Measurements & Calculations Unit 3 Measurements & Calculations

Scientific Notation: Used to write very large or very small numbers Expressed as the product of 2 factors Mantissa: Express the significant digits as a number between 1 and 10, but not 10. Power of 10

Examples of use The mass of one proton is 1.673 x 10-24 g or 0.000000000000000000000001673 g The number of copper atoms in one mole of copper is 6.02 x 1023 atoms or 602,000,000,000,000,000,000,000 atoms

532 = 20,120 = 0.385 = 0.006904 = 5.32 x 102 2.012 x 104 3.85 x 10-1 6.904 x 10-3

Uncertainty in Measurements When making measurements, record all the certain numbers plus the first uncertain number.

50 mL beaker 25 mL graduated cylinder 10 mL volumetric pipet

Significant Digits are all digits which are certain, plus one uncertain digit. Red not significant Green is significant 0.3 zero for cosmetic is NOT significant 250. or .0025 zero to locate the decimal is NOT significant 102 or 0.00503 zero between non-zero numbers is significant 0.002500 zero to the right of decimal is significant

How many significant digits? 7.5 x 103 6840 0.007802 956,000.2 0.0180

Multiple or division: answer has same number of significant figures as least precise measurement used in calculation Addition or subtraction: answer has same number of decimal places as least precise measurement used in calculation In a series of calculation, carry the extra digits through to the final result, then round!

Metric System: System international Measurement system based on 10. Length: meter The distance light travels in a vacuum in 1/299,792,458 s Volume: liter A cube that is 10 cm per side. 1 cm3 = 1 mL Mass: kilogram 1 gram is the mass of 1 mL of H2O at 4 oC Time: second Temperature: Celsius or Kelvin

You need to know these and how to convert between them! Metric Prefixes You need to know these and how to convert between them!

Dimensional Analysis Convert 581 cm to m Process used to convert from one unit of measurement to another unit of measurement. Multiply by a fraction equal to 1, which will eliminate one unit and substitute in another unit. Convert 581 cm to m 581 cm 1 1 m 100 cm = 5.81 m x

The closeness of measurements to the accepted true value. Precision The reproducibility in measurements. Coming up with similar results again and again. Accuracy The closeness of measurements to the accepted true value.

Temperature Conversions O C + 273 = K O C = 5/9 (o F – 32 ) O F = 9/5 o C + 32

Density = mass/volume (grams/mL) or ( grams /cm3 ) Hydrogen = 0.000069 g/mL Maplewood = 0.7 Glass = 2.6 Gold = 19.3 Diamond = 3.5 Osmium = 22.5 Silver = 10.5 Ice H2O = 0.9 Lead = 11.4 Liquid H2O = 1.0 Mercury = 13.6

Demo D4 - Polyethylene (2 white spheres) .91 g/mL D2 – Polyethylene (yellow bead) .95 ABS (black rod) 1.04 D6 – Polystyrene (orange sphere and red bead) 1.06 Nylon (green rod) 1.15 Nylon (blue sphere) 1.16 Acrylic (colorless sphere and small red ball) 1.18 Cellulose acetate (green sphere) 1.28 D3 – PVC – 1 (clear rod) 1.40

Satellite Antenna Hydraulic Bladder

A crown supposedly made of pure gold has a mass of 1,650 g, and a volume of 180 mL. What is the density? Is it pure gold? Density of gold = 19.3 g/mL

Density = mass/volume (units of g/mL or g/cm3) A block of wood has a mass of 2.52 Kg. What is the density of the wood? 51 mm 1.08 m 6.2 cm

Lower density Numbers become less! The hydrometer sinks more. Density of H2O Each small line, is .01 Higher density Numbers become greater! The hydrometer floats higher.

c. Fill in the following and calculate: Measure density = _______________ gram solution/mL of solution b. Nutritional label ___________grams sugar per ____________mL solution c. Fill in the following and calculate: (______ grams sugar /_______mL solution)( 1 mL solution/______g of solution)= ______ g sugar per g of beverage d. Calculate % sugar = (________ g sugar per g of beverage)(100) e. Calculate the percent error in the experimental determination of the sugar content using the following equation: Percent error = l calculated value – experimental value l x 100 calculated value

Review 1. a) 2,560 mL b) .0936 Kg c) .7139 m 5. .717 g/mL 2. a)1.1 x 104 6. Volume = 143.6 cm3 b)4.31 x 1015 density = 1.04 g/cm3 3. No, it will not float! 4. a) 22 oC b) 288 K c) 20 oC