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Chemistry is where you learn 2 + 2 = 10 or something. —Dennis Rodman Chemistry Math With Chemistry-specific graphs

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Variables Independent Independent Variable “I” change Variable “I” change Graphed on “x” axis Graphed on “x” axis Dependent Dependent Variable which “Depends” on independent variable Variable which “Depends” on independent variable Tested during experiment Tested during experiment Graphed on “y” axis Graphed on “y” axis Control Control Variables you control so they do not change and mess up your experiment Variables you control so they do not change and mess up your experiment Never graphed Never graphed

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Graphing Variables Slope = rise/run Slope = mass/volume Slope = density We don’t graph just to graph; the graph and the data tells us something meaningful.

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Line of Best Fit Real data never (almost never) falls exactly on the line! The line is an “average” Once you know the line of best fit, you can use it to predict other values. The line represents the data.

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We never “connect the dots” in a graph. Don’t connect the dots. The line of best fit doesn’t have to go through ANY of the data points. However, some points might be exactly on the line. Ideally the points above the line = the points below the line

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y = mx + b To graph without your calculator, you need 2 points to define a line. To graph without your calculator, you need 2 points to define a line. Use the y-intercept for the first point (x = 0 when y = b) Use the y-intercept for the first point (x = 0 when y = b) Set y = 0 to find the second point (x = − b/m when y = 0). Set y = 0 to find the second point (x = − b/m when y = 0). Use a RULER to draw your lines! Use a RULER to draw your lines!

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Helpful Formulas Unit 1 Density Density D = m/V D = m/V Temperature Conversions Temperature Conversions K = °C + 273 (note K does not have a ° symbol) K = °C + 273 (note K does not have a ° symbol) °C = K − 273 °C = K − 273 °C = (°F − 32) ÷ 1.8 °C = (°F − 32) ÷ 1.8 ΔT = T 2 − T 1 orΔT = T final − T initial ΔT = T 2 − T 1 orΔT = T final − T initial

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Directly Proportional Directly proportional means that as one goes up, the other goes up too. Directly proportional means that as one goes up, the other goes up too. For matter, kinetic energy (KE) is directly proportional to Kelvin temperature (K) For matter, kinetic energy (KE) is directly proportional to Kelvin temperature (K) If you graph these variables, you will get a straight line with a POSITIVE slope. If you graph these variables, you will get a straight line with a POSITIVE slope.

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Inversely Proportional Inversely proportional means that as one goes up, the other goes down (and vice versa). Inversely proportional means that as one goes up, the other goes down (and vice versa). For any gas, pressure (P) is inversely proportional to volume (V) For any gas, pressure (P) is inversely proportional to volume (V) If you graph these variables, you will get a straight line with a NEGATIVE slope. If you graph these variables, you will get a straight line with a NEGATIVE slope.

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Let’s Do Some Math! Density Density If a marble weighs 10.0 g and has a volume of 5.0 mL what is the density of the marble? Use correct units. If a marble weighs 10.0 g and has a volume of 5.0 mL what is the density of the marble? Use correct units. Another marble with the same density has a mass of 15.0 g. What is the volume of that marble? Use correct units. Another marble with the same density has a mass of 15.0 g. What is the volume of that marble? Use correct units. A different marble has a density of 3.0 g/mL. If that marble has a volume of 10.0 mL, what is the mass of that marble? Use correct units. A different marble has a density of 3.0 g/mL. If that marble has a volume of 10.0 mL, what is the mass of that marble? Use correct units.

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Let’s Do Some Math! Temperature Temperature If it is 104°F in Fredericksburg, what is the temp in °C? If it is 104°F in Fredericksburg, what is the temp in °C? What is the temp in K? What is the temp in K? If it is -40°F in Fredericksburg, what is the temp in °C? If it is -40°F in Fredericksburg, what is the temp in °C? What is the temp in K? What is the temp in K? If a sample of matter is 298K, what is the temp in °C? If a sample of matter is 298K, what is the temp in °C?

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Helpful Formulas Unit 1 How to Figure out your Quiz Grade: How to Figure out your Quiz Grade: Your Grade ÷ 25 × 100 = SCORE Your Grade ÷ 25 × 100 = SCORE Calculating Error Calculating Error Error = |Your Number − True Number| Error = |Your Number − True Number| % Error = Error ÷ True Number × 100 % Error = Error ÷ True Number × 100

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Let’s Do Some Math! Error Analysis Error Analysis The accepted value for the density of a penny is 7 g/cm 3. The accepted value for the density of a penny is 7 g/cm 3. You measure 5 pennies and calculate the density as You measure 5 pennies and calculate the density as 7.50 g/cm 3 7.50 g/cm 3 7.20 g/cm 3 7.20 g/cm 3 6.90 g/cm 3 6.90 g/cm 3 7.40 g/cm 3 7.40 g/cm 3 6.90 g/cm 3 6.90 g/cm 3 What is the average density? What is the error? What is the percent error? What is the average density? What is the error? What is the percent error?

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Let’s Do Some Math! What is the average density? 7.18 g/cm 3. What is the average density? 7.18 g/cm 3. What is the error? |7.18 − 7| = 0.18 g/cm 3. What is the error? |7.18 − 7| = 0.18 g/cm 3. What is the percent error? 0.18 ÷ 7 x 100 = 2.57142857 What is the percent error? 0.18 ÷ 7 x 100 = 2.57142857 You should record your final answer as 2.6% after rounding. You should record your final answer as 2.6% after rounding.

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Helpful Formulas Unit 1 SI Units and Conversions SI Units and Conversions Need to know what these prefixes mean Need to know what these prefixes mean Kilo (k)ex 1 kg = 1000 g Kilo (k)ex 1 kg = 1000 g Centi (c)ex 100 cm = 1 m Centi (c)ex 100 cm = 1 m Milli (m)ex 1,000 mL = 1 L Milli (m)ex 1,000 mL = 1 L Micro (μ)ex 1,000,000 μg = 1 g Micro (μ)ex 1,000,000 μg = 1 g Nano (n)ex 1,000,000,000 nm = 1 m Nano (n)ex 1,000,000,000 nm = 1 m

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Dimensional Analysis The base unit can change, but the prefix means the same thing The base unit can change, but the prefix means the same thing 100 cm = 1 m 100 cm = 1 m 100 cg = 1 g 100 cg = 1 g 100 cL = 1 L 100 cL = 1 L Centi ALWAYS means that there are 100 divisions of the base unit. Centi ALWAYS means that there are 100 divisions of the base unit.

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Let’s Do Some Math! Convert 45 cm to mm? Convert 45 cm to mm? To do this you need to know the conversion factors To do this you need to know the conversion factors 100 cm = 1 m 100 cm = 1 m 1,000 mm = 1 m. 1,000 mm = 1 m. First step: convert cm to meters. First step: convert cm to meters. Second step: convert meters to mm. Second step: convert meters to mm. To find the answer: cancel out units until you have the units you are looking for. To find the answer: cancel out units until you have the units you are looking for.

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Let’s Do Some Math! Convert 45 cm to mm? Convert 45 cm to mm? 45 cm × 1 m × 1,000 mm = ? 45 cm × 1 m × 1,000 mm = ? 100 cm 1 m 100 cm 1 m 45 cm × 1 m × 1,000 mm = 450 mm 45 cm × 1 m × 1,000 mm = 450 mm 100 cm 1 m 100 cm 1 m

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Let’s Do Some Math! Convert 345 μg to kg? Convert 345 μg to kg? Convert 14.6 mL to L? Convert 14.6 mL to L? Convert 1 hour to seconds? Convert 1 hour to seconds? Convert 100 cm 3 to mL Convert 100 cm 3 to mL Convert 500 nm to mm? Convert 500 nm to mm?

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Let’s Do Some Math! Answers: Answers: Convert 345 μg to kg? 3.45 x 10 -7 kg Convert 345 μg to kg? 3.45 x 10 -7 kg Convert 14.6 mL to L? 0.0146 L Convert 14.6 mL to L? 0.0146 L Convert 1 hour to seconds? 3,600 sec Convert 1 hour to seconds? 3,600 sec Convert 100 cm 3 to mL 100 mL Convert 100 cm 3 to mL 100 mL Convert 500 nm to mm? 5 x 10 -4 mm Convert 500 nm to mm? 5 x 10 -4 mm

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Let’s Do Some Math! Answers: Answers: Convert 345 μg to kg? 3.45 x 10 -7 kg Convert 345 μg to kg? 3.45 x 10 -7 kg Convert 14.6 mL to L? 0.0146 L Convert 14.6 mL to L? 0.0146 L Convert 1 hour to seconds? 3,600 sec Convert 1 hour to seconds? 3,600 sec Convert 100 cm 3 to mL 100 mL Convert 100 cm 3 to mL 100 mL Convert 500 nm to mm? 5 x 10 -4 mm Convert 500 nm to mm? 5 x 10 -4 mm

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Some Other Chemistry Graphs Phase Diagrams Heating Curves Radioactive Decay Reaction Progress Not all chemistry graphs will be straight lines. But most will. Let’s see some distinctive ones which aren’t.

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Phase Diagram for H 2 O A phase is a “state” of matter. Solid phase Liquid phase Gas phase We don’t “do” plasma. Critical Point Triple Point

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Phase Diagram The triple point is the only point on the graph where all 3 phases are at equilibrium. The critical point is the END of the graph. Critical Point Triple Point

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Phase Diagram The lines show the pressure/temperature points where the phase changes from one to the other. When P = 1 atm, you can read the MP and BP right off the graph. Boiling Point Melting Point

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Heating Curve for H 2 O Solid between A&B, liquid between C&D, gas between E&F

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Heating Curve for H 2 O Melts between B & C Boils between D & E Why doesn’t the temp rise when water is melting?

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Radioactive Decay After 1 half life, 50% remains. After 2 half lives, 25% remains. HALF of whatever is left decays during each half life.

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Rxn Progress Rxn Progress The reaction is exothermic (products have less energy than reactants). Enzyme = biological catalyst. Rxn = abbreviation for reaction

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Rxn Progress This reaction is endothermic. Products are higher than reactants (have more potential energy).

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Chemistry: SI Units & Conversions

Chemistry: SI Units & Conversions

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