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Units and Measurements for AP Chemistry

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By — McGraw-Hill Professional
Updated on Feb 8, 2011

Practice problems for these concepts can be found at:

Almost all calculations in chemistry involve both a number and a unit. One without the other is useless. Every time you complete a calculation, be sure that your units have cancelled and that the desired unit is written with the number.

Always show your units!

Units

The system of units used in chemistry is the SI system (Système International), which is related to the metric system. There are base units for length, mass, etc. and decimal prefixes that modify the base unit. Since most of us do not tend to think in these units, it is important to be able to convert back and forth from the English system to the SI system. These three conversions are useful ones, although knowing the others might allow you to simplify your calculations:

      mass:        1 pound = 0.4536 kg (453.6 g)
      volume:     1 quart = 0.9464 dm3 (0.9464 L)
      length:       1 inch = 2.54 cm (exact)

As shown above, the SI unit for volume is the cubic meter (m3), but most chemists use the liter (L, which is equal to 1 cubic decimeter (dm3)) or milliliter (mL). Appendix A lists the SI base units and prefixes, as well as some English–SI equivalents.

We in the United States are used to thinking of temperature in Fahrenheit, but most of the rest of the world measures temperature in Celsius. On the Celsius scale water freezes at 0°C and boils at 100°C. Here are the equations needed to convert from Fahrenheit to Celsius and vice versa:

Many times, especially in working with gases, chemists use the Kelvin scale. Water freezes at 273.15 K and boils at 373.15 K. To convert from Celsius to kelvin:

    K C = ° +273 15

Absolute zero is 0 K and is the point at which all molecular motion ceases.

The density of a substance is commonly calculated in chemistry. The density (D) of an object is calculated by dividing the mass of the object by its volume. (Some authors will use a lowercase d to represent the density term; be prepared for either.) Since density is independent of the quantity of matter (a big piece of gold and a little piece have the same density), it can be used for identification purposes. The most common units for density in chemistry are g/cm3 or g/mL.

Measurements

We deal with two types of numbers in chemistry—exact and measured. Exact values are just that—exact, by definition. There is no uncertainty associated with them. There are exactly 12 items in a dozen and 144 in a gross. Measured values, like the ones you deal with in the lab, have uncertainty associated with them because of the limitations of our measuring instruments. When those measured values are used in calculations, the answer must reflect that combined uncertainty by the number of significant figures that are reported in the final answer. The more significant figures reported, the greater the certainty in the answer.

The measurements used in calculations may contain varying numbers of significant figures, so carry as many as possible until the end and then round off the final answer. The least precise measurement will determine the significant figures reported in the final answer. Determine the number of significant figures in each measured value (not the exact ones) and then, depending on the mathematical operations involved, round off the final answer to the correct number of significant figures. Here are the rules for determining the number of significant figures in a measured value:

  1. All non-zero digits (1, 2, 3, 4, etc.) are significant.
  2. Zeroes between non-zero digits are significant.
  3. Zeroes to the left of the first non-zero digit are not significant.
  4. Zeroes to the right of the last non-zero digit are significant if there is a decimal point present, but not significant if there is no decimal point.

Rule 4 is a convention that many of us use, but some teachers or books may use alternative methods.

By these rules, 230500. would contain 6 significant figures, but 230500 would contain only 4.

Another way to determine the number of significant figures in a number is to express it in scientific (exponential) notation. The number of digits shown is the number of significant figures. For example 2.305 × 10–5 would contain 4 significant figures. You may need to review exponential notation.

In determining the number of significant figures to be expressed in the final answer, the following rules apply:

  1. For addition and subtraction problems, the answer should be rounded off to the same number of decimal places as the measurement with the fewest decimal places.
  2. For multiplication and division problems, round off the answer to the same number of significant figures in the measurement with the fewest significant figures.

Remember: Carry as many numbers as possible throughout the calculation and only round off the final answer.

The use of an improper number of significant figures may lower your score on the AP exam.

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