Typically, when alkenes react with halogens at low temperatures, an addition reaction occurs. However, upon increasing the temperature or under reaction conditions that form radicals, providing a low but steady concentration of halogen radicals, allylic substitution reaction is favored. This is because allylic hydrogens are very reactive as the formed intermediate is resonance stabilized. For example, when propene is treated with chlorine in the gas phase at 400 °C, it undergoes allylic...

How does one determine if bingo numbers are evenly distributed or if some numbers occurred with a greater frequency? Or if the types of movies people preferred were different across different age groups or if a coffee machine dispensed approximately the same amount of coffee each time. These questions can be addressed by conducting a hypothesis test. One distribution that can be used to find answers to such questions is known as the chi-square distribution. The chi-square distribution has...

The chi-square test is a statistical hypothesis test. It is used to check whether there is a significant difference between an expected value and an observed value. In the context of genetics, it enables us to either accept or reject a hypothesis, based on how much the observed values deviate from the expected values.
The chi-square test was developed by Pearson in 1990.
The first step of performing a Chi-square analysis is to establish a null hypothesis, which assumes that there is no real...

The stability and compatibility of column material with samples are crucial for efficient purification in chromatographic techniques. Various operating parameters such as pH, temperature, or solvent affect the packing of the column material, thereby determining the purification efficiency. The choice of column material also plays an essential role in deciding the operating parameters and can be modified based on the proteins that need to be purified.
Gel Filtration Chromatography
When the...

The chromatography technique was first invented in 1901 by Michael S. Tswett, a Russian botanist, to separate plant pigments using organic solvents. Further, in 1941, Archer John Porter Martin and R. L. M. Synge modified the technique by packing silica gel into a column. A mixture of amino acids was then separated on the packed column using chloroform and water mixture as the mobile phase. This was the first report on column chromatography. At present, column chromatography is a widely used...

In addition to being held together by the intervertebral discs, adjacent vertebrae also articulate with each other at synovial joints formed between the superior and inferior articular processes called zygapophysial joints (facet joints). These are plane joints that provide for only limited motions between the vertebrae. The orientation of the articular processes at these joints varies in different regions of the vertebral column and serves to determine the types of motions available in each...