Measurement in Science

Scientific Observation… Empirical knowledge is gained by conducting experiments and making observations. There are 2 types of observations that can be gathered from experiments. Qualitative Observations: Describe the features of an object or substance using the senses. Ex: Colour, gas bubbles, odour, precipitate. Quantitative Observation: requires some sort of measuring equipment, usually numerical with a unit. Ex: Temperature, Volume, pH.

Measurement – A Quantitative Observation Measured results are required for quantitative observations. Various factors will affect your confidence in your measured results. Such as… –Type of measuring equipment used –Amount to be measured (too large or too small) –Condition of equipment All these factors must be minimized and controlled in order to increase confidence and decrease “uncertainty” in your measurements

The International System of Units Lengthmeter m Masskilogram kg Timesecond s Amount of substancemole mol Thermodynamic temperatureKelvin K Electric currentamperes amps Luminous intensitycandela cd QuantityNameSymbol Dorin, Demmin, Gabel, Chemistry The Study of Matter, 3 rd Edition, 1990, page 16

Prefixes in the SI System Power of 10 for Prefix SymbolMeaning Scientific Notation _______________________________________________________________________ mega-M 1,000, kilo-k 1, deci-d centi-c milli-m micro-  nano-n The Commonly Used Prefixes in the SI System Zumdahl, Zumdahl, DeCoste, World of Chemistry  2002, page 118

Laboratory Equipment used for accurate measurements Burette Graduated Cylinder Pipette Volumetric Flask

Laboratory Equipment used for approximate measurements Beaker Erlenmeyer Flask

Units of Measuring Volume 1 L = 1000 mL Timberlake, Chemistry 7 th Edition, page 3

Reading a Meniscus

The graduated cylinder on the left has scale marks 0.1 mL apart, so it can be read to the nearest 0.01 mL. Reading across the bottom of the meniscus, a reading of 5.72 mL is reasonable (5.73 mL or 5.71 mL are acceptable, too).

Accuracy vs. Precision Certainty of Measurements Accuracy refers to the ability of the measurement to match the “true” value. How close are you to the real number? Precision refers to the ability of a measurement to be consistently reproduced

Accuracy vs. Precision Random errors: reduce precision Good accuracy Good precision Poor accuracy Good precision Poor accuracy Poor precision Systematic errors: reduce accuracy

Example: At STP, 5mL of pure water should have a mass of exactly 5 grams. The following students weighed a cylinder containing 5mL of pure water three times. Comment on their accuracy and precision: Student AStudent BStudent C 5.0g6.2g6.4g 5.1g6.1g5.9g 4.9g6.2g4.2g

Estimating the last digit in measurements: The maximum possible precision of a measurement is 1/10 (0.1) times the smallest division on the measuring instrument Eg. If your ruler’s smallest division is the tenth’s place, your measurement should be to the hundredths place If your ruler’s divisions are to the one’s, you estimate to the tenth’s.

Rules for Rounding 1.If the last digit to be removed is… a.less than 5, the preceding digit stays the same. For example, 1.33 round to 1.3. b.equal to or greater than 5, the preceding digit is increased by 1. For example, 1.36 rounds to 1.4, and 3.15 rounds to 3.2. If you have more than one step in a calculation, do not round until you arrive at the final answer!!!

Significant Digits Significant figures are used to show the accuracy of a measurement. All measurements consist of a number of digits about which we are certain, and a final digit that has been estimated. The expression of this measurement must show this certainty

R ULES FOR S IGNIFICANT D IGITS 1.All non-zero digits are significant. (Ex. 367 has 3 sigfigs) 2.All zeros between non-zero digits are significant. (Ex 307 has 3 sfs) 3.Zeros to the right of the last number smaller than one are significant. (Ex has 3 sfs)

4.All zeros to the right of the last whole number are not considered significant unless measured directly by the measuring device. (Ex km has 2 sfs; 70. g has 2 sfs; has 4 sfs) 5.All zeros to the left of a number less than one, are not significant. (Ex g has 2sfs)

6.Exact numbers (numbers derived from counting) are not considered measurements. When multiplying or dividing an uncertain value by an exact number, the answer has the same place setting as the measured value. (Ex. 3 x 14.7 mL will be expressed to the tenth)

S IGNIFICANT D IGITS IN C ALCULATIONS 7.When adding or subtracting, the answer is expressed to the same place setting as the quantity with the highest place setting, which means round off your answer to the least number of decimals in the problem. 8.When multiplying or dividing, the answer should be rounded off to the same number of significant digits as the number having the fewest significant digits.

State the number of significant digits in the following: a) g b) g c)370.0 g d)560. g e)1.23x10 4 g