**Trigonometry in Chemistry**

By: Paola Ossa

By: Paola Ossa

**What is Trigonometry?**

A branch of mathematics dealing with the relations of the sides and angles of triangles and with the relevant functions of any angles.

Making the Connection

A Lewis structure is a two-dimensional representation of a molecule's structure. The Lewis structure for CO2 appears in Figure 1. The electron pairs that create the covalent bonds between the carbon atom and the oxygen atoms repel each other. In order to minimize the repulsion between the covalent bonds, the bonds must be separated from each other by 180°.

Making the Connection

The three-dimensional model of methane is a tetrahedron, with the carbon atom at the center of the tetrahedron and the four hydrogen atoms at the vertices

Degree

Bachelor's degree in chemistry or dealing with mathematics

How is it used in Chemistry?

Trigonometry is used in a substantial amount of ways in chemistry. One way is by chemists using the molecular geometry of bonded atoms to comprehend the structure of molecules

Basis of Trig

Making the Connection

Now to determine the optimal bond angle, draw a perpendicular line from the carbon atom (C) to the plane containing three of the hydrogen atoms. Let Q represent the foot of this perpendicular line (Figures 3 and 4), and let y represent the distance between the carbon atom and any of the hydrogen atoms. Let a represent the distance from Q to one of the hydrogen atoms, and let x represent the measure of the required bond angle.

Bragg's Law

This is also one of the most frequently met relationships in chemistry that involves a trigonometric function. It describes the way in which x-rays of wavelength (Lamda) are diffracted from the surface of a crystal in which the lattice planes are separated by a distance d . It is found that in this case the reflected x-ray beam appears at only certain angles (theta); the first of these is described as the first order reflection with n = 1, the next as second order with n = 2, and so on. The equation which explains this behaviour is:

This is the radian, which is related to the degree by the simple relationship

Converting radians to degrees, and degrees to radians

Most applications involving trigonometry in chemistry require use of the sine function. This is defined for an angle (theta)θin terms of the right angled triangle by the equation

Ph.D for research jobs

chemistry

physics

electrical engineering

science

College Degree

Math Classes Required

Geometry

Trigonometry

Calculus I and II

Statistics

College Algebra

The End.

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