• Syllabus
• Assignment

9-20-08
Please see Assignment page for the list of proofs to know for Exam 1. I will make copies of the proofs and drop them off tomorrow morning as well. If you can't get on campus to pick up a copy, then email me and I will send it to you as an attachment. I won't be able to post it online.

9-20-08
I can't come in today. I will be in my office tomorrow (Sunday 9-21) from 10:00 to 10:30am. Sorry if I've caused you any inconvenience.

9-18-08
I will have your homeworks in my office on Saturday (9-20) from 3:00pm to 3:30pm, if you want to come by and pick up your homework. If that time does not work for you and you want me to leave it outside my office door, then send me an email (maula.allen@marin.edu) and let me know. I should be able to get the proofs posted by Saturday evening.

9-17-08
I'm pasting the Chemical Balance problem here. If you're getting weird symbols and just can't read it, then send me an email and I will attach it to a reply.

Let me know if you have any questions about constructing the equations. Have fun!

Application:  Chemical Balance Equations

Chemical reactions can be described by equations.  The expressions on the left side are called the reactants, and those on the right side are the products, which are produced from the reaction of chemicals on the left.  Unlike mathematical equations, the two sides are separated by an arrow, which indicates that the reactants form the products, or which indicates a reversible equation; that is, once the products are formed, they begin to form reactants.  A chemical equation is balanced, provided that the number of atoms of each type on the left is the same as the number of atoms of the corresponding type on the right. 

The following is an example of how to construct a homogeneous system of equations whose solution provides appropriate values to balance the atoms in the reactants with those in the products.

Ex.
Sodium hydroxide (NaOH) reacts with sulfuric acid (H2SO4) to form sodium sulfate (Na2SO4) and water (H2O).  The chemical equation is

                                    NaOH + H2SO4             Na2SO4 + H2O.

To balance this equation, we insert unknowns, multiplying the chemicals on the left and right to get an equation of the form

                                    x NaOH + yH2SO4             zNa2SO4 + wH2O.

Next we compare the number of sodium (Na), oxygen (O), hydrogen (H), and sulfur (S) atoms on the left side with the numbers on the right.  We obtain four linear equations:

                                    Na:  x = 2z
                                      O:  x  + 4y = 4z + w
                                      H:  x + 2y  =  2w
                                      S:  y = z

Observe that we made use of the subscripts because they count the number of atoms of a particular element.  Rewriting these equations in standard form, we see that we have a homogeneous linear system in four unknowns.

Writing the system in matrix form, then reducing to row echelon from, we have the solution, x = w, y = ½ w, z = ½ w.  Since w can be chosen arbitrarily and we are dealing with atoms, it is convenient to choose w = 2, which gives x = 2, y = 1, and z = 1.  In this case our balanced equation is

                                    2NaOH + H2SO4           Na2SO4 + 2H2O.