Measurement and Calculations Making observations is a key part of the scientific process. Observations become more meaningful when measurements are made.

Two types of observations: Qualitative (kind): Examples: color, texture Quantitative (amount): Examples: mass, volume, length, density

A quantitative observation is called a measurement A measurement always consists of two parts: a number and a unit

Scientific Notation Why? Makes very large and very small numbers easier to use

Rules for Scientific Notation Number can be represented as the product of a number between 1 and 10 and a power of 10. Move decimal so it directly follows the first non-zero digit in the base. Powers of 10 greater than 1 have positive exponents. Powers of 10 less than 1 have negative exponents.

Example 23,500 2.35 x 104

Example 0.0560 5.60 x 10 -2

Example 25.0 2.50 x 101

Units The part of a measurement called the unit tells us what scale or standard is being used. The two most widely used systems are the English system and the metric system.

Commonly Used Metric Prefixes

SI Fundamental Units of MEASUREMENT In 1960 an international committee of scientists met to revise the metric system. They developed the Systems International (SI) Fundamental Units of Measurement.

They developed units that are defined by standards of measurement which are of constant value.

SI Fundamental Units For Chemistry Quantity Unit Symbol Length meter m Mass kilogram kg Time second s Temperature Kelvin K Amount mole mol Electric current ampere amp Luminous intensity candela can

Length, Volume, and Mass 1) Length SI unit is meter 1 meter = 39.37 inches (about a yard) 1 inch = 2.54 centimeters measure length using a ruler or meter stick

Common Metric Units for Length

2) Volume SI unit is meter3 1 dm3 = 1 L 1 cm3 = 1 mL

Measure volume using a graduated cylinder

3) Mass SI unit is kilogram Metric unit is gram Measure mass using a balance

Uncertainty in Measurement Two kinds of numbers 1) Exact a. counted 2 children 26 letters b. defined 12 inches per foot 1000 g per kilogram

2) Inexact Numbers a. Measurements Uncertainty always exists in measured quantities: equipment limitations skill of person taking the measurements

What does the pin measure? 2.84? 2.85? 2.86?

All the digits that occupy a place for which an actual measurement is made are called certain numbers Any digit that is estimated is called an uncertain number

When making measurements, always record all certain numbers plus one uncertain number

The numbers recorded in a measurement (all the certain numbers plus one uncertain number) are called significant figures

Significant Figures Significant = “measured” Not significant = “place holder”

Rules for Significant Figures 1. Non-zero digits are always significant. 1.9 = 2 sf 17.123 = 5 sf 567 = 3 sf

2. Trapped zeroes are always significant. 1.01 = 3 sf 35.05 = 4 sf 300.09 = 5 sf

3. Leading zeros are never significant. 0.0003 = 1 sf 0.00105 = 3 sf

4. Trailing zeros are significant only if the decimal point is present. 1.10 = 3 sf 0.009000 = 4 sf 2,500 = 2 sf

6.22 x 103 5. If a number is written in scientific notation, ALL of the numbers in the base are significant. 6.22 x 103 = 3 sf 5.000 x 104 = 4 sf

Rounding in Calculations Digits less than 5 round down Digits equal to or greater than 5 round up In a series of calculations, don’t round until the end

Significant Figures in Calculations When multiplying or dividing, the answer must have the same number of significant figures as the measurement with the fewest.

Example: Multiply the following 2.0 mL 3.55 mL X 6.12 mL 2 sf 3 sf 3 sf 43.452 mL 43 mL Round answer to 2 significant figures

When adding or subtracting, the answer must have the same number of decimal places as the measurement with the fewest.

Example: Add the following 2 decimal places 0 decimal places 3 decimal places 203.680 g 204 g Round answer to 0 decimal places

Rounding Significant Figures You cannot change the magnitude of the number when rounding! Calculations cannot be more exact than the measurements on which they are based!

102,433 rounded to 3 sig fig. = 102,000 not 102

395,952 rounded to 1 sig fig. = 400,000 not 4

0.092602 rounded to 2 sig fig. = 0.093 not 0.093000

Dimensional Analysis Also known as the “Factor-Label Method” or “Factoring the Units” A systematic method for solving problems in which units are carried throughout the entire problem.

Using conversion factors helps ensure that answers have the proper units.

Examples of Conversion Factors 12 in = 1 ft 100 cm = 1 m 12 in or 1 ft 1 ft 12 in 100cm or 1m 1 m 100cm

When determining the number of significant figures in an answer, consider only the measured digits and ignore the conversion factors.

Example #1 A lab bench is 175.0 inches long. What is its length in feet?

Given: 175.0 inches (4 sf) Uknown: _____ feet Conversion factor: 12 in or 1 ft 1 ft 12 in

175.0 in x 1 ft = 12 in 14.583333 ft = 14.58 ft

Example #2 A marble rolled 50.0 millimeters. How many meters did it roll?

Given: 50.0 mm (3 sf) ? : _____m Conversion factor: 1000 mm or 1 m 1 m 1000 mm

50.0 mm x 1 m = 1000 mm 0.05 m .0500 m

Example #3 In Europe, a car was driven at 165 km/hr. What was the speed in mi/min?

Given: 165 km/1 hr (3 sf) ? : _____ mi/ 1 min

Conversion factors: 1.609 km or 1 mi 1 mi 1.609 km AND 1 hr or 60 min 60 min 1 hr

1.71 mi/min 1 hr 1.609 km 60 min 1.709136109 mi/min = 165 km x 1 mi x 1 hr = 1 hr 1.609 km 60 min 1.709136109 mi/min = 1.71 mi/min

Heat vs. Temperature Heat – total kinetic energy (movement) of particles in a sample. Temperature – measurement of the average kinetic energy (speed) of the particles in a sample.

Question Which would have a higher temperature, a cup of boiling hot coffee or a bathtub of warm water?

Answer Boiling cup of coffee would have a higher temperature (avg. kinetic energy)

Question Which would contain more heat?

Answer Warm bathtub would have more heat (total kinetic energy)

Measuring Temperature: Common units are oF, oC, and K Kelvin is used in chemistry because it starts at absolute zero which is the total absence of heat.

Absolute Zero – the temperature at which all molecular motion stops (the coldest temperature possible)

Temperature Conversions K = °C + 273 C = K - 273

Example #1: Convert 250 Kelvin to Celsius C = K - 273 250 -273 = -23 0C

Example #2: Convert 17 0C to Kelvin K = °C + 273 17 + 273 = 290 K

Mass per unit volume of a material Density Mass per unit volume of a material Formula: density (d) = mass (m) volume (v) Units: g/mL or g/cm3 Remember: 1 ml = 1 cm3

Rubbing Alcohol and Water d = 0.85 g/mL Water d = 1.0 g/mL

Calculating Density Example #1: An iron bar with a mass of 94.5 g has dimensions of 12 cm x 2.0 cm x 0.50 cm. What is its density? (2 sf) 12 cm 2 cm 0.50 cm

Step 1: Calculate the volume V = l x h x w 12 x 2.0 x .50 = 12 cm3

Step 2: Solve for density d = m/V 94.5 g 12 cm3 7.9 g/cm3

Example #2: What volume will be occupied by an 83.5 gram sample of Gold (Au) if the density of Gold is 19.3 g/mL? (3 sf)

Answer Step 1: Rearrange the density equation d = m/V V = m/d

Answer Step 2: Solve for volume V = m d 83.5/19.3 4.33 mL

Example #3: If the density of water is 1 Example #3: If the density of water is 1.0 g/mL, what is the density of 25 mL of water? 2 sf

Answer d = m/v m = (d)(v) (1.0)(25) 25 g

Percent Error Allows you to calculate how far off a measured value is from an accepted value.

Formula % Error = Accepted – Experimental x 100 Accepted

Example: Calculate % Error if the measured value for the density of a sample of Aluminum metal (Al) is 2.1 g/mL, but the accepted value is 2.7 g/mL. 2 sf

Answer 2.7 – 2.1 = 0.6/2.7 = .22 x 100 = 22% If you don’t hit = (enter) before you divide, the answer will be wrong! If you don’t hit = (enter) before you multiply, the answer will be wrong!

Accuracy vs. Precision Accuracy how closely individual measurements agree with the correct or accepted value Precision how closely individual measurements agree with each other

Good precision Good accuracy and precision Neither