elementary step

Examples of elementary step in the following topics:

• Rate Laws for Elementary Steps

  • The rate law for an elementary step is derived from the molecularity of that step.
  • The sum of each elementary step in a reaction mechanism must yield the overall reaction equation.
  • The molecularity of the elementary step, and the reactants involved, will determine what the rate law will be for that particular step in the mechanism.
  • For now, just keep in mind that the rate laws for each elementary step are determined by the molecularity of each step only.
  • The molecularity of an elementary step in a reaction mechanism determines the form of its rate law.

• Rate-Determining Steps

  • The rate of a multi-step reaction is determined by the slowest elementary step, which is known as the rate-determining step.
  • However, most chemical reactions occur over a series of elementary reactions.
  • The complete sequence of these elementary steps is called a reaction mechanism.
  • The reaction mechanism is the step-by-step process by which reactants actually become products.
  • In kinetics, the rate of a reaction with several steps is determined by the slowest step, which is known as the rate-determining, or rate-limiting, step.

• Steady-State Approximation

  • In our discussion so far, we have assumed that every reaction proceeds according to a mechanism that is made up of elementary steps, and that there is always one elementary step in the mechanism that is the slowest.
  • This slowest step determines the rate of the entire reaction, and as such, it is called the rate-determining step.
  • In such a case, we must assume that the reaction rate of each elementary step is equal, and the overall rate law for the reaction will be the final step in the mechanism, since this is the step that gives us our final products.
  • Now, both of these rates can be written as rate laws derived from our elementary steps.
  • The first term takes into account the disappearance of N2O2 in the reverse reaction of the initial step, and the second term takes into account the disappearance of N2O2 as a reactant in the second elementary step.

• Heterogeneous and Multiple Equilibria

  • Both steps must be included in the equilibrium constant equation.
  • These equilibria can be split into two steps:
  • K1 and K2 are examples the equilibrium constants for each step.
  • Thus, for a reaction involving two elementary steps:
  • Calculate the equilibrium constant of a multiple-step reaction, given the equilibrium constant for each step

• The Rate Law

  • For the general reaction$aA + bB \rightarrow C$ with no intermediate steps in its reaction mechanism, meaning that it is an elementary reaction, the rate law is given by:

• Overall Reaction Rate Laws

  • As discussed in the previous concept, if the first step in a reaction mechanism is the slow, rate-determining step, then the overall rate law for the reaction is easy to write, and simply follows the stoichiometry of the initial step.
  • Since the first step is the rate-determining step, the overall reaction rate for this reaction is given by this step: $\text{rate}=k[H_2][ICl]$.
  • If the rate-determining step is not the first step in the reaction mechanism, the derivation of the rate law becomes slightly more complex.
  • Step two is the slow, rate-determining step, so it might seem reasonable to assume that the rate law for this step should be the overall rate law for the reaction.
  • Combine elementary reaction rate constants to obtain equilibrium coefficients and construct overall reaction rate laws for reactions with both slow and fast initial steps

• Further Simplification of Matrices

  • Gauss–Jordan elimination is an algorithm for getting matrices in reduced row echelon form using elementary row operations.
  • Gauss–Jordan elimination goes a step further by placing zeros above and below each pivot; such matrices are said to be in reduced row echelon form.
  • Use elementary row operations on matrix [A|b] to transform A into diagonal form.
  • Then, use elementary row operations to transform A into diagonal form:
  • Now that it is in diagonal coefficient form, the final step is to get everything on the diagonal to equal one.

• Elementary Education

  • If so, then working in elementary education might be for you.
  • However, before you consider a career as an elementary school teacher, you should be able to answer the following questions: What does an elementary school teacher do?
  • Elementary education majors are often required to complete a teaching practicum – a student-teaching internship at an elementary school that is supervised and evaluated by a veteran teacher.
  • There are so many options for those considering a career in elementary education.
  • A teacher and her students in an elementary school classroom (USA, 2008. )

• Types of Operations: Evolving from K, 1st, 2nd, 3rd, and 4th Grade

  • We have now been introduced to all of the operations of the elementary curriculum:
  • What number sets are we operating on in the elementary curriculum up to and including 4th grade?

• Simplifying Matrices With Row Operations

  • Using elementary operations, Gaussian elimination reduces matrices to row echelon form.
  • By means of a finite sequence of elementary row operations, called Gaussian elimination, any matrix can be transformed to a row echelon form.  
  • Use elementary row operations on the augmented matrix $[A|b]$ to transform $A$ to upper triangle form.
  • Use elementary row operations to reduce the matrix to reduced row echelon form:
  • Use elementary row operations to put a matrix in simplified form