CHEM 1406 Concept Review: Chemistry and Measurement

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International System of Units (SI):  The official system of measurement throughout the world, based largely on the metric system. 

Comparative Measurements

Measurement	Metric	SI	English	Measured Using…
Length	meter (m)	meter (m)	foot (ft)	meter stick or ruler
Volume	liter (L)	cubic meter (m3)	gallon (gal)	graduated cylinder or beaker
Mass	gram (g)	kilogram (kg)	pound (lb)	scale or balance
Temperature	degree Celcius (˚C)	Kelvin (K)	degree Fahrenheit (˚F)	thermometer
Time	second (s)	second (s)	second (s)	atomic clock

 

 

Scientific Notation

A way of representing numbers (especially very large or very small numbers) in reference to a power of ten.  The general form of a number in scientific notation is as follows:

M x 10ⁿ

Where “M” is a value greater than or equal to 1 and less than 10, and “n” is the power of ten.

 

To convert into scientific notation, follow these simple steps:

        1. Decide where you would have to move the decimal point to make it a number between 1 and 10

  Example:         

 

        2. Then count how many spaces you had to move the decimal point. (Note that in large numbers you won’t see a decimal              point in the number so just place a decimal point after the “one’s place.”)

  Example:          

 

        3. Write the new number as having the same number of significant figures as the old number and multiply it times 10 to the power of the number of spaces you moved. If the number was small (less than 1), give it a negative exponent.  If the number was large, give it a positive exponent.

  Example:        

To convert from scientific notation back to normal notation, simply move the decimal point the number of spaces as the exponent of 10.  If the exponent is negative, move the decimal in the direction that will make the number smaller.  If the exponent is positive, move the decimal in the direction that will make the number bigger.

 

 

Significant Figures

The numbers that reflect the degree of certainty to which a value is measured.  This consists in ALL digits known with CERTAINTY and ONE ESTIMATED digit.  The last significant figure (the one furthest to the right) in any measured number is the estimated digit or “error digit”

Exact Numbers:  Numbers determined by counting (10 pencils) or by definition (1 ft. = 12 in.).  These numbers have unlimited significant figures and therefore do not effect significant figures in calculations.

The Rules of Zero (for Significant Figures)

1)  Leading zeroes (zeroes before non-zero numbers) are NEVER significant. 

     EXAMPLE:  0.00000259 m  (NOT significant)

2)  Sandwiched zeroes (zeroes between non-zero numbers) are ALWAYS significant. 

     EXAMPLE:  10029 J  (Significant)

3)  Trailing zeroes (zeroes after non-zero numbers) are ONLY significant IF the value has a decimal point.

      EXAMPLE:  12500 lbs (NOT significant)                 12.500 lbs (significant)

 

 

Calculating with Significant Figures

    In order to ensure that our calculated values continue to express the appropriate level of certainty corresponding to the measurements used in calculation, rules are used to determine how many significant figures a calculated value should have.  They differ according to the mathematical process used in calculation.

Multiplication/Divison Rule:  The product or quotient of two or more measured values must have the same number of significant figures as the measured value with the fewest significant figures.

Addition/Subtraction Rule:  The sum or difference of two or more measured values must have the same error as the measured value with the greatest error.  The error of a measured value is in its estimated digit.

EXAMPLE:  The estimated (uncertain) digit is bolded.

124.56             (The error is in the hundredths place)

+  4.5              (The error is in the tenths place.)

129.1               (Answer must have its final significant figure (estimated digit) in the tenths place.)

 

 

Dimensional Analysis:

A method of problem solving that keeps track of units and cancels them using conversion factors. 

Conversion Factor:  A fraction where the numerator is equal (or at least directly related to) the denominator.  Any time you can set one value equal to another, those values can be used as a conversion factor.

EXAMPLES:   $1\:inch=2.54\:cm\:\longrightarrow\:\left(\frac{2.54\:cm}{1\:inch}\right)\:or\:\left(\frac{1\:inch}{2.54\:cm}\right)$

 

Dimensional Analysis Example Problem:  John Smith is 6.0 ft. tall.  What is his height in meters?

1. Start with what is equal to the value you are looking for. The problem asks for height. What is equal to the man’s height? 6.0 ft.

 

2. Whatever unit is initially in the numerator must come down in the denominator of the next conversion factor so that it can cancel out. This also gives you a hint as to what conversion factor to use.

 

 

3. Continue to add conversion factors until you get to the answer you are looking for.

 $6.0\:ft\times\left(\frac{12\:inches}{1\:ft}\right)\:\times\left(\frac{2.54\:cm}{1\:in}\right)\times\left(\frac{1\:m}{100\:cm}\right)=1.8\:m$

 

 

Density Formula

$Density=\frac{mass}{volume}$