Morse curve

Examples of Morse curve in the following topics:

• Bond Energy

  • A Morse curve shows how the energy of a two atom system changes as a function of internuclear distance.
  • The attractive and repulsive forces are balanced at the minimum point in the plot of a Morse curve.
  • A Morse curve will have different energy minima and distance dependence for bonds formed between different pairs of atoms.
  • The bond energy is the amount of work that must be done to pull two atoms completely apart; in other words, it is the same as the depth of the "well" in the potential energy curve.

• Osmotic Pressure

  • The osmotic pressure (II) of an ideal solution can be approximated by the Morse equation:

• Steric Effects

  • The green dashed curve in the illustration on the right represents this attraction, which increases with the inverse sixth power of the distance between the atoms (r).
  • This is demonstrated by the red dashed curve in the diagram.
  • Consequently, as the two atoms come together, an initial attraction becomes a strong repulsion, as shown by the dark blue curve.
  • If a covalent bond forms between the atoms, the energy versus distance curve displays a distinct minimum, representing a bond energy of Eb, at a distance (req) equal to the average bond length.

• Curved Arrow Notation

  • It is now common practice to show the movement of electrons with curved arrows, and a sequence of equations depicting the consequences of such electron shifts is termed a mechanism.
  • In general, two kinds of curved arrows are used in drawing mechanisms:

• Heating Curve for Water

  • A heating curve shows how the temperature changes as a substance is heated up at a constant rate.
  • There are two main observations on the measured curve:
  • Looking from left to right on the graph, there are five distinct parts to the heating curve:
  • The above equation (described in part 1 of the curve) cannot be used for this part of the curve because the change in temperature is zero!

• Organic Reactions Overview

  • Organic reaction mechanisms are written using curved arrows that depict transfers of either nonbonding or bonding electrons to form a new bond or exist as nonbonding electrons attached to an atom.
  • Without the curved arrows, it may be unclear as to how to the alkene and diene are converted to the cycloalkene.
  • Identify the function of curved arrow notation in the depiction of organic reactions

• Weak Acid-Strong Base Titrations

  • A titration curve reflects the strength of the corresponding acid and base, showing the pH change during titration.
  • The titration curve demonstrating the pH change during the titration of the strong base with a weak acid shows that at the beginning, the pH changes very slowly and gradually.
  • At the equivalence point and beyond, the curve is typical of a titration of, for example, NaOH and HCl.

• Buffer Range and Capacity

  • A titration curve visually demonstrates buffer capacity.
  • The middle part of the curve is flat because the addition of base or acid does not affect the pH of the solution drastically.
  • However, once the curve extends out of the buffer region, it will increase tremendously when a small amount of acid or base added to the buffer system.

• Diprotic and Polyprotic Acids

  • Diprotic and polyprotic acids show unique profiles in titration experiments, where a pH versus titrant volume curve clearly shows two equivalence points for the acid; this is because the two ionizing hydrogens do not dissociate from the acid at the same time.
  • The titration curve of a polyprotic acid has multiple equivalence points, one for each proton.

• Strong Acid-Weak Base Titrations

  • A known volume of base with unknown concentration is placed into an Erlenmeyer flask (the analyte), and, if pH measurements can be obtained via electrode, a graph of pH vs. volume of titrant can be made (titration curve).
  • The curve depicts the change in pH (on the y-axis) vs. the volume of HCl added in mL (on the x-axis).