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UNITS AND UNIT ANALYSIS

Introduction

Quantitative physical properties are recorded as a number with a unit where the unit indicates what instrument was used. In this country, the most common system of units is the English System but in science, the preferred system is the Metric System (SI). The SI system is preferred because all units that are proportional to some basic unit are given in terms of powers of ten of the basic unit. In this chapter, the units for length, mass, temperature, amount and time in both systems are given as well as some compound units. Changing from one unit to another is referred to as unit analysis problems and these are developed along with the ...view middle of the document...

The general form of these problems is given by

[pic] (1)

where CF is a conversion factor that makes the units on both sides of Eq. (1) agree (an equation in science is incorrect if the units on both sides do not agree).

Suppose that the information in the problem is the distance to Dallas of 5700000 in and the objective is to determine the distance in miles. Then Eq. (1) becomes

[pic] . (2)

In Eq. (2), CF must convert in into mi or symbolically

[pic] (3)

where the arrow means that the unit on the left is converted to the unit on the right, i.e. in is converted into mi. The problem is that the number of inches in one mile is not widely known. However, it is widely known that there are 12in in one foot or

[pic] (4)

which is considered to be an exact expression. Equation (4) is used to construct (simple) conversion factors. If rearranged to the form

[pic] (5)

it can convert length in inches to length in ft or in the form of Eq.(1)

[pic] (6)

where yin is the information. When Eq. (4) is expressed as

[pic] (7)

it can convert length in ft to length in inches or from Eq. (1)

[pic] . (8)

Another fairly well known conversion is that

[pic] . (9)

With this knowledge, the CF in Eq. (2) can be written symbolically as

[pic] (10)

which means that one has a product of two conversion factors. The first one converts in into ft and the second converts ft into mi. Using Eqns. (4) and (9) the conversion factor becomes

[pic] (11)

so that Eq. (2) becomes

[pic] (12)

In general, when working with problems in unit analysis, it is helpful to set the problem up with Eq. (1), determine with your known knowledge a symbolic expression for CF as in Eq. (10), then write CF in terms of actual conversion factors as in Eq. (11) and then finally solve the problem as in Eq. (12).

The Basic Units

The basic units to be discussed here are mass, length, time, temperature and the amount.

Length

Metric CF English

basic unit meter(m) foot(ft)

others 1km=1000m 1mi=5280ft

1m=100cm 1yd=3ft

1m=1000mm 1ft=12in

2.54cm=1in

The above table contains some of the more common units in the two systems. One notices that, in the SI system, all units are related by powers of 10 but that this is hardly the case in the English system. The entry in the CF column (2.54cm=1in) is a somewhat arbitrarily selected conversion between the two systems.

For the previous example, suppose that the distance to Dallas was given is 90.mi and the objective is to determine the distance in km. The Eq. (1) becomes

[pic] . (13)

Knowing the above information, the symbolic form for CF would be

[pic] .

Using the above information gives

[pic]

and using Eq. (13) gives

[pic] .

Chemistry often deals with very small lengths when...

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