Physical Science: Tables & Formulas SI Base Units Base Quantity Amount of substance Electric current Length Luminous intensity Mass Time Temperature Unit Name mole ampere meter candela kilogram second Kelvin Unit Symbol Mol A M Cd Kg S K SI Derived Units Derived Quantity Name (Symbol) Area Volume Speed/velocity Acceleration Frequency Force Pressure, stress Energy, work, quantity of heat Power Electric charge Electric potential difference Electric resistance Square meter (m2) Cubic meter (m3) Meter per second (m/s) Meter per second squared (m/s2) Hertz (Hz) Newton (N) Pascal (Pa) Joule (J) Watt (W) Coulomb (C) Volt (V) Ohm (Ω) Expression in terms of other SI units Expression in terms of SI base units N.m2 N. m J/s -W/A V/A s-1 m . kg . s-2 m-1 . kg . s-2 m2 . kg . s-2 m2 . kg . s-3 s.A m2·kg·s-3·A-1 m2·kg·s-3·A-2 Prefixes used to designate multiples of a base unit Prefix tera giga mega kilo centi milli micro Nano pico Symbol T G M k c m u n p Meaning trillion billion Million Thousand One hundredth One thousandth One millionth One billionth One trillionth Multiple of base unit 1, 000, 000, 000, 000 1, 000, 000, 000 1, 000, 000 1, 000 1/100 or .01 1/1000 or .001 1/1000000 or .000001 1/1000000000 or .000000001 1/1000000000000 or.000000000001 Scientific Notation 1012 109 106 103 10-2 10-3 10-6 10-9 10-12 In general, when converting from base units (m, l, g, etc) or derived units (m2,m3, m/s, Hz, N, J, V, etc) to a multiple greater (kilo, mega, giga, or tera) than the base or derived unit- then divide by the factor. For example: 10m = 10/1000km = 1/100 km = .01km. Page 1 of 10 When converting from base units or derived units to a multiple smaller (centi, milli, micro, nano) than the base or derived unit- then multiply by the factor. For example: 10m = 10 x 100cm = 1000cm. Subatomic Particles Particle Proton Neutron Electron Charge +1 0 -1 Mass 1 1 0 Location nucleus nucleus Outside the nucleus Common Cations Ion Name (symbol) Lithium (Li) Sodium (Na) Potassium (K) Rubidium (Rb) Cesium (Cs) Beryllium (Be) Magnesium (Mg) Calcium (Ca) Strontium (Sr) Barium (Ba) Aluminum (Al) Ion Charge 1+ 1+ 1+ 1+ 1+ 2+ 2+ 2+ 2+ 2+ 3+ Common Anions Element Name (symbol) Fluorine Chlorine Bromine Iodine Oxygen Sulfur Nitrogen Ion Name (symbol) Fluoride Chloride Bromide Iodide Oxide Sulfide Nitride Ion Charge 1111223- Common Polyatomic Ions Ion Name Carbonate Chlorate Cyanide Hydroxide Nitrate Ion Formula CO32ClO3CNOHNO3- Ion Name Nitrite Phosphate Phosphite Sulfate Sulfite Ion Formula NO2PO43PO33SO42SO32Page 2 of 10 Prefixes for Naming Covalent Compounds Number of Atoms 1 2 3 4 5 Prefix Mono Di Tri Tetra penta Number of Atoms 6 7 8 9 10 Prefix Hexa Hepta Octa Nona deca Types of Chemical Reactions Type of reaction Combustion Synthesis Decomposition Single Replacement Double Replacement Generalized formula HC + O2 H2O + CO2 A + B AB AB A + B A + BC AC + B AX + BY AY + BX Specific Example 2C2H6 + 7O2 6H2O + 4CO2 2Na + Cl2 2NaCl 2H2O 2H2 + O2 2Al + 3CuCl2 3Cu + 2AlCl3 Pb(NO3)2 + K2CrO4 PbCrO4 + 2KNO3 The Effects of Change on Equilibrium in a Reversible Reaction (Le Châtelier’s Principle) Condition Temperature Pressure Concentration Effect Increasing temperature favors the reaction that absorbs energy (endothermic) Increasing pressure favors the reaction that produces less gas. Increasing conc. of one substance favors reaction that produces less of that substance Common Acids Acid Hydrochloric (muriatic) acid Nitric acid Sulfuric acid Acetic acid Citric acid Formic Formula HCl HNO3 H2SO4 CH3COOH C6H8O7 HCOOH Strength strong strong strong weak weak weak Formula KOH NaOH Ca(OH)2 NH3 Strength strong strong strong weak Common Bases Base Potassium hydroxide (potash) Sodium hydroxide (lye) Calcium hydroxide (lime) ammonia Page 3 of 10 pH scale Strong acids more acidic 0 1 2 3 4 weak acids 5 6 Neutral Weak bases 7 8 9 More basic 10 11 12 strong bases 13 14 Types of Nuclear Radiation Radiation Type Alpha particle Beta particle Gamma Symbol 4 2 He 0 -1 e γ Charge +2 -1 0 Nuclear Equation 225 Ac 87 221Fr + 2 4He 89 14 14 0 6 C 7 N + -1 e n/a Equations Units: g/cm3 or g/mL Density = mass ÷ volume (D = m/v) Rearranged: mass = Density x Volume Units: grams or Volume = mass ÷ density Units: cm3 or mL Moles = mass (grams) x Molar Mass (grams / mol) Molar Mass = atomic mass in grams Energy = mass x (speed of light)2 E = mc2 Units: joules Speed = distance ÷ time Units: meters / second v=d÷t Rearranged: distance = speed x time Units: meters time = distance ÷ speed Units: seconds Momentum = mass x velocity p=mxv Units: kg Acceleration = (final velocity - initial velocity) ÷ time . m/s a = Δv ÷ t Units: meters / (second)2 Rearranged: Δv = acceleration x time Units: meters/second time = Δv ÷ a Units: seconds Force = mass x acceleration F=mxa Units: kg . m/s2 or Newtons (N) Rearranged: mass = Force ÷ acceleration Units: g or kg acceleration = Force ÷ mass Units: meters / (second)2 Page 4 of 10 Weight = mass x gravity (9.8 m/s2 ) Work = Force x distance Units: kg . m/s2 or Newtons (N) W=Fxd Units: Joules (J) Rearranged: Force = Work ÷ distance Units: Newtons distance = Work ÷ Force Units: meters Power = Work ÷ time P=W÷t Units: J/s or Watts (W) Rearranged: Work = Power x time Units: Joules (J) time = Work ÷ Power Units: seconds (s) Mechanical Advantage = Output Force ÷ Input Force (Resistance Force ÷ Effort Force) or Mechanical Advantage = Input Distance ÷ Output Distance (Effort Distance ÷ Resistance Distance) Gravitational Potential Energy = mass x gravity (9.8 m/s2) x height Joules Rearranged: m = GPE ÷ (g . h) h = GPE ÷ (m . g) Kinetic Energy = ½ mass x (velocity)2 KE = .5 mv2 Rearranged: m = 2KE ÷ v2 v= GPE = m x g x h Units: Units: Joules Efficiency of a Machine = (Useful Work Output ÷ Work Input) x 100 Temperature Conversions Celsius-Fahrenheit Conversion: Fahrenheit temperature = (1.8 x Celsius temperature) + 32.00 F = 1.8 (C) + 320 Celsius temperature = (Fahrenheit temperature – 32) ÷ 1.8 C = (F – 32) ÷ 1.8 Celsius-Kelvin Conversion: Kelvin = Celsius + 273 Celsius = Kelvin -273 Page 5 of 10 Specific Heat Equation Energy = mass x Specific Heat Value x E=m.c.Δt change in temperature Rearranged: mass = Energy ÷ (c x Δ T) Units: kg Units: Joules Δ T = Energy ÷ (c x mass ) Units: K or 0C Wave Speed Equation v=fxλ Wave’s Speed = frequency x wavelength Rearranged: Frequency = Wave Speed ÷ wavelength Wavelength = Wave Speed ÷ frequency Units: m/s f=v÷λ Units: Hertz λ=v÷f Units: meters / second Speed of light (in a vacuum) = 3.0 x 108 m/s (300,000,000 m/s) Speed of Sound (in air at 25 0C) = 346 m/s Speed of Sound (in water at 25 0C) = 1490 m/s Speed of Sound (in iron at 25 0C) = 5000 m/s Ohm’s Law Equation Current = Voltage ÷ Resistance I=V/R Rearranged: Voltage = Current x Resistance Resistance = Voltage ÷ Current Units: Amperes (A) V=IxR Units: Volts (V) R=V/I Units: Ohms (Ω) Electric Power Equation Power = Current x Voltage Variations: P = I2 x R P=IxV Units: watts (W) or Kilowatts (kW) P = V2 / R Rearranged: Voltage = Power ÷ Current V=PxI Units: Volts (V) Current = Power ÷ Voltage I=P÷V Units: Amperes (A) Page 6 of 10 Electromagnetic Spectrum: Relates the energy, frequency and wavelength of various types of electromagnetic waves (radio, TV, micro, infrared, visible, ultraviolet, X-ray, and gamma). As energy and frequency increase the wavelength decreases. Page 7 of 10 Page 8 of 10 AM radio - 535 kilohertz to 1.7 megahertz Short wave radio - bands from 5.9 megahertz to 26.1 megahertz Citizens band (CB) radio - 26.96 megahertz to 27.41 megahertz Television stations - 54 to 88 megahertz for channels 2 through 6 FM radio - 88 megahertz to 108 megahertz Television stations - 174 to 220 megahertz for channels 7 through 13 Garage door openers, alarm systems, etc. - Around 40 megahertz Standard cordless phones: Bands from 40 to 50 megahertz Baby monitors: 49 megahertz Radio controlled airplanes: Around 72 megahertz, which is different from... Radio controlled cars: Around 75 megahertz Wildlife tracking collars: 215 to 220 megahertz MIR space station: 145 megahertz and 437 megahertz Cell phones: 824 to 849 megahertz New 900-MHz cordless phones: Obviously around 900 megahertz! Air traffic control radar: 960 to 1,215 megahertz Page 9 of 10 Global Positioning System: 1,227 and 1,575 megahertz Deep space radio communications: 2290 megahertz to 2300 megahertz Page 10 of 10