QCF258 – Science 2 Resource Book Useful Data Physical Constants Formulae Periodic Table Page | 1 Useful Data Scientific notation Ratio to basic unit ππππ−ππ ππππ−ππ ππππ−ππ ππππ−ππ ππππ−ππ ππππ−ππππ ππππ−ππππ ππππ−ππππ Prefix Abbreviation ππππππππ ππππππππππ ππππππππππ ππππππππππ ππππππππ ππππππππ ππππππππππ ππππππππ ππ ππ ππ ππ ππ ππ ππ ππ Acid-base indicators Name pKa Methyl orange Bromophenol blue Bromocresol green Methyl red Bromothymol blue Phenol red Phenolphthalein 3.7 4.2 4.7 5.1 7.0 7.9 9.6 Ratio to basic unit 101 102 103 106 109 1012 Prefix Abbreviation ππππππππ βππππππππ ππππππππ ππππππππ ππππππππ π‘π‘π‘π‘π‘π‘π‘π‘ ππππ β ππ ππ πΊπΊ ππ Volume and capacity conversions 1 dm3 = 1 x 10-3 m3 = 1 x 103 cm3 = 1 L pH range of colour change 3.1 – 4.4 3.0 – 4.6 3.8 – 5.4 4.4 – 6.2 6.0 – 7.6 6.8 – 8.4 8.3 – 10.0 Colour change (acidic to basic) Red to yellow Yellow to blue Yellow to blue Pink to yellow Yellow to blue Yellow to red Colourless to pink Formula and charges for common polyatomic ions Cations Anions ammonium πππ»π»4 + hydronium π»π»3 ππ+ acetate (ethanoate) πΆπΆπ»π»3 πΆπΆπΆπΆππ− hydroxide carbonate πΆπΆππ3 2− hypochlorite πΆπΆπΆπΆππ4 2− perchlorate πΆπΆπΆπΆππ3 − chlorate πΆπΆπΆπΆππ2 − chlorite chromate πΆπΆ6 π»π»5 ππ7 3− citrate cyanide πΆπΆπΆπΆ − dichromate dihydrogen phosphate hydrogen phosphate hydrogen sulfate (bisulfate) nitrate nitrite permanganate peroxide πΆπΆπΆπΆ2 ππ7 2− phosphate π»π»π»π»ππ4 − thiosulfate π»π»2 ππππ4 − π»π»π»π»ππ4 2− sulfate sulfite ππππ − πΆπΆπΆπΆπΆπΆ− ππππ3 − ππππ2 − πΆπΆπΆπΆππ4 − ππππππ4 − ππ2 2− ππππ4 3− ππππ4 2− ππππ3 2− ππ2 ππ3 2− hydrogen carbonate (bicarbonate) π»π»π»π»ππ3 − Page | 2 Physical Constants Avagadro’s number (NA) = 6.022 × 1023 mole-1 Dissociation constant for water at 25 °C (KW) = 1.00 × 10−14 Acceleration due to gravity (g) = 9.80 ms–2 Universal gravitational constant (G) = 6.67 × 10−11 Nm2 kg −2 Speed of light (c) = 3.00 × 108 ms–1 Radius of Earth = 6.38 × 106 m Earth–Moon separation = 3.85 × 105 km Earth–Sun separation = 1.50 × 108 km Mass of Earth = 5.98 × 1024 kg Mass of Moon = 7.35 × 1022 kg Mass of Sun = 1.99 × 1030 kg Mass of proton = 1.67 × 10–27 kg Mass of neutron = 1.68 × 10–27 kg Atomic mass unit = 1 amu = 1.66057 × 10-27 kg 1 eV = 1.60 × 10–19 J Mass of electron = 9.11 × 10–31 kg Charge on electron = –1.60 × 10–19 C Specific heat capacity of water (c) = 4200 J kg-1 K-1 = 75 J mol-1 K-1 Latent heat of fusion for water (L) = 3.4 × 105 J kg-1 Latent heat of vaporisation for water (L) = 2.3 × 106 J kg-1 1 calorie = 4.184 J Normal atmospheric pressure = 1 atm = 101.3 kPa = 760 mm Hg Molar volume of gas at STP (0 °C, 1 atm) = 22.4 L = 22.4 dm3 Molar volume of gas at RTP (25 °C, 1 atm) = 24.5 L = 24.5 dm3 Gas constant (R) = 0.082 L atm K-1 mol-1 = 8.314 L kPa K-1 mol-1 = 8.314 J K-1 mol-1 Page | 3 Formulas Working Scientifically: Error Analysis π΄π΄π΄π΄π΄π΄π΄π΄π΄π΄π΄π΄π΄π΄π΄π΄ π’π’π’π’π’π’π’π’π’π’π’π’π’π’π’π’π’π’π’π’π’π’ = ± π₯π₯ππππππ − π₯π₯ππππππ ππππππππππ =± 2 2 ππππππππππππππππππππ π’π’π’π’π’π’π’π’π’π’π’π’π’π’π’π’π’π’π’π’π’π’ (%) = ππππππππππππππππ π’π’π’π’π’π’π’π’π’π’π’π’π’π’π’π’π’π’π’π’π’π’ 100 × ππππππππππππππππππππππ 1 ππππππππππππππππ π£π£π£π£π£π£π£π£π£π£ − π‘π‘π‘π‘π‘π‘π‘π‘ π£π£π£π£π£π£π£π£π£π£ 100 ππππππππππππππππππππ ππππππππππ (%) = οΏ½ οΏ½× π‘π‘π‘π‘π‘π‘π‘π‘ π£π£π£π£π£π£π£π£π£π£ 1 Combining uncertainties: + or - add absolute uncertainties x or ÷ add percentage uncertainties Chemistry Fundamentals ππππππππππππ ππππ ππππππππππ (ππ) = ππππππππππππππππ (ππ) = ππ1 ππ1 = ππ2 ππ2 π·π·π·π·π·π·π·π·π·π·π·π·π·π· = ππππππππ ππππππππππ ππππππππ ππππππππππ ππππ π π π π π π π π π π π π ππ = π£π£π£π£π£π£π£π£π£π£π£π£ ππππ π π π π π π π π π π π π π π π π ππ ππππππ = ππ ππ ππππππ = Chemical Equilibrium πΎπΎππ = πΎπΎππ = [πΆπΆ ]ππ [π·π·]ππ [π΄π΄]ππ [π΅π΅]ππ (πππΆπΆ )ππ (πππ·π· )ππ (πππ΄π΄ )ππ (πππ΅π΅ )ππ πΎπΎππ = πΎπΎπΆπΆ (π π π π )βππ ππππ ππππ π π π π π π π π π π π π ππ ππππ ππππ π π π π π π π π π π π π ππ for an aqueous reaction: aA + bB β cC + dD for a gaseous reaction: aA + bB β cC + dD where: βππ = ∑ ππππππππππππππππ − ∑ ππππππππππππππππππ Page | 4 Formulas Acids and Bases πΎπΎπ€π€ = [π»π» + ] [ππππ − ] = 1.00 × 10−14 ππππ + ππππππ = 14 [ππππ − ] = 10−ππππππ ππππππ = − log 10 [ππππ − ] [π»π» + ] = [π»π»3 ππ+ ] = 10−ππππ ππππ = − log 10 [π»π» + ] = − log 10 [π»π»3 ππ+ ] πΎπΎπ€π€ = πΎπΎππ πΎπΎππ = 1.00 × 10−14 πππΎπΎππ = − log 10 [πΎπΎππ ] [π»π» + ] = οΏ½πΎπΎππ πΆπΆ πππΎπΎππ + ππππππ = 14 πΎπΎππ = 10−πππΎπΎππ πππΎπΎππ = − log 10 [πΎπΎππ ] 1 ππππ = 2 (πππΎπΎππ − log πΆπΆ) 1 [ππππ − ] = οΏ½πΎπΎππ πΆπΆ ππππππ = 2 (πππΎπΎππ − log πΆπΆ) πΎπΎππ = 10−πππΎπΎππ πΎπΎππ = πΎπΎππ = [π»π»3 ππ + ][π΄π΄− ] [π»π»π»π»] [π΅π΅π΅π΅ + ][ππππ − ] [π΅π΅] Working Scientifically: Graphical Analysis π¦π¦ = ππππ + ππ where: π¦π¦ = π΄π΄π₯π₯ ππ where: Linear Motion π£π£ππππ = ππππππ βπ£π£ π£π£ − π’π’ = = π‘π‘ π‘π‘ π π = π’π’ π‘π‘ + 1 2 A = coefficient and and c = y-intercept n = power Projectile Motion π π π’π’ + π£π£ = π‘π‘ 2 π£π£ = π’π’ + ππππ βπ¦π¦ ππ = ππππππππππππππππ = βπ₯π₯ ππ π‘π‘ 2 π£π£ 2 = π’π’2 + 2ππππ π£π£π¦π¦ = ππ π‘π‘ + π’π’π¦π¦ 1 π π π¦π¦ = 2 ππ π‘π‘ 2 + π’π’π¦π¦ π‘π‘ π£π£π¦π¦ 2 = 2πππ π π¦π¦ + π’π’π¦π¦ 2 π£π£π₯π₯ = π’π’π₯π₯ π π π₯π₯ = π’π’π₯π₯ π‘π‘ General Maths π₯π₯ = −ππ±√ππ2 −4ππππ 2ππ where: πππ₯π₯ 2 + ππππ + ππ = 0 Page | 5 Formulas Force and Motion Force and Materials πΉπΉππππππ = ππππ πΉπΉ = (−) πππ₯π₯ πΉπΉππ = ππ = ππππ ππ = πΈπΈ = ππ = πΉπΉπΉπΉ cos ππ = βπΈπΈ βπΈπΈππ = πΊπΊπΊπΊπΊπΊ = ππππβ 1 πΈπΈππ = πΎπΎπΎπΎ = 2πππ£π£ 2 βπΈπΈ ππ = π‘π‘ π‘π‘ π΄π΄ ππ πΉπΉπΏπΏππ = ππ π΄π΄π΄π΄ ππ = π₯π₯ πΏπΏ0 πΉπΉ = πΈπΈπΈπΈ π₯π₯ πΏπΏππ βππ = π½π½ππππ βππ π£π£ = 1 ππ 2ππππ ππππ = ππ π£π£ 2 ππ πΌπΌπΌπΌπΌπΌπΌπΌπΌπΌπΌπΌπΌπΌ = πΉπΉπΉπΉ = βππ οΏ½ πππ’π’ππππππππππππ = οΏ½ πππ£π£ππππππππππ 1 2 2 ππ π£π£ππππππππππ = ππ2 ππ πΉπΉππ = (−) ππ = ππ = = ππππ πΉπΉππππππ = πΉπΉππ = ππ = ππππ 2 ππ π’π’ππππππππππππ = οΏ½ ππ = Circular Motion ππππππππππ ππππππππππππ 100 ππ = × % ππππππππππ ππππππππππ 1 1 2 πΉπΉ βπΏπΏ = πΌπΌπΏπΏππ βππ ππππππππππππ ππππππππππππ 100 ππ = × % ππππππππππππ ππππππππππ 1 οΏ½ 1 π₯π₯ = πΏπΏ − πΏπΏππ πΈπΈππ = πΈπΈπΈπΈπΈπΈ = 2 πΉπΉπΉπΉ = 2 ππ π₯π₯ 2 πΉπΉππππππππ = πππΉπΉππ = ππππ ππ = 1 where: ππππ 2 ππ 2ππ ππ = 2ππππ = ππ ππ2 ππ πΊπΊπΊπΊπΊπΊ ππ 2 πΉπΉππ πΊπΊπΊπΊ = 2 ππ ππ ππ 2 4ππ 2 = ππ 3 πΊπΊπΊπΊ Page | 6 Formulas Electrical Circuits Heating Processes ππ = πΌπΌπΌπΌ ππ = πππΎπΎ = πππΆπΆ + 273 πΎπΎ ππ ππ ππ = πΌπΌπΌπΌ ππ = ππππβππ ππ = ππππ ππ = πΌπΌπΌπΌ = πΌπΌ 2 π π = ππ = βπΈπΈ ππ = π‘π‘ π‘π‘ ππ 2 ππ1 ππ1 = ππ2 ππ2 π π ππ1 ππ2 = ππ1 ππ2 ππ1 ππ2 = ππ1 ππ2 πππ‘π‘π‘π‘π‘π‘ = ππ1 + ππ2 + … ππππ π π π‘π‘π‘π‘π‘π‘ = π π 1 + π π 2 + … π π ππ ππ1 ππ1 ππ2 ππ2 = ππ1 ππ2 πΌπΌπ‘π‘π‘π‘π‘π‘ = πΌπΌ1 + πΌπΌ2 + … πΌπΌππ ππππ = ππππππ 1 1 1 1 = + +β― π π π‘π‘π‘π‘π‘π‘ π π 1 π π 2 π π ππ π π = ππππ π΄π΄ General Maths cos ππ = ππππππππππππππππ βπ¦π¦π¦π¦π¦π¦π¦π¦π¦π¦π¦π¦π¦π¦π¦π¦π¦π¦ ππππππππππππππππ βπ¦π¦π¦π¦π¦π¦π¦π¦π¦π¦π¦π¦π¦π¦π¦π¦π¦π¦ ππππππππππππππππ tan ππ = ππππππππππππππππ 1 π΄π΄ = ππππ 2 πππ‘π‘π‘π‘π‘π‘ = πππ΄π΄ + πππ΅π΅ + β― π₯π₯π΄π΄ = ππππππππππππππππ sin ππ = ππ = ππππππ − πΌπΌπΌπΌ ππ1 ππ2 = ππ1 ππ2 ππ ππππππππππππππππ ππ = 43 ππ ππ 3 πππ΄π΄ πππ‘π‘π‘π‘π‘π‘ πππ΄π΄ = π₯π₯π΄π΄ πππ‘π‘π‘π‘π‘π‘ βπ»π» = π»π»(πππππππππππππ‘π‘π π ) − π»π»(ππππππππππππππππππ) βπ»π» = οΏ½(ππππππππππ ππππππππππππ) − οΏ½(ππππππππππ ππππππππππππ) ππ = ππβπ»π» Page | 7 The Periodic Table of the Elements 1 18 1 2 H Hydrogen 1.01 3 He 2 4 Li Be Lithium Beryllium 11 12 6.94 Na C Carbon 12.01 Atomic number 24.31 20 K Potassium 39.10 37 Rb Rubidium 85.47 55 Cs Ca Calcium 40.08 38 Sr Strontium Mean relative atomic mass Radium Ra 7 8 9 10.81 12.01 13 12 21 22 23 24 25 26 27 28 29 Titanium Vanadium 44.96 39 Y Yttrium La Ti 47.87 40 Zr Zirconium 91.22 72 Hf Hafnium V 50.94 41 Nb Niobium 92.91 73 Ta Tantalum Cr Mn Fe Co 54.94 43 55.85 44 58.93 45 Ruthenium Rhodium Chromium Manganese Mo Tc 52.00 42 Molybdenum Technetium 95.94 74 (98.91) 75 Tungsten Rhenium W Re Iron Ru Cobalt Rh 101.07 76 102.91 77 Osmium Iridium Os Ir Ni Cu Zn 58.29 46 63.55 47 65.39 48 69.72 49 Palladium Silver Cadmium Indium Nickel Pd Copper Ag Cd Ga Silicon Phosphorus Sulfur Ge P S 30.97 33 32.07 34 Arsenic Selenium As 72.61 50 74.92 51 Tin Antimony Sb Se 78.96 52 Te Tellurium Thallium Lead Bismuth Polonium Astatine Radon Hg Tl Pb Bi Po Seaborgium Bohrium Hassium Meitnerium Darmstadtium Roentgenium Copernicium Nihonium Flerovium Moscovium Livermorium 58 59 60 61 62 63 64 65 66 67 68 69 70 71 140.12 90 Th Thorium 232.04 140.91 91 Pa Protactinium 231.04 144.24 (144.91) 150.36 92 93 94 U Uranium 238.03 Np Neptunium Pu Plutonium Eu Europium 151.96 95 Am Americium Gd Gadolinium Ds (269) Tb Terbium 157.25 96 158.93 97 Curium Berkelium Cm Xe Mercury Au Dubnium Sm Xenon I Gold Pt Rutherfordium Samarium Iodine Platinum Actinium Pm 83.80 54 131.29 86 207.21 114 Nd 79.90 53 126.90 85 204.38 113 Pr Kr 127.60 84 200.59 112 Praseodymium Neodymium Promethium Krypton Br 121.76 83 196.97 111 Ce Bromine 118.71 82 195.08 110 (268) 39.95 36 114.82 81 192.22 109 Mt 35.45 35 112.41 80 190.23 108 Hs Ar Argon 107.87 79 186.21 107 Bh Cl Chlorine Neon 106.42 78 183.84 106 Sg 18 16 180.95 105 Db 17 15 178.49 104 Rf 20.18 14 138.91 89** Ac 19.00 16.00 Sn 11 Ne 14.01 Si 4.00 10 F Fluorine In 10 Sc Aluminium O Oxygen Germanium 9 N Nitrogen Gallium 8 Scandium C Carbon Zinc 7 Cerium Actinide Series** 6 30 6 (223.02) 226.03 (227.03) (261.11) (262.11) (263.12) (264.12) (265.13) Lanthanide Series* 5 28.09 32 5 Lanthanum Francium 17 26.98 31 4 Barium 137.33 88 16 B 3 88.91 57* 132.91 87 15 Al 87.62 56 Ba 14 Boron Mg Magnesium 22.99 19 Fr Name 9.01 Sodium Cesium Symbol 6 13 Helium Bk Rg (272) Dy Dysprosium Cn (277) Ho Holium Nh (284) Er Erbium Fl (289) Tm Thulium Mc (289) Yb Ytterbium Lv (293) 168.93 101 173.05 102 174.97 103 Californium Einsteinium Fermium Mendelevium Nobelium Lawrencium 237.05 (244.06) (243.06) (247.07) (247.07) (251.08) (252.08) Md No (294) Og Oganesson (294) Lu 167.26 100 Fm Ts Tennessine Lutetium 164.93 99 Es Rn 208.98 (208.98) (209.98) (222.02) 115 116 117 118 162.50 98 Cf At Lr (257.10) (258.10) (259.10) (262.11) November 2016