Chem 105 106 Equation Sheet Fall 2018 PDF

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Chemistry 105 Equation Sheet Con sta nts Consta stants a0 = 0.5291772059 Å c = 2.99792458 × 108 m/s e = 1.6021765 x 10-19 C ɛ0 = 8.8541877 x 10-12 F/m h = 6.626 × 10-34 J·s kB = 1.38065 × 10-23 J/K 𝑁·𝑚2 × 109 𝐶 2

ke = 8.987551

me = 9.109383 × 10-31 kg mn = 1.6749273 × 10-27 kg mp = 1.6726217 × 10-27 kg NA = 6.022142 × 1023 mol-1 𝐽

R = 8.31447 𝑚𝑜𝑙∙𝐾 = 0.0820575 = 1.987207 RH =1.0974 ×

𝐿 ∙ 𝑎𝑡𝑚 𝑚𝑜𝑙∙𝐾 𝑐𝑎𝑙

𝑚𝑜𝑙∙𝐾

107

m-1

Conver versio sions xact) Con ver sio ns (* = eexa xa ct) Len Lengt gt gth h 1 in = 2.54 cm* 1 ft = 12 inches* 1 yd = 3 ft* 1 m = 39.37 inches* 1mile = 5280 feet* 1mile = 1.609 km Ma Mass ss 1 lb = 453.59237 g = 16 oz. avdp.* 1 US lb = 12 troy ounces * 1 ton = 2000 lb * 1 amu = 1.660538 × 10-24 g Vol Volume ume 1 US gal = 3.7854 L = 4 US qt * 1 US qt = 32 US fl. ozs. * 1 US fluid oz. = 29.5735 mL 1 cm3 = 0.001 L * 1 in3 = 16.4 cm3

Pre Pressu ssu ssure re 1 atm = 760 torr * = 101325 Pa * = 406.783 in H2O = 14.6959 lb/in2 (psi) 1 torr = 1 mm Hg (at 0 °C)* 1 Pa = 1 kg·m-1·s-2* 1 bar = 100,000 Pa * For Force ce 1 N = 1 kg·m·s-2 Pow Power er 1 Watt = 1 J/s Ene Energy rgy 1 J = 1 kg·m2/s2 = 0.2390cal 1 J = 1 V·C = 0.009869 L·atm 1 eV = 1.602 × 10-19 J 1 L∙atm = 101.3 J For mula Formula mulass ρ = m/V TF =

9℉

5℃

TC + 32 °F

1𝐾

ℎ 4𝜋 1 1 1 = 𝑅𝐻 ( 2 − 2 ) 𝑛1 𝑛2 𝜆 ∆𝑥 ∆(𝑚𝑣) ≥ 𝑄 𝑄

1 2 V(r) = 4𝜋𝜀 𝑟 0

𝐹(𝑟) = 𝑘𝑒 μ = Qr

𝑄1 𝑄2 𝑟2

ΔE = q + w ∆Euniv = 0

∆Suniv ≥ 0

S = kB ln W q = mCΔT

w =  Pext ΔV

ΔH = ΔE + PΔV 𝑞𝑟𝑒𝑣 ∆𝑆 = 𝑇 ΔG = ΔH – TΔS

ΔG = ΔG° + RT ln Q ° ° ° ∆𝐻𝑟𝑥𝑛 = Σ𝑛𝐻𝑓,𝑝𝑟𝑜𝑑 − Σ𝑚𝐻𝑓,𝑟𝑒𝑎𝑐𝑡

° ≈ Σ𝑛𝐷𝑏𝑟𝑜𝑘𝑒𝑛 ∆𝐻𝑟𝑥𝑛

− Σ𝑚𝐷𝑓𝑜𝑟𝑚𝑒𝑑

TK = 1℃TC + 273.15 K

PV = nRT

E = hν

𝑅𝑎𝑡𝑒𝐴 𝑇𝑖𝑚𝑒𝐵 𝑀𝐵 = =√ 𝑀𝐴 𝑅𝑎𝑡𝑒𝐵 𝑇𝑖𝑚𝑒𝐴

c = λν

ℎ 𝑚𝑣 Ekinetic = ½ m𝑣2

𝜆=

E = mc2

Φ = ℎ𝜈 - KEelectron 𝐸𝑛 = −𝑍2

𝑅𝐻 ℎ𝑐 𝑛2

* = exact ν = frequency 𝑣 = 𝑣𝑒𝑙𝑜𝑐𝑖𝑡𝑦 © Updated 9/18/2018 BYU Department of Chemistry and Biochemistry

Ptot = P1 + P2 + P3 + . . .

𝐾𝐸𝑎𝑣𝑒 =

3 𝑅𝑇 2

3𝑅𝑇 𝑢𝑟𝑚𝑠 = √𝑣 2 = √ 𝑀

pX =  log X

Kw = [H3O+][OH-]

Chemistry 106 Equation Sheet

Consta stant ntss Con sta nt c = 2.99792458 × 108 m/s e = 1.6021765 x 10-19 C F = 9.648534 × 104 C mol-1 h = 6.626 × 10-34 J·s kB = 1.38065 × 10-23 J/K KB (water) = 0.51 °C/m KF (water) = 1.86 °C/m Kw = 1.0 × 10-14 me = 9.109383 × 10-31 kg mn = 1.6749273 × 10-27 kg mp = 1.6726217 × 10-27 kg NA = 6.022142 × 1023 mol-1 R = 8.31447

𝐽

𝑚𝑜𝑙∙𝐾 𝐿 ∙ 𝑎𝑡𝑚

= 0.0820575

𝑚𝑜𝑙∙𝐾

Conver versio sions xact) Con ver sio ns (* = eexa xa ct) Len Length gth 1 in = 2.54 cm* 1 ft = 12 inches* 1 yd = 3 ft* 1 m = 39.37 inches* 1mile = 5280feet* = 1.609km Ma Mass ss 1 lb = 453.59237 g = 16 oz. avdp.* 1 US lb = 12 troy ounces * 1 ton = 2000 lb * 1 amu = 1.660538 × 10-24 g Volu Volume me 1 L = 1.05669 US qt. 1 US gal = 4 US qt * = 128 US fl. ozs. * 1 US fluid oz. = 29.5735 mL 1 cm3 = 0.001 L * 1 in3 = 16.4 cm3 Tim Time e 1 year = 3.15569 × 107 s For Force ce 1 N = 1 kg·m·s-2

Pre Pressu ssu ssure re 1 atm = 760 torr * = 101325 Pa * = 406.783 in H2O = 14.6959 lb/in2 (psi) 1 torr = 1 mm Hg (at 0 °C)* 1 Pa = 1 kg·m-1·s-2* 1 bar = 100,000 Pa * Ene Energ rg rgy y 1 J = 1 kg·m2/s2 = 0.2390cal 1 J = 1 V·C = 0.009869 L·atm 1 eV = 1.602 × 10-19 J 1 Watt = 1 J/s 1 L∙atm = 101.3 J 1 Ampere = 1 C/s Ra Radioa dioa dioacti cti ctivit vit vity y 1 Curie (Ci) = 3.7 × 1010 disintegrations/s = 1 Bq 1 Gy = 1 J/kg Formu mula lass For mu la ρ = m/V TF =

9℉

5℃ 1𝐾

·TC + 32 °F

TK = 1℃·TC + 273.15 K

Ptot = P1 + P2 + P3 + . . . ∆𝐻𝑣𝑎𝑝 1 𝑃1 1 ln ( ) = ( − ) 𝑃2 𝑇 𝑅 𝑇2 1 PV = nRT Psolv = X solv P°solv

Cg = kHPg

ΔTb = i·KB·m ΔTf = i·KF·m Π = iMRT

S = kB·ln W c = λν E = hν E = mc2 A = kN [A]t = -kt + [A]0 ln [A]t = – kt + ln [A]0

* = exact ν = frequency 𝑣 = 𝑣𝑒𝑙𝑜𝑐𝑖𝑡𝑦 © Updated 9/18/2018 BYU Department of Chemistry and Biochemistry

1

𝑡1/2 𝑡

𝐴𝑡 = 𝐴0 ( ) 1 2 1 = 𝑘𝑡 + [𝐴] 0 [𝐴]𝑡 [𝐴]0 t½ = 2𝑘 0.693 t½ = 𝑘 t½ =

1

𝑘[𝐴]0

𝐸𝑎 + ln 𝐴 𝑅𝑇 𝑘2 𝐸𝑎 1 1 ln ( ) = − ( − ) 𝑘1 𝑅 𝑇2 𝑇1 𝑘𝑐𝑎𝑡 𝐸𝑎𝑢𝑛𝑐 − 𝐸𝑎𝑐𝑎𝑡 ln ( )= 𝑘𝑢𝑛𝑐 𝑅𝑇 pX =  log X ln𝑘 = −

pH = pKa + log

[𝐵] [𝐴]

Q = mCΔT ΔE = q + w ° ° ∆𝐻𝑟𝑥𝑛 = Σ𝑛𝐻𝑓,𝑝𝑟𝑜𝑑

° − Σ𝑚𝐻𝑓,𝑟𝑒𝑎𝑐𝑡

° ∆𝐻𝑟𝑥𝑛 ≈ Σ𝑛𝐷𝑏𝑟𝑜𝑘𝑒𝑛

− Σ𝑚𝐷𝑓𝑜𝑟𝑚𝑒𝑑

ΔG = ΔH – TΔS ΔGrxn° =  RT·ln K 𝐾2 ΔH° 1 1 ln ( ) = − ( − ) 𝐾1 𝑅 𝑇2 𝑇1 ΔG = ΔG° + RT·ln Q ΔG =  nFE w =  Pext ΔV 𝑞𝑟𝑒𝑣 ∆𝑆 = 𝑇 𝐸𝑐𝑒𝑙𝑙 = 𝐸𝑟𝑒𝑑 (𝑐𝑎𝑡) − 𝐸𝑟𝑒𝑑 (𝑎𝑛) 𝑅𝑇 𝑜 − 𝐸𝑐𝑒𝑙𝑙 = 𝐸𝑐𝑒𝑙𝑙 ln 𝑄 𝑛𝐹 −𝑏 ± √(𝑏2 − 4𝑎𝑐) 𝑥= 2𝑎

% ionization = 𝑛𝐸°

log K = 0.0592

[𝐻+ ]𝑒𝑞 𝐻𝐴𝑖

× 100%...