Units of Measurement SI Units System used by scientists worldwide
Prefixes used with SI units
Meter Liter Gram deca dc hecto h kilo k deci d milli m centi c 1 0.001 0.01 0.1 10 100 1,000 Staircase Rule: The direction you slide your finger is the direction the decimal place goes!
Derived Units A unit that is defined by a combination of base units Volume Density
Density A ratio that compares the mass of an object to its volume The units for density are often g/cm 3 Formula:
Example Problem Suppose a sample of aluminum is placed in a 25-mL graduated cylinder containing 10.5mL of water. The level of the water rises to 13.5mL. What is the mass of the sample of aluminum? Volume: final-initial 13.5mL-10.5mL= 3.0mL Density: 2.7 g/mL (Appendix C) Mass: ????
Temperature Kelvin is the SI base unit for temperature Water freezes at about 273K Water boils at about 373K Conversion: 0 C +273 =Kelvin
Using and Expressing Measurements A measurement is a quantity that has both a number and a unit. Measurements are fundamental to the experimental sciences. For that reason, it is important to be able to make measurements and to decide whether a measurement is correct.
Dimensional Analysis*Very Important* A method of problem solving that focuses on the units to describe matter Conversion factor- a ratio of equivalent values used to express the same quantity in different units Example: 9.00 inches to centimeters Conversion factor: 1 in = 2.54 cm
We often use very small and very large numbers in chemistry. Scientific notation is a method to express these numbers in a manageable fashion. Definition: Numbers are written in the form M x 10 n, where the factor M is a number greater than or equal to 1 but less than 10 and n is a whole number. 5000 = 5 x 10 3 = 5 x (10 x 10 x 10) = 5 x 1000 = 5000 Numbers > one have a positive exponent. Numbers < one have a negative exponent.
Ex. 602,000,000,000,000,000,000,000 Ex. 0.001775 In scientific notation, a number is separated into two parts. The first part is a number between 1 and 10. The second part is a power of ten. 6.02 x10 23 1.775 x10 -3
Your success in the chemistry lab and in many of your daily activities depends on your ability to make reliable measurements. Ideally, measurements should be both correct and reproducible. Accuracy: a measure of how close a measurement comes to the actual or true (accepted) value of whatever is being measured. Precision: a measure of how close a series of measurements are to one another
Good Accuracy Good Precision Poor Accuracy Good Precision Good Accuracy Poor Precision Poor Accuracy Poor Precision
Error - the difference between the accepted value and the experimental value Accepted Value: referenced/true value Experimental Value: value of a substance's properties found in a lab.
Example A student takes an object with an accepted mass of 150 grams and masses it on his own balance. He records the mass of the object as 143 grams. What is his percent error?
The significant figures in a measurement include all of the digits that are known, plus the last digit that is estimated. Measurements must always be reported to the correct number of significant figures because calculated answers often depend on the number of significant figures in the values used in the calculation. Instruments differ in the number of significant figures that can be obtained from their use and thus in the precision of measurements.
1. Every nonzero digit in a reported measurement is assumed to be significant. The measurements 24.7 meters, 0.743 meter, and 714 meters each express a measure of length to 3 significant figures. 2. Zeros appearing between nonzero digits are significant. The measurements 7003 meters, 40.79 meters, and 1.503 meters each have 4 significant figures.
3. Leftmost zeros appearing in front of nonzero digits are NOT significant. They act as placeholders. The measurements 0.0071 meter, and 0.42 and 0.000099 meter each have only 2 significant figures. By writing the measurements in scientific notations, you can eliminate such place holding zeros: in this case 7.1 x10 -3 meter, 4.2x10 -1 meter, and 9.9x10 -5 meter.
4. Zeros at the end of a number to the right of a decimal point are always significant. The measurements 43.00 meters, 1.010 meters, and 9.000 meters each have 4 significant figures. 5. Zeros at the rightmost end of a measurement that lie to the end of an understood decimal point are NOT significant if they serve as placeholders to show the magnitude of the The zeros in the measurements 300 meters, 7000 meters, and 27,210 meters are NOT significant.
6. There are two situations in which numbers have unlimited number of significant figures. The first involves counting. If you count 23 people in the classroom, then there are exactly 23 people, and this value has an unlimited number of significant figures. The second situation involves exactly defined quantities such as those found within a system of measurement. For example, 60 min= 1 hour, each of these numbers have unlimited significant figures.
Rounding Rules: Addition/Subtraction When you add/subtract measurements, your answer must have the same number of digits to the RIGHT of the decimal point as the value with the FEWEST digits to the right of the decimal point Example: 28.0 cm 23.538 cm + 25.68 cm 77.218 cm Rounded to77.2 cm Fewest Decimal places
Rounding Rules: Multiplication/Division When you multiply or divide numbers, your answer must have the same number of significant figures as the measurements with the FEWEST significant figures Example: 3.20cm x 3.65cm x 2.05cm= = 23.944 cm 3 Rounded= 23.9 cm 3 Each has 3 sig fig’s