Solving Chemical Equations

I hate the guessing method in balancing equations. It's fine for simple equations, but at times it takes too much time without getting the actual results. It bothered me enough that I decided to look on the Internet for a different method. The best article was from wikipedia: http://en.wikipedia.org/wiki/Chemical_equation This page is my version of explaining the process in the article. ? CO + ? NO --> ? CO2 + ? N2 1. Instead of the ?, put in letters to represent the coefficients a CO + b NO --> c CO2 + d N2 2. Setup equality equations for each element in the equation. -list the elements involved in the equation -for each element, write its number of atoms in relationship to the coefficient in front of it, but differentiate between the left and right side of the equation by putting an equal sign in between. The last part should make sense in the example below For C, there is one C @ a on the left side of the equation, and on the right there is one C @ c. Thus, C: 1a = 1c We do the same for the other elements O: 1a + 1b = 2c N: 1b = 2d 3. Now using the equations above, solve for each variable in terms of a. a = 1a b = 2c - 1a c = 1a 2d = 1b -Looking at our variables, b and d are not in terms of a yet. c = a, thus 2c = 2a and we can use substitution on b b = 2c - 1a = 2a - 1a 2d = 1b, substitute b for a, so 2d = 1a , d = 1/2a 4. If all of the variables' coefficients of a are whole numbers then you now have your solution. If not, use the "problem" coefficient(s)'s lowest common denominator as the factor to multiply each coefficient by. Below are the coefficients we have, notice how d is not a whole number, and its denominator is 2. Use that number to multiply each variable's coefficient. a = 1a = 1*2 = 2 b = 1a = 1*2 = 2 c = 1a = 1*2 = 2 d = 1/2a = (1/2)*2 = 1 5. Substitute the numerical coefficients we just found in place of their respective variables in the equation. a CO + b NO --> c CO2 + d N2 2 CO + 2 NO --> 2 CO2 + 1 N2