Basic Measurement and Calculation Review

The SAT II Chemistry test will not directly test you on any of the skills that this appendix discusses. However, a good working knowledge of the information in this chapter will still prove very helpful during the exam. Remember, you can't use a calculator during the test!

The SI System

The Système Internationale (International System), SI, more commonly known as the metric system, is the only system of measurement that you'll see on the SAT II Chemistry test. Here's a quick refresher course on how to use this system.

Standard Prefixes

The metric system is fairly straightforward. The table of prefixes below is only partial, but it includes the ones that you need to be familiar with for the test.

Prefix	Power	Meaning	Examples of measurements
nano (n)	10^-9	one-billionth	nanometer (nm): wavelength of light
micro (m)	10^-6	one-millionth	micrometer (mm): width of a hair
milli (m)	10^-3	one-thousandth	milliliter (mL): volume of acid in burette
centi (c)	10^-2	one-hundredth	centimeter (cm): length of paper
deci (d)	10^-1	one-tenth	deciliter (dL): amount of liquid
kilo (k)	10^3	one thousand times	kilogram (kg): your weight

Also useful to know are the units in the table below. Most of them will probably be familiar to you.

What is being measured	Common units
length	meter (m)
mass	gram (g)
volume	liter (L) or cm^3
temperature	degree Celsius (˚C) and kelvin (K)
time	second (s)
pressure	kilopascal (kPa); atmosphere (atm); mmHg
energy	joules ( J); calorie (cal)
amount of substance	mole (mol)

Scientific Notation

This is an easy way to express really large or really small numbers conveniently. The general format for numbers expressed this way is

some number
10^{some power}

For instance, 6.022
10²³ is really big, and 3.00
10^-6 is really small. Notice that the proper position for the decimal is to the right of the first nonzero digit. If you must move the decimal to get it into this position, moving the decimal to the left makes the exponent appear larger, while moving decimal to the right makes the exponent appear smaller. For example, 0.000567 in scientific notation would be 5.67
10^-4.

You need to be able to handle numbers of this sort without a calculator. Basically, you need to remember the following. For multiplication, add exponents, and fordivision, subtract exponents. To get the log of a value, raise it to the power of ten. This is mostly useful for pH calculations. Now try some problems.

Example

(4.5
10⁵)(3.0
10⁸).

Explanation

The answer is 1.35
10¹⁴ (or rounded, 1.4
10¹⁴). In solving this, think: 3
5 = 15, and then add the exponents: 5 + 8 = 13. Move the decimal to the right of the first nonzero digit, or one place to the left.

Example

Try another one: 
.

Explanation

The answer is 3.4
10^-12. In solving this, think: 6.8/2 = 3.4, and then subtract the exponents: (-2) - (10) = -12.

Example

Let's try another: Find the log of 1.0
10^-7.

Explanation

The answer is -7. The thought process is as follows. The log of 1.00 is 0. The log of 10^-7 is just the power of 10.

Temperature Conversions

The only two temperature scales that are needed for the SAT II Chemistry test are the Celsius scale and the Kelvin scale. One degree on the Celsius scale is the same increment as 1 kelvin on the Kelvin scale.

Celsius scale: This is the scale used in the chemistry laboratory for most experiments. The freezing point of water is 0ºC, and the boiling point of water is 100ºC. This was the original metric standard for temperature.

Kelvin scale: This is the scale used for working through gas law problems. There are no negative numbers on this scale. At 0K, all motion theoretically ceases.

Calculations Involving Metric Measurements (Dimensional Analysis)

Dimensional analysis offers an easy way to solve problems using conversion factors and unit cancellations. Conversion factors are ratios that equal 1. You know many of these ratios of equivalencies from everyday living. For example, 1 gallon equals 4 quarts, 12 inches equals 1 foot, etc. This is a useful technique for calculations that might come up on the test, so work through the following problems to practice it.

Example

How many inches tall is a person who is 5 feet, 4 inches tall?

Explanation

Example

How many milliliters would there be in 3.5 liters of soda?

Explanation

You'll have to do plenty of conversions like the one above to solve problems on the exam. Be sure that you are familiar with all the metric prefixes listed earlier so that you can be successful when you need to convert numbers.

Density

Density is a complex unit. It is defined as mass per unit of volume:

All pure substances have a unique density at a given temperature. Density is an intensive physical property, meaning that it does not change with sample size. Usually the solid form of a pure substance is denser than the liquid form of the same substance. This makes sense because in most solids, the particles are much closer together than in their liquid counterparts.

Typical units for density of solids and liquids are grams per milliliter or grams per cubic centimeter. (Remember: 1 cm³ = 1 mL.) Typical units for density of gases are grams per liter.

Example

Find the density of a substance that has a mass of 45.0 g and a volume of 3.0 mL.

Explanation

Example

What would be the mass of a substance that occupies a space of 2.0 cm³ and has a density of 7.5 g/cm³?

Explanation

.

Rearrange the equation to solve for mass: M = D
V.

Then

M = (7.5 g/cm³)(2.0 cm³) = 15 g

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