Carbon dioxideCarbon dioxide (chemical formula ) is a chemical compound made up of molecules that each have one carbon atom covalently double bonded to two oxygen atoms. It is found in the gas state at room temperature, and as the source of available carbon in the carbon cycle, atmospheric is the primary carbon source for life on Earth. In the air, carbon dioxide is transparent to visible light but absorbs infrared radiation, acting as a greenhouse gas. Carbon dioxide is soluble in water and is found in groundwater, lakes, ice caps, and seawater.
OxideAn oxide (ˈɒksaɪd) is a chemical compound containing at least one oxygen atom and one other element in its chemical formula. "Oxide" itself is the dianion (anion bearing a net charge of –2) of oxygen, an O2– ion with oxygen in the oxidation state of −2. Most of the Earth's crust consists of oxides. Even materials considered pure elements often develop an oxide coating. For example, aluminium foil develops a thin skin of (called a passivation layer) that protects the foil from further oxidation.
Fischer–Speier esterificationFischer esterification or Fischer–Speier esterification is a special type of esterification by refluxing a carboxylic acid and an alcohol in the presence of an acid catalyst. The reaction was first described by Emil Fischer and Arthur Speier in 1895. Most carboxylic acids are suitable for the reaction, but the alcohol should generally be primary or secondary. Tertiary alcohols are prone to elimination. Contrary to common misconception found in organic chemistry textbooks, phenols can also be esterified to give good to near quantitative yield of products.
Volume of an n-ballIn geometry, a ball is a region in a space comprising all points within a fixed distance, called the radius, from a given point; that is, it is the region enclosed by a sphere or hypersphere. An n-ball is a ball in an n-dimensional Euclidean space. The volume of a n-ball is the Lebesgue measure of this ball, which generalizes to any dimension the usual volume of a ball in 3-dimensional space. The volume of a n-ball of radius R is where is the volume of the unit n-ball, the n-ball of radius 1.
