Polyprotic acids of the type H2M constitute two ionizable protons. As a result, on titration with a base, they exhibit two equivalence points in the titration curve. During titration, the species H2M, HM−, and M2− will be present in the solution at different points. The fractions of H2M, HM−, and M2− present at the various instances of the titration are denoted by α0, α1, and α2, respectively.
A graph with the alpha values is plotted against the volume of...

Matter: Pure Substances and Mixtures
According to its composition, the matter can be classified into two broad categories — pure substances and mixtures. 
A pure substance is a form of matter that has a constant composition throughout with uniform properties. For example, any sample of sucrose has the same composition and same physical properties, such as melting point, color, and sweetness, regardless of the source from which it is isolated. 
A mixture is composed of two or...

Continuous probability distributions are used to model random variables that can take on any real value within a specified range. These variables do not take on isolated or countable values but rather exist on a continuum. For example, the height of an individual can be measured with increasing precision—such as 163.5 or 165.25 centimeters—demonstrating that height is a continuous random variable.The behavior of such variables is described using a probability density function (PDF),...

Bones contain a relatively small number of cells entrenched in a matrix of organic and inorganic components. Although bone cells compose only a small amount of the bone volume, they are crucial to its function. Four types of cells are found within the bone tissue— osteoblasts, osteocytes, osteogenic cells, and osteoclasts.
Osteoblasts and Osteocytes
The osteoblast is the bone cell responsible for forming new bone tissue. It is found in the growing portions of bone, including the...

A composite body is a body made up of multiple parts, connected to form a larger, unified object. Each part has its own weight and center of gravity, which must be considered to determine the center of gravity of the composite body. In cases where the density or specific weight is constant, the center of gravity coincides with the centroid.
Composite bodies have widespread applications in mechanical engineering, from automobiles to aircraft to rockets. For example, an automobile wheel comprises...

The blood in our bodies comprises three major components: blood plasma, formed elements, and the extracellular matrix. Blood plasma is a yellowish fluid that constitutes 55% of the total blood volume. It is primarily made up of water and essential substances such as electrolytes and proteins. Blood plasma serves as a medium for transporting blood cells and also contains nutrients, enzymes, hormones, antibodies, and gases.
Formed elements constitute the remaining 45% of the blood volume. These...