) shows that gold is the least active metal. That should not be surprising, because gold does not tarnish. If we were to consider the Group 1 elements only on the activity list, lithium is the least active and francium is the most active, with each larger element being more active than the smaller one above it on the Periodic Chart. On the other side of the chart we could consider an activity series for anions. Taking just the halogens, the smallest halogen, fluorine is the most active. As the size of the halogen increases down the chart, the activity decreases. If an element is more active than the element of the same sign in an ionic solution, the more active element will replace it.

DOUBLE REPLACEMENT REACTIONS

ALSO CALLED DOUBLE DISPLACEMENT OR METATHESIS

Some texts refer to single and double replacement reactions as solution reactions or ion reactions. That is understandable, considering these are mostly done in solutions in which the major materials we would be considering are in ion form. Chemtutor thinks that there is some good reason to call double replacement reactions de-ionizing reactions because a pair of ions are taken from the solution in these reactions. Let’s take an example.

AgNO3(aq) + KCl(aq) AgCl(s) + KNO3(aq)

Above is the way the reaction might be published in a book, but the equation does not tell the whole story. Dissolved silver nitrate becomes a solution of silver ions and nitrate ions. Potassium chloride ionizes the same way. When the two solutions are added together, the silver ions and chloride ions find each other and become a solid precipitate. (They ‘rain’ or drop out of the solution, this time as a solid.) Since silver chloride is insoluble in water, the ions take each other out of the solution.

Ag+ + (NO3)- + K+ +Cl- AgCl + K+ + (NO3)-

Here is another way to take the ions out of solution. Hydrochloric acid and sodium hydroxide (acid and base) neutralize each other to make water and a salt. Again the solution of hydrochloric acid is a solution of hydrogen (hydronium ions in the acid and base section) and chloride ions. The other solution to add to it, sodium hydroxide, has sodium ions and hydroxide ions. The hydrogen and hydroxide ions take each other out of the solution by making a covalent compound (water).

HCl(aq) + NaOH(aq) HOH(l) + NaCl(aq)   or

H+ + Cl- + Na+ + (OH)- HOH + Na+ + Cl-

One more way for the ions to be taken out of the water is for some of the ions to escape as a gas.

CaCO3(s) + 2 HCl(aq) CaCl2(aq) + H2O(l) + CO2(g)

Ca2+ + (CO3)2- + 2 H+ + 2 Cl- Ca2+ + 2 Cl- + H2O + CO2

The carbonate and hydrogen ions became water and carbon dioxide. The carbon dioxide is lost as a gas to the ionic solution, so the equation can not go back.

One way to consider double replacement reactions is as follows: Two solutions of ionic compounds are really just sets of dissolved ions, each solution with a positive and a negative ion material. The two are added together, forming a mixture of four ions. If two of the ions can form (1) an insoluble material, (2) a covalent material such as water, or (2) a gas that can escape, it qualifies as a reaction. Not all of the ions are really involved in the reaction. Those ions that remain in solution after the reaction has completed are called spectator ions, that is, they are not involved in the reaction. There is some question as to whether they can see the action of the other ions, but that is what they are called.

 

Problems

WRITE THE FORMULA FOR EACH MATERIAL CORRECTLY AND THEN BALANCE THE EQUATION. THERE ARE SOME REACTIONS THAT REQUIRE COMPLETION. FOR EACH REACTION TELL WHAT TYPE OF REACTION IT IS.

  1. sulfur trioxide and water combine to make sulfuric acid.
  2. lead II nitrate and sodium iodide react to make lead iodide and sodium nitrate.
  3. calcium fluoride and sulfuric acid make calcium sulfate and hydrogen fluoride (Hydrofluoric acid)
  4. calcium carbonate will come apart when you heat it to leave calcium oxide and carbon dioxide.
  5. ammonia gas when it is pressed into water will make ammonium hydroxide.
  6. sodium hydroxide neutralizes carbonic acid
  7. zinc sulfide and oxygen become zinc oxide and sulfur.
  8. lithium oxide and water make lithium hydroxide
  9. aluminum hydroxide and sulfuric acid neutralize to make water and aluminum sulfate.
  10. sulfur burns in oxygen to make sulfur dioxide.
  11. barium hydroxide and sulfuric acid make water and barium sulfate.
  12. aluminum sulfate and calcium hydroxide become aluminum hydroxide and calcium sulfate.
  13. copper metal and silver nitrate react to form silver metal and copper II nitrate.
  14. sodium metal and chlorine react to make sodium chloride.
  15. calcium phosphate and sulfuric acid make calcium sulfate and phosphoric acid.
  16. phosphoric acid plus sodium hydroxide.
  17. propane burns (with oxygen)
  18. zinc and copper II sulfate yield zinc sulfate and copper metal
  19. sulfuric acid reacts with zinc
  20. acetic acid ionizes.
  21. steam methane to get hydrogen and carbon dioxide
  22. calcium oxide and aluminum make aluminum oxide and calcium
  23. chlorine gas and sodium bromide yield sodium chloride and bromine

ANSWERS

1. SO3 + H2O H2SO4
SYNTHESIS

2. Pb(NO3)2 + 2NaI PbI2 + 2NaNO3
DOUBLE REPLACEMENT (lead II iodide precipitates)

3. CaF2 + H2SO4 CaSO4 + 2 HF
DOUBLE REPLACEMENT (calcium sulfate precipitates)

4. CaCO3 CaO + CO2
DECOMPOSITION

5. NH3 + H2O NH4OH
SYNTHESIS

6. 2 NaOH + H2CO3 Na2CO3 + 2 H2O
DOUBLE REPLACEMENT OR ACID-BASE NEUTRALIZATION

7. 2 ZnS + O2 2 ZnO + 2 S
ANIONIC SINGLE REPLACEMENT

8. Li2O + H2O 2 LiOH
SYNTHESIS

9. 2 Al(OH)3 + 3 H2SO4 6 H2O + Al2(SO4)3
DOUBLE REPLACEMENT OR ACID-BASE NEUTRALIZATION

10. S + O2 SO2
SYNTHESIS

11. Ba(OH)2 + H2SO4 2 H2O + BaSO4
DOUBLE REPLACEMENT OR ACID-BASE NEUTRALIZATION

12. Al2(SO4)3 + 3 Ca(OH)2 2 Al(OH)3 + 3 CaSO4
DOUBLE REPLACEMENT
(BOTH calcium sulfate and aluminum hydroxide are precipitates.)

13. Cu + 2AgNO3 2Ag + Cu(NO3)2
CATIONIC SINGLE REPLACEMENT

14. 2Na + Cl2 2 NaCl
SYNTHESIS

15. Ca3(PO4)2 + 3 H2SO4 3 CaSO4 + 2 H3PO4
DOUBLE REPLACEMENT

16. H3(PO4) + 3 NaOH Na3PO4 + 3 H2O
DOUBLE REPLACEMENT (NEUTRALIZATION)

17. C3H8 + 5 O2 4 H2O + 3 CO2
BURNING OF A HYDROCARBON

18. Zn + CuSO4 ZnSO4 + Cu
CATIONIC SINGLE REPLACEMENT

19. H2SO4 + Zn ZnSO4 + H2
CATIONIC SINGLE REPLACEMENT

20. HC2H3O2 H+ + (C2H3O2)-
IONIZATION (NOTICE THAT IT IS REVERSIBLE)

21. 2 H2O + CH4 4 H2 + CO2

22. 3 CaO + 2 Al Al2O3 + 3 Ca
CATIONIC SINGLE REPLACEMENT

23. Cl2 + 2 NaBr 2 NaCl + Br2
ANIONIC SINGLE REPLACEMENT

Contributors

 

Copyright © 1997-2009  Chemtutor, LLC.  All rights reserved.

Publication of any part is prohibited without prior written consent, except for instructor use publishing for instructor's own classroom students. All hard copy materials distributed under this exception must have on every page distributed reference to http://www.chemtutor.com as source. Under the same exception granted to classroom teachers, full recognition of Chemtutor must be given when all or any part is included in any other electronic representation, such as a web site, whether by direct inclusion or by hyperlink.


 

You must to post a comment.
Last Modified
10:06, 2 Oct 2013

Page Rating

Was this article helpful?

Tags

Creative Commons License UC Davis ChemWiki is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 United States License. Permissions beyond the scope of this license may be available at copyright@ucdavis.edu. Questions and concerns can be directed toward Prof. Delmar Larsen (dlarsen@ucdavis.edu), Founder and Director. Terms of Use

By STEMWiki Hyperlibrary