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out units in dimensional analysis Will I m Mass n final Base Quantities and Units t Volume Use the measurements in the table below to determine the density of the object Mass of object (g) Initial Volume (water only, mL) Final Volume (water + object, mL) Density = Mass - Volume Volume final initial A sample of ethyl alcohol has a mass of 25.3 g. The density of ethyl alcohol is 0.789 g/mL. Find the volume of this sample. Density = => Volume = Toxic Mass Volume Quantity Symbol (found in equations) initial Q3&s T * Density Units: kg/m³ g/cm³ (<-solid) g/mL (<-liquid) kg/L Derived Quantities and Units Corrosive 4.80 g 7.2 mL 9.3 mL 4.80 g 9.3 mL 7.2 mL Mass Density SI Unit Name meter kilogram mole second Kelvin 25.3 g 0.789 g/mL 4.80 g 2.1 ml m SI Unit Abbreviation kg mol S k = 2.3 g/mL = 32. 1 mL Def: all other quantities are combinations made by multiplying or dividing base quantities and their units Derived Quantity Area Volume Density Velocity/speed Concentration Molar mass PREFIX SYMBOL NUMBER O SI Unit Prefixes T M ■ Steps Units combined O M*M M*M*M O g/M*M*M O m/hr g/volume k h Quantity Symbol (found in equations) A V 1012 109 106 10³ 10² 10¹ D V M (Molarity) 9 (grame) m (meters) da Base unit (liters) O 0.150 m 15.0 cm Example (Big to Small) O 0.150 km ? cm deci P centi 10⁰ 101 10 SI Unit Abbreviation m ² m³(solid) L(liquid) g/ml or g/cm³ km/hr mol/L g/mol milli E micro P 10-3 10- nano n O Subtract exponents O Move decimal that amount in the direction of the wanted unit Example (Base to Big/Small) O 0.150 m ? cm cm³= mL To Remember ● The Great Man king henry's daughter beth died drinking chocolate milk until nine pm. EASY WAY 10-9 pico p 10-12 0 10 -> 10 , so 0 (-2) = 2, centi is wanted unit So move decimal 2 places to the right (towards centi) 3 -2 10 -> 10 , so 3 - (-2) = 5, so move decimal 5 places to the right (towards centi) 0.150 km = 15000 cm O Conversion factors: Distance Time Mass ● Example (Small to Big) O 384.0 mg = ? dg -1 -3 10 <- 10 , so (-1)-(-3) = 2, so move decimal 2 places to the left (towards deci) 384.0 mg = 3.840 dg Volume O O ● O 2. Multi step DA Dimensional Analysis (DA) ■ Def: going from one unit to another unit by multiplying conversion factors (aka ratios) and canceling out the repeated units. 1. Single step DA Example O Example O O FOR REFERENCE - know the basics 3. Double Unit DA Example O 1 ft = 12 in 1 yd = 3 ft 1 mi = 5280 ft 1 mi = 1760 yd 1 yard = 0.9144 m 1 foot = 0.3048 m 1 inch = 2.54 sm* A person who is 5.75 feet tall is how many inches? 5.75 ft x = 69.0 inches 12 inch 1 ft How many kg in 261 g? 261 g X 1kg 10 9 4. Cubed Unit DA 60 seconds 1 minute* 60 minutes = 1 hour* 1440 minutes = 24 hours = 1 day* 75 Km 1 hr 1 kilogram = 2.2 pounds 1 cm³ = 1 mL* How many seconds are in 3 days? 24 hrs X 1 day 60 minutes 1 hr 3 days X How many mg in 498.82 cg? cg->mg 1 cg = 10-²g 1 mg = 10 ³g 10-2-(-3) = 101 cg > mg 1 cg = 10¹ mg 498.82 cg X = 261 × 10 -³kg = 0.261 kg 10 mg 1 cg 1 mi 1.61 Km If my car is going 75 Km/hr, how many miles/sec is it going? (1 mi = 1.61 Km). X X X = 4988.2 mg 1 hr 60 mins 1 minute 60 secs X = 259200 seconds = 300000 seconds 1 min 60 secs = 0.17944 miles/sec O O O ● Example O Examples • Significant figures (Sig Figs) O Def: Significant figures (aka Sig Figs) include all known digits plus one estimated digit (the more DIGITS, the more PRECISE; indicates level of precision) Rules ■ Adding or subtracting ● 70,000. 70,000.0 70,000 0.0077 0.00770 77,077 70,780 12 L 12 beakers O ■ All non-zero digits are significant I "Sandwiched" zeros are significant ■ Trailing zeros are significant if there is a decimal point ■ Leading Zeros are NOT significant Adding and Subtracting ● 5.93 cm³ is how many m³ ? 3 5.93 cm X 1m 100 cm ■ Multiplying or Dividing ● 8.3010 *10-3 3.40 *106 1m 100 cm Round to least number of decimal points Example O X 31.7 g + 6.9 g = 38.6 g O 1895 g - 322.1 g = 1572.9 g = 1573 g Round to least number of sig figs Example O 5 sig figs 6 sig figs 1 sig figs X 2 sig figs 3 sig figs 5 sig figs 4 sig figs 2 sig figs 2 sig fig or infinite 1m 100 cm 5 sig figs 3 sig figs 4.20 cm x 15.04 cm x 19.55 cm = 1264.3375= 1260 cm³ -6 3 = 5.93 x 10 m Scientific Notation O Def: Scientific Notation involves multiplying a number between 1 and 10 by the power of ten O Rules ■ Adding or subtracting ■ Multiplying or Dividing Multiplication O O Examples ● Make the exponents the same before adding or subtracting Example O 0.000045 23,000 105 ● 2.0*10+5.5*10 2=2.0*10 4 + 0.055*10 4-2.055*10 4-2.1*104 O O Multiply first factors Add the exponents Example ■ Division O O O 300,000,000 3 *108 4.5 *10-5 2.3 *104 Divide the first factors Subtract the exponents Example ■ = 2.5 * 10 5.0 =0.5 * 10³ =5.0* 10² ● Adjust if needed so number is between 1 - 10 Use scientific Notation when you write more than 3 zeros, or if it's needed to represent correct number of sig figs 2.5*10 17x 5.0*10 14 =(2.5x5.0)*10 17+14 = 12.5*10 31 = 1.25*10 32 1.05 *10³ 2.5*10¹7 5.0*10¹4 17-14 . Precision and Accuracy O Def: Precision is how close a set of data are to each other O Def: Accuracy is how close the measured value is to the true value O Lab equipment & precision ■ Graduated cylinder is more precise than beaker Equipment with mm is more precise than cm O Examples ■ Percent Error = ■ A measurement was taken three times. The correct measurement is 32.0 g. Circle whether each set of measurements is accurate, precise, both, or neither ● 32.1 g, 32.2 g, 31.9 g (both) ● 38.2 g, 67.5 g, 98.0 g (neither) 78.5 g, 78.6 g, 78.7 g (precise) Accurate Precise Percent Error ● Def: indicates level of Accuracy ● Percent Error = Not Accurate Precise • Measurement Accurate Not Precise Calculated Value - Actual Value Actual Value Example O An experiment was taken of 10.4mL and the actual measurement Not Accurate Not Precise was 9.7 mL. Determine the percent error |Calculated Value - Actual Value 100 = Actual Value o Taking Measurements 10 mm 1 cm * 100 10.4 mL-9.7ml 100 = 0.7 9.7 9.7 mL ● 12 pencils per box * 3 boxes = 36 pencils O Def: A measurement consists of two parts, a number and a unit (SI) O Measured Numbers: numbers found by measuring with an instrument always has an estimated digit (Round answer using sig figs) *100= 7.2% O Exact Numbers: counted objects were not measured and do not use sig fig rules (NO Round answer using sig figs) ■ Conversion factors are exact numbers and are NOT used to determine sig fig rounding ■ Example cm 2 13 13 -12 37 7 I E-35 2 21 5 678 60 50 ME 14 15 I 16 9.5 cm 5.30 cm or 53.0 mm 1.30 mL 56.0 mL 14.00 cm 12.45 mL 36.00 mL . Classification of Matter O Matter: Anything that has mass O Pure substance: has constant composition Element: 1 type of atom (can be either atoms or molecules) ● Molecule: 2+ atoms chemically combined Compound: 2+ different types of elements combined in a fixed ratio (can only be molecules) Mixture: has variable composition Example: ● ● Homogenous (aka solution): same; uniform ■ Element Heterogenous: different; not uniform - layers O O ■ Compound O ■ Mixture O EX: wine, brass, air, ketchup, mustard, water with food coloring Solution: made of a solute and solvent (H₂O) ■ EX: salt water O Atoms of an element EX: cereal in milk, ice in soda, pizza, density column, italian salad dressing, Suspension: mixtures of a liquid and solid that does not dissolve ■ EX: oil and vinegar, sand and water Colloid: Mixtures of fine solids in a liquid medium EX: Fog ■ ● Molecules of an element Mixture of elements Mixture of compounds Solid O Examples: ■ States ■NO+H₂O₂ or HF + NO Mixture of Two compounds N₂+Br₂ Mixture of Two elements ■ O₂+NO₂ Mixture of an Element and a Compound ● Mixture of elements and compounds N₂ Pure substance, an element NaCl or KCIPure substance, a compound Liquid Gas molecule no Element (on periodic table) no Pure substances Can be separated by chemical means/? yes Compound (water) Matter Purity Can be separated by physical means? Colloid yes Impure substances (Mixtures) no uniform? Heterogenous physical Suspension yes Homogenous (aka solution) Changes chemical ● Physical properties & Chemical properties (haven't learned yet) o Physical properties: a characteristic that can be observed without changing the identity (nature) of the matter O ■ Intrinsic: observation of a substance that are dependent on the composition and do not change sample size • Density, color, luster, malleable, ductility, water stability, melting and boeing ponts, conductivity, odor ■ Extrinsic: depends on the number, type and condition of particles present in sample ● Mass, volume, temp, pressure Chemical properties: describe the behavior of a substance in the presence of another substance ■ Bubbles in acid, flammability, forms chorides • Physical change & Chemical change O A physical change: involves a change in one or more physical properties but no change in composition ■ heating/cooling, changing a phase, dissolving, changing the volume/shape of object, changes concentration, filtering, boiling O A chemical change (aka reaction): transforms of substance into one or more new substances ■ Change in temperature (exothermic - gives off heat, endothermic - absorbs heat), release of gas, formation of a solid (precipitate - solid that comes out of a solution), change in color, change in odo, production of light Changes Appearance or phase Physical change conductivity,odor changes? Intrinsic Extrinsic (Depends on composition) (depends on sample size) Nature or composition Density,color, luster,malleable, mass, volume,temp.pressure water solubility,melt/boil point, .phase Chemical change Bubbles,gas,odor/color change,temp, fire Physical Change Not necessarily followed by a chemical change Chemical Change Followed by a physical change NOT TO BE CONFUSED WITH PHYSICAL/CHEMICAL PROPERTY • Phases of Matter O Matter exist in three states (phases) 1. Solid: definite volume, definite shape. If you put solid water cubes in a cup, they will still be cubed, not cup shaped. Usually, solids are denser than liquids (water is an exception). Particles that are in solid state are "stuck together" because of intermolecular forces (force/attraction between molecules). They have the lowest kinetic and potential energy of any phase ⠀⠀⠀⠀ 2. Liquid: definite volumes, indefinite shape. If you pour liquid water into a cup, the liquid water will be cup shaped. But it wont take up the whole cup, just the amount of water that was originally there. Usually, these are less dense than solids. There are intermolecular forces that keep the particles together, but they are trading places quickly. They have medium kinetic and potential energy. 3. Gas: indefinite volume, indefinite shape. If you take gaseous water and put it into a room, it will take up the whole room and be room shaped. These have the lowest density. These particles have overcome their intermolecular forces and have a lot of energy. They move in one straight line until they collide (elastically) with another particle and change direction like a bouncy ball. They have the highest kinetic and potential energy. Temperature (°C) Temperature (°C) 100 (boling point) 0 imeting point) Solid KE: constant PE: increases KE: increases PE: constant Melting (fusion) sublimation Liquid KE: constant PE: increases Heating Curve -Freezing (solidification) KE: increases PE: constant Boiling (vaporization) condensation Time increasing Gas KE: increases PE: constant Temperature(CC) Temperature (°C) 100 0 Gas KE: decreases PE: constant KE: constant PE: decreases Boiling (vaporization) condensation Cooling Curve deposition Liquid Time increasing KE: decreases PE: constant ↑ KE: constant PE: decreases Melting (fusion) Freezing →→ (solidification) Solid KE: decreases PE: constant • Heating and Cooling curve o Heating Curve: Temperature of a substance as heat is added over time o Freezing point of water is 0°C o Boiling point of water is 0°C o They are the same b/c ● ■ Within a phase, as heat is added, the temperature increases ■ Heat can cause a substance to change from solid to liquid & liquid to gas ■ During a phase change the temperature is the same; NO CHANGE Temperature is the average kinetic energy of the molecule o o So, when the temperature increases the molecules move faster o Energy of movement is kinetic (movement) or potential (position) energy ■ In a phase change the distance between molecules changes ■ When molecules spread out, potential energy increases ■ Potential energy changes do NOT affect the temperature (or kinetic energy) Energy Equation o q=mcAT q m C (or s) AT heat mass Specific heat capacity J q = (g)-(°C) cancel out and get J g 9°C Change in temperature °C (Tfinal - Tinitial) o Memorize equations for each phase & See ws #1.13 for problems to solve (2) dal Temperature (°C) Temperature (°C) Temperature (°C) Temperature (°C) Heating Curve Calculations for Water Solid Sold Solid Liquid AT ice Q = mc₁ Energy (1) Liquid • Q = mAH fus Energy () Liquid Energy (1) Liquid 038 Liquid Energy (1) Gas duckingscencebombs.wordpress.com Cice=2.108 Gas Q = mcwater AT Energy (1) duckingsciencebombs.wordpress.com He=334 풍 Gas duckingsciencebombs.wordpress.com = 4.184 Cwater Q = mAH vap Gas duckingsciencebombs.wordpress.com 4Hvap = 2257 I Gas Q=msteam 4 duckingsciencebombs.wordpress.com Csteam = 1996 4T Temperature (°C) Latent Heat of Fusion H=nA q = mc₂AT Heating Curve Latent Heat of Vaporization H=nAp q= mc₂AT Time increasing q=mc,AT