A Gran plot is used to predict the equivalence volume or endpoint of a potentiometric or acid-base titration without reaching the endpoint. Typically, titration data is collected as a function of the titrant's volume up to a point less than the equivalence volume and then transformed into a linear format. The straight line is extended to the x-axis, indicating the necessary titrant volume to achieve the equivalence point.
For potentiometric titration, the Gran plot is created by plotting the...

So far, glycolysis has cost the cell two ATP molecules and produced two small, three-carbon sugar molecules. These molecules will proceed through the second half of the pathway, and sufficient energy will be extracted to pay back the two ATP molecules used as an initial investment and produce a profit for the cell of two additional ATP molecules and two even higher-energy NADH molecules.
Step 1 - 5: Glycolysis Preparatory Phase
The first phase of glycolysis has 5 steps where the glucose is...

Different methods, such as visual observance of metal-ion indicators, spectroscopic techniques, and potentiometric methods, can determine the endpoint of an EDTA titration.
In the visual method, metal-ion indicators (metallochromic dyes), which have distinct colors in their free and complex forms, are added to the mixture to signal the titration's end point. They form stable complexes with metal ions, but these complexes are weaker than the corresponding metal–EDTA complexes. As a result, EDTA...

Nonstandard Reaction Conditions
The interconnection between standard cell potentials and various thermodynamic parameters such as the standard free energy change ΔG° and equilibrium constant K has been previously explored. For example, a redox reaction involving zinc(II) and tin(II) ions at 1 M concentration with Eºcell = +0.291 V and ΔG° = −56.2 kJ is spontaneous.

The highest and lowest values of a function, relative to a reference axis, are known as extreme values. These include absolute maximum and absolute minimum values, which represent the highest and lowest points the function reaches across its entire domain. Within a restricted portion of the function, the highest and lowest values are referred to as local maximum and local minimum values, respectively.Periodic functions, such as sine and cosine, show extreme values at infinitely many points due...

The function that decreases as the input becomes very large provides a clear example of how mathematical functions can behave at extreme values. When the input increases continuously, the output becomes smaller and smaller, getting closer to a particular fixed value. Although the output never actually reaches this value, it moves nearer to it without limit. This behavior is a fundamental concept in understanding how functions behave as the input grows indefinitely. The graphical representation...