Chemistry Equations and Constants Periodic Table of the Elements The periodic table organizes elements based on their atomic number and chemical properties. Groups are vertical columns (e.g., 1A, 2A, 3A) that share similar chemical behaviors. Periods are horizontal rows (e.g., 1, 2, 3) that reflect the filling of electron shells. Specific elements and their atomic masses are listed (e.g., H = 1.008, He = 4.003, Li = 6.941). Lanthanides and actinides are listed separately at the bottom. Fundamental Physical Constants Avogadro’s Number: N a = 6.02214 × 10 23 / m o l N_a = 6.02214 \times 10^{23} /mol N a = 6.02214 × 1 0 23 / m o l Atomic Mass Unit: a m u = 1.66054 × 10 − 27 k g amu = 1.66054 \times 10^{-27} kg am u = 1.66054 × 1 0 − 27 k g Charge of the Electron: e = 1.60218 × 10 − 19 C e = 1.60218 \times 10^{-19} C e = 1.60218 × 1 0 − 19 C Faraday Constant: F = 9.64853 × 10 4 C / m o l F = 9.64853 \times 10^4 C/mol F = 9.64853 × 1 0 4 C / m o l Mass of the Electron: m e = 9.10939 × 10 − 31 k g m_e = 9.10939 \times 10^{-31} kg m e = 9.10939 × 1 0 − 31 k g Mass of the Neutron: m n = 1.67493 × 10 − 27 k g m_n = 1.67493 \times 10^{-27} kg m n = 1.67493 × 1 0 − 27 k g Mass of the Proton: m p = 1.67262 × 10 − 27 k g m_p = 1.67262 \times 10^{-27} kg m p = 1.67262 × 1 0 − 27 k g Planck’s Constant: h = 6.62607 × 10 − 34 J ⋅ s h = 6.62607 \times 10^{-34} J \cdot s h = 6.62607 × 1 0 − 34 J ⋅ s Speed of Light: c = 2.99792 × 10 8 m / s c = 2.99792 \times 10^8 m/s c = 2.99792 × 1 0 8 m / s Acceleration of Gravity: g = 9.80665 m / s 2 g = 9.80665 m/s^2 g = 9.80665 m / s 2 Rydberg Constant: R H = 1.09677 × 10 7 m − 1 R_H = 1.09677 \times 10^7 m^{-1} R H = 1.09677 × 1 0 7 m − 1 Universal Gas Constant:R = 8.31447 J / m o l ⋅ K R = 8.31447 J/mol \cdot K R = 8.31447 J / m o l ⋅ K R = 0.082058 L ⋅ a t m / m o l ⋅ K R = 0.082058 L \cdot atm/mol \cdot K R = 0.082058 L ⋅ a t m / m o l ⋅ K Conversions and Relationships Length:1 k m = 1 × 10 3 m = 0.621 m i l e 1 km = 1 \times 10^3 m = 0.621 mile 1 km = 1 × 1 0 3 m = 0.621 mi l e 1 i n c h = 2.54 c m 1 inch = 2.54 cm 1 in c h = 2.54 c m 1 f t = 12 i n 1 ft = 12 in 1 f t = 12 in 1 p m = 1 × 10 − 12 m = 0.01 A ˚ 1 pm = 1 \times 10^{-12} m = 0.01 Å 1 p m = 1 × 1 0 − 12 m = 0.01 A ˚ Mass:1 k g = 1 × 10 3 g = 2.205 l b 1 kg = 1 \times 10^3 g = 2.205 lb 1 k g = 1 × 1 0 3 g = 2.205 l b 1 m e t r i c t o n = 1 × 10 3 k g 1 metric ton = 1 \times 10^3 kg 1 m e t r i c t o n = 1 × 1 0 3 k g Volume:1 d m 3 = 1 × 10 − 3 m 3 = 1 l i t e r 1 dm^3 = 1 \times 10^{-3} m^3 = 1 liter 1 d m 3 = 1 × 1 0 − 3 m 3 = 1 l i t er 1 c m 3 = 1 m L 1 cm^3 = 1 mL 1 c m 3 = 1 m L 1 m 3 = 35.3 f t 3 1 m^3 = 35.3 ft^3 1 m 3 = 35.3 f t 3 1 g a l l o n = 3.785 l i t e r s 1 gallon = 3.785 liters 1 g a ll o n = 3.785 l i t ers Energy:1 J = 1 k g ⋅ m 2 / s 2 = 1 C ⋅ V 1 J = 1 kg \cdot m^2/s^2 = 1 C \cdot V 1 J = 1 k g ⋅ m 2 / s 2 = 1 C ⋅ V 1 c a l o r i e = 4.184 J 1 calorie = 4.184 J 1 c a l or i e = 4.184 J Temperature:T ( K ) = T ( ° C ) + 273.15 T(K) = T(°C) + 273.15 T ( K ) = T ( ° C ) + 273.15 T ( ° C ) = ( T ( ° F ) – 32 ) ( 5 / 9 ) T(°C) = (T(°F) – 32)(5/9) T ( ° C ) = ( T ( ° F ) –32 ) ( 5/9 ) H 2 O H_2O H 2 O Pressure:1 P a = 1 N / m 2 = 1 k g / m ⋅ s 2 1 Pa = 1 N/m^2 = 1 kg/m \cdot s^2 1 P a = 1 N / m 2 = 1 k g / m ⋅ s 2 1 a t m = 1.01325 × 10 5 P a 1 atm = 1.01325 \times 10^5 Pa 1 a t m = 1.01325 × 1 0 5 P a 1 a t m = 760 t o r r = 760 m m H g 1 atm = 760 torr = 760 mmHg 1 a t m = 760 t orr = 760 mm H g Math:π = 3.1416 \pi = 3.1416 π = 3.1416 e = 2.7183 e = 2.7183 e = 2.7183 Equations Δ E = Δ U = q + w \Delta E = \Delta U = q + w Δ E = Δ U = q + w Δ H = Δ E + Δ ( P V ) \Delta H = \Delta E + \Delta(PV) Δ H = Δ E + Δ ( P V ) q = m c Δ T q = mc\Delta T q = m c Δ T w = − P e x t Δ V w = -P_{ext} \Delta V w = − P e x t Δ V Δ H < e m > r x n ° = ∑ m o l ⋅ Δ H < / e m > f ° ( p r o d u c t s ) − ∑ m o l ⋅ Δ H f ° ( r e a c t a n t s ) \Delta H<em>{rxn}° = \sum mol \cdot \Delta H</em>f° (products) - \sum mol \cdot \Delta H_f° (reactants) Δ H < e m > r x n ° = ∑ m o l ⋅ Δ H < / e m > f ° ( p ro d u c t s ) − ∑ m o l ⋅ Δ H f ° ( re a c t an t s ) Δ H r x n ° = ∑ m o l ⋅ B E ( b o n d s b r o k e n ) − ∑ m o l ⋅ B E ( b o n d s f o r m e d ) \Delta H_{rxn}° = \sum mol \cdot BE(bonds \ broken) - \sum mol \cdot BE(bonds \ formed) Δ H r x n ° = ∑ m o l ⋅ BE ( b o n d s b ro k e n ) − ∑ m o l ⋅ BE ( b o n d s f or m e d ) c = λ ν c = \lambda \nu c = λ ν Δ E = h ν \Delta E = h\nu Δ E = h ν Δ E = h c λ \Delta E = \frac{hc}{\lambda} Δ E = λ h c Δ E = − 2.18 × 10 − 18 J ( 1 n < e m > f 2 − 1 n < / e m > i 2 ) \Delta E = -2.18 \times 10^{-18} J(\frac{1}{n<em>f^2} - \frac{1}{n</em>i^2}) Δ E = − 2.18 × 1 0 − 18 J ( n < e m > f 2 1 − n < / e m > i 2 1 ) M = molar mass d = M P R T d = \frac{MP}{RT} d = RT MP M = m R T P V M = \frac{mRT}{PV} M = P V m RT P V = n R T PV = nRT P V = n RT P < e m > 1 V < / e m > 1 n < e m > 1 T < / e m > 1 = P < e m > 2 V < / e m > 2 n < e m > 2 T < / e m > 2 \frac{P<em>1V</em>1}{n<em>1T</em>1} = \frac{P<em>2V</em>2}{n<em>2T</em>2} n < e m > 1 T < / e m > 1 P < e m > 1 V < / e m > 1 = n < e m > 2 T < / e m > 2 P < e m > 2 V < / e m > 2 K E = 3 2 R T = 1 2 m v 2 KE = \frac{3}{2}RT = \frac{1}{2}mv^2 K E = 2 3 RT = 2 1 m v 2 F < e m > e = k Q < / e m > 1 Q 2 d 2 F<em>e = \frac{kQ</em>1Q_2}{d^2} F < e m > e = d 2 k Q < / e m > 1 Q 2 v r m s = 3 R T M v_{rms} = \sqrt{\frac{3RT}{M}} v r m s = M 3 RT R a t e < e m > A R a t e < / e m > B = M < e m > B M < / e m > A \frac{Rate<em>A}{Rate</em>B} = \sqrt{\frac{M<em>B}{M</em>A}} R a t e < / e m > B R a t e < e m > A = M < / e m > A M < e m > B P < e m > A = X < / e m > A ⋅ P t o t a l P<em>A = X</em>A \cdot P_{total} P < e m > A = X < / e m > A ⋅ P t o t a l ( P + n 2 a V 2 ) ( V − n b ) = n R T (P + \frac{n^2a}{V^2})(V - nb) = nRT ( P + V 2 n 2 a ) ( V − nb ) = n RT l n ( P < e m > 2 P < / e m > 1 ) = Δ H < e m > v a p R ( 1 T < / e m > 2 − 1 T 1 ) ln(\frac{P<em>2}{P</em>1}) = \frac{\Delta H<em>{vap}}{R}(\frac{1}{T</em>2} - \frac{1}{T_1}) l n ( P < / e m > 1 P < e m > 2 ) = R Δ H < e m > v a p ( T < / e m > 2 1 − T 1 1 ) l n ( k < e m > 2 k < / e m > 1 ) = E < e m > a R ( 1 T < / e m > 2 − 1 T 1 ) ln(\frac{k<em>2}{k</em>1}) = \frac{E<em>a}{R}(\frac{1}{T</em>2} - \frac{1}{T_1}) l n ( k < / e m > 1 k < e m > 2 ) = R E < e m > a ( T < / e m > 2 1 − T 1 1 ) k = A e − E a R T k = Ae^{\frac{-E_a}{RT}} k = A e RT − E a P < e m > s o l v e n t = X < / e m > s o l v e n t P ° s o l v e n t P<em>{solvent} = X</em>{solvent}P°_{solvent} P < e m > so l v e n t = X < / e m > so l v e n t P ° so l v e n t Δ P = ( X < e m > s o l u t e P ° < / e m > s o l v e n t ) i \Delta P = (X<em>{solute}P°</em>{solvent})i Δ P = ( X < e m > so l u t e P ° < / e m > so l v e n t ) i Π = ( M R T ) i \Pi = (MRT)i Π = ( MRT ) i Δ T < e m > b p = ( k < / e m > b p ⋅ m ) i \Delta T<em>{bp} = (k</em>{bp} \cdot m)i Δ T < e m > b p = ( k < / e m > b p ⋅ m ) i Δ T < e m > f p = ( k < / e m > f p ⋅ m ) i \Delta T<em>{fp} = (k</em>{fp} \cdot m)i Δ T < e m > f p = ( k < / e m > f p ⋅ m ) i S < e m > g a s = k < / e m > H ⋅ P g a s S<em>{gas} = k</em>H \cdot P_{gas} S < e m > g a s = k < / e m > H ⋅ P g a s [ A ] < e m > t = − k t + [ A ] < / e m > 0 [A]<em>t = -kt + [A]</em>0 [ A ] < e m > t = − k t + [ A ] < / e m > 0 l n [ A ] < e m > t = − k t + l n [ A ] < / e m > 0 ln[A]<em>t = -kt + ln[A]</em>0 l n [ A ] < e m > t = − k t + l n [ A ] < / e m > 0 1 [ A ] < e m > t = k t + 1 [ A ] < / e m > 0 \frac{1}{[A]<em>t} = kt + \frac{1}{[A]</em>0} [ A ] < e m > t 1 = k t + [ A ] < / e m > 0 1 t < e m > 1 / 2 = [ A ] < / e m > 0 2 k t<em>{1/2} = \frac{[A]</em>0}{2k} t < e m > 1/2 = 2 k [ A ] < / e m > 0 t 1 / 2 = l n 2 k t_{1/2} = \frac{ln2}{k} t 1/2 = k l n 2 t < e m > 1 / 2 = 1 k [ A ] < / e m > 0 t<em>{1/2} = \frac{1}{k[A]</em>0} t < e m > 1/2 = k [ A ] < / e m > 0 1 Solubility Rules All common compounds of Group 1A ions and N H 4 + NH_4^+ N H 4 + All common nitrates, acetates, and most perchlorates are soluble. All common chlorides, bromides, and iodides are soluble, except those of A g + , P b 2 + , C u + , Ag^+, Pb^{2+}, Cu^+, A g + , P b 2 + , C u + , H g 2 2 + Hg_2^{2+} H g 2 2 + P b 2 + Pb^{2+} P b 2 + All common sulfates are soluble, except those of C a 2 + , S r 2 + , B a 2 + , A g + , Ca^{2+}, Sr^{2+}, Ba^{2+}, Ag^+, C a 2 + , S r 2 + , B a 2 + , A g + , P b 2 + Pb^{2+} P b 2 + All common metal hydroxides are insoluble, except those of Group 1A and the larger members of Group 2A (starting with C a 2 + Ca^{2+} C a 2 + All common carbonates and phosphates are insoluble, except those of Group 1A and N H 4 + NH_4^+ N H 4 + All common sulfides are insoluble, except those of Groups 1A, 2A, and N H 4 + NH_4^+ N H 4 + 1 a t m ⋅ L = 101.3 J 1 atm \cdot L = 101.3 J 1 a t m ⋅ L = 101.3 J