•Chemistry is an observation science •Observations frequently require taking measurements•Measurements have some degree of uncertainty•All measured numbers have 2 parts:

Chapter 2: Measurements in Chemistry

Scientists use the Metric System:

Units of MeasurementMeasurement Metric Base Unit

Length

Volume

Mass

Temperature

Time

Prefix Symbol Numerical Value Sci Notation Equality

Prefixes that Increase the Size of the Unit:Giga G 1,000,000,000 1 x 109

mega M 1,000,0001 x 106 1 Mg = 106 g or 1 g = 10-6 Mg

kilo k 1,000 1 x 103 1 km = 1000 m or 1 m = 10-3 km

Prefixes that Decrease the Size of the Unit:deci d 0.1 1 x 10-1 1 dL = 0.1 L or 1 L = 10 dL

centi c 0.01 1 x 10-2 1 cm = 0.01 m or 1 m = 100 cm

milli m 0.001 1 x 10-3 1 ms = 10-3 s or 1 s = 1000 ms

micro m 0.000001 1 x 10-6 1 mg = 10-6 g or 1 g = 106 mg

nano n 0.000000001 1 x 10-9

Metric Prefixes:

What is the relationship between volume and length?

1 Liter = the space occupied by a 10 cm cube

Exact and Inexact Numbers?Exact number = number whose value has no uncertainty• defined numbers• counted numbers

Inexact number = a number with a degree of uncertainty• measured numbers

Uncertainty in Measurement

Significant figures = all digits that are known with certainty + 1 estimated digit

Precision = the degree to which a measurement is reproducible

The precision of a measurement is determined by the instrument used:

• Digital equipment – record all digits• Analog equipment – incremental (closest) marks

Guidelines for Determining Significant Figures in Measured Numbers

Significant FiguresDigits known with certainty + one estimated digit

Nonzero Digits1, 2, 3 … 9 are always significant

ZeroMay or may not be significant

Leading ZerosZeros at the beginning of a number

are never significant

Trailing ZerosAre significant only if

the decimal point is shown

Confined ZerosZeros between non-zero digits

are always significant

How many Significant Figures?562.00 0.033 45,100 348

Calculations & Significant Figures:The answer to a calculation involving measured numbers cannot have greater significance than any of the measurements!

Addition and Subtraction: The answer has the same precision as the least precise measurement.

Example: A graduted cylinder contained 25.5 ml of water. A glass marble was added to the cylinder and the volume reading increased to 33.2 ml. What was the volume of the marble?

Multiplication and Division: The answer has the same number of significant figures as the measurement with the fewest significant figures.

Example: The marble (from the previous example) has a mass of 22.0186 grams. What is it’s density?

Rules for rounding: •If the digit to be dropped is less than 5, simply drop it•If the digit to be dropped is 5 or greater, round up

Round to 2 significant figures:258.59 0.06617 182,540

Perform the following calculations involving measured numbers, express your answer to the proper number of significant figures:

a) 6.731 x 0.0021 =

b) 8.4 1.8 + 5.2

c) 120 0.0045 = (write the answer in scientific notation)

Scientific Notation: a convenient way of expressing large or small numbers

A number in Scientific Notation has 2 parts:

coefficient - a number between 1 and 10 it includes only significant figuresexponential term – a number expressed as x 10n

n = an integer (positive or negative)

Convert to scientific notation:47,000 0.00211

Convert to standard notation:5.442 x 103 8.25 x 10-5

1.23 x 10-34

Scientific Notation & Calculators:-enter the coefficient as you would for a regular number -press EXP or EE-enter the exponent

Examples:a. (9.41 x 1012) x (2.7722 x 10-5) =

b. (2.5 x 104) (6.8 x 106) =

Conversion Factors—Metric System:What does it mean? 1 cm = 0.01 meter

or 100 cm = 1 meter

Write the equality as a ratio:

A ratio can be used as a conversion factor.

Consider a meterstick:1 meter = 100 cmHow many cm are equal to 2.5 meters?

1 meter = 1000 mmHow many meters are equal to 650 mm?

Unit Conversion within the Metric System:•Start with the given measured number•What units are to be changed?•Find the relationship between units (equality)•Write as a ratio with the “old” unit in the denominator & the “new” unit in the numerator•Cancel the units•Multiply/divide the numbers•Record your answer to the proper number of sig. figs.

a. Convert 1.5x105 milliseconds (ms) to seconds

b. Convert 35 microliters (mL) to Liters

c. Convert 2130 decigrams (dg) to kilograms (kg)

Unit Conversion within the English System:a. Convert 349 inches to feet

English-to-Metric & Metric-to-English Conversions:

Example: Convert 128 lb to kiligrams

Example: Convert 36.5 inches to cm

Multistep conversions:•Start with the given measured number•What units are to be changed? (make a unit map)•Find the relationship between units for each step•Write each as a ratio with the “old” unit in the denominator & the “new” unit in the numerator•Write the conversion as a series of multiplication steps.•Cancel the units• Multiply/divide the numbers•Record your answer to the proper number of sig. figs.

Example: convert 9.85 Liters to gallons (given that 1 Liter = 1.057 qt; 1 gallon = 4 qt.)

Example: Convert 35 mi/hr to m/min (given that 1 mile = 1609 meters)

Example: A 150 lb. man requires a drug dosage of 2.5 mg/kg. How many milligrams of the drug should he take? (1 kg = 2.205 lb.)

Converting squared or cubed units:

1. Convert 0.25 m2 to cm2.

2. One side of a sheet of paper has an area of 93.5 in2.Convert this to square cm?

Density = mass

volume

Density = mass

volume

Example: A piece of metal has a mass of 78.12 g and a volume of 9.5 cm3. What is it’s density? What metal is it?

Metal Density (g/cm3) Mg 1.7 Al 2.7 Zn 7.1 Sn 7.3 Fe 7.9 Brass 8.4 Cu 8.9 Pb 11.4 Au 19.3 Pt21.1

Density Animationhttp://www.wiredchemist.com/anim-density

Example: A shiny gold-colored nugget has a mass of 26.5

grams and a volume of 3.4 cm3. Is it gold?

Example: Carbon dioxide has a density of 0.001963 g/ml. What is the mass of a 5.0Liter sample of CO2?

Example: An empty graduated cylinder has a mass of 215 grams. After filling it with liquid (946 ml) it is weighed again;

the mass of the cylinder + liquid is 1854 grams. What is the density of the liquid?

215 grams 1854 grams

Temperature - a measure of the intensity of heatTemperature Scales:• Celcius (C)• Fahrenheit (F)• Kelvin (K)

Conversions between temperature scales:

Converting from Celcius to Fahrenheit: A mixture of salt and water has a temperature of -5.0C. What is the temp on the Fahrenheit scale?

Converting from Fahrenheit to Celcius: A child has a temperature of 103.1F. What is the temp on the Celcius scale?

Converting from Celcius to Kelvin: On the planet Mercury, the average daytime temperature is 683 K. What is the temp on the Celcius scale?