
The equilibrium constant of a reaction is fixed at any particular temperature. It depends only on the natures of the initial reactants and the final products; what happens as reactants change into products has no effect on the equilibrium constant or position of equilibrium.

The rate of a chemical reaction is affected both by the temperature and by the pathway (reaction mechanism) through which reactants change into products. This pathway c

The chemical formulae of many substances can be understood by arguing that their atoms attain noble gas structures by chemical combination.

In ionic compounds, this is achieved by the transfer of electrons from one atom to another; in molecular substances, it happens through the sharing of electron pairs in covalent bonds. But in both cases, bonds between atoms consist of shared pairs of electrons. In covalent compounds the sharing is fairl
The expressions we have derived for reflection and transmission coefficients were based on the assumption that the intensity of a beam is the product of the speed of its particles and their linear number density. This assumption seems very natural from the viewpoint of classical physics, but we should always be wary about carrying over classical ideas into quantum physics. In this section we shall establish a general quantummechanical formula for the beam intensity. The formula will be consi
If a process is repeated in identical fashion a very large number of times, the probability of a given outcome is defined as the fraction of the results corresponding to that particular outcome.
Babylonian mathematics
This unit looks at Babylonian mathematics. You will learn how a series of discoveries have enabled historians to decipher stone tablets and study the various techniques the Babylonians used for problemsolving and teaching. The Babylonian problemsolving skills have been described as remarkable and scribes of the time received a trainng far in advance of anything available in medieval Christian Europe 3000 years later.Author(s):
This unit provides an overview of the processes involved in developing models. It starts by explaining how to specify the purpose of the model and moves on to look at aspects involved in creating models, such as simplifying problems, choosing variables and parameters, formulating relationships and finding solutions. You will also look at interpreting results and evaluating models.
This unit, the third in a series of five, builds on the ideas introduced and developed in Modelling poll
In unit MSXR209_1 you saw how some of the stages of a mathematical modelling process can be applied in the context of modelling pollution in the Great Lakes. In this unit you are asked to relate the stages of the mathematical modelling process to another practical example, this time modelling the skid marks caused by vehicle tyres. By considering the example you should be able to draw out and clarify your ideas of mathematical modelling.
This unit, the second in a series of five, builds
This unit explores a realworld system â€“ the Great Lakes â€“ where mathematical modelling has been used to understand what is happening and to predict what will happen if changes are made. The system concerned is extremely complex but, by keeping things as simple as possible, sufficient information will be extracted to allow a mathematical model of the system to be obtained.
This unit is an adapted extract from the course Author(s):
Having discussed nth roots, we are now in a position to define the expression a^{x}, where a is positive and x is a rational power (or exponent).
Definition
If aÂ >Â 0, m Author(s):
5.1 Arithmetic with real numbers
At the end of Section 1, we discussed the decimals
and asked whether it is possible to add and multiply these numbers to obtain another real number. We now explain how this can be done using the Least Upper Bound Property of Author(s):
6.2 Getting the feel of big and small numbers
Very small and very large numbers can be difficult to comprehend. Nothing in our everyday experience helps us to get a good feel for them. For example numbers such as 10^{99} are so big that if Figure 1 was drawn to scale, you would be dealing with enormous distances. How big is big?
First express 1â€‰000â€‰000â€‰000 in scientific notation as 10^{9}. Next, to find out how many times bigger 10^{99} is, use your calculator to divide 10^{99} by 10^{9Author(s): The Open University}
1 Express each of the following numbers in scientific notation.
(a) Light travels 9460Â 700Â 000Â 000Â km in a year.
(b) The average distance from the centre of the Earth to the centre o
Here is a tale based on an ancient Eastern legend, which gives an idea of the impact of raising a number to a power.
Example 6
A long time ago there lived a very rich king whose son's life was saved by a poor old beggar woman. The king was naturally very grateful to the woman, so he offered to
To find the cube of a number, multiply three copies of it together. For example:
You can use your calculator to find cubes. 2^{3} is â€˜two cubedâ€™ or â€˜two to the power threeâ€™. Just as â€˜square rootâ€™ is the opposite process to squaring, so 'cube root' is the o
The content acknowledged below is Proprietary (see terms and conditions) and is used under licence.
All materials included in this unit are derived from content originated at the Open University.
The main teaching text of this unit is provided in the workbook below. The answers to the exercises that you'll find throughout the workbook are given in the answer book. You can access it by clicking on the link under the workbook.
Click 'View document' to open the workbook (PDF, 1 MB).
After studying this unit you should:
know some basic definitions and terminology associated with scalars and vectors and how to represent vectors in two dimensions;
understand how vectors can be represented in three (or more) dimensions and know both plane polar and Cartesian representations;
know ways to operate on and combine vectors.
This unit introduces the topic of vectors. The subject is developed without assuming you have come across it before, but the unit assumes that you have previously had a basic grounding in algebra and trigonometry, and how to use Cartesian coordinates for specifying a point in a plane.
This is an adapted extract from the Open University course Mathematical methods and models (MST209)
After studying this unit you should:
be able to solve homogeneous secondorder equations;
know a general method for constructing solutions to inhomogeneous linear constantcoefficient secondorder equations;
know about initial and boundary conditions to obtain particular values of constants in the general solution of secondorder differential equations.
The content acknowledged below is Proprietary (see terms and conditions) and is used under licence.
All materials included in this unit are derived from content originated at the Open University.