Chem 1302 formulas - Simple Formula Sheet PDF

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Chapter One: Gases Formula Sheet Moles, Molar Mass, Mass

𝑛 =

Avogadros #, Moles, Molecules

𝑚 𝑀

𝑁 =

Density

𝑛 𝑁𝐴

𝑑=

Ideal Gas Law

Ideal Gas Law & Molar Mass & Density

𝑝𝑉 = 𝑛𝑅𝑇

𝑀=

Boyle's Law

Charles Law

𝑉1

𝑝1𝑉1 = 𝑝2𝑉2

𝑇1

𝑑𝑅𝑇 𝑝

=

Combined Gas Law

𝑉2

𝑝1𝑉1

𝑇2

𝑇1

Dalton’s Law of Partial Pressure

Mole Fraction

𝑝𝑇 = 𝑝𝐴 + 𝑝𝐵...

𝑋𝐴 =

Average Molar Mass of Gas Mixture

Avg. 𝐸 of Gas Molecule

𝑀𝑎𝑣𝑔. = 𝑋𝐴𝑀𝐴 + 𝑋𝐵𝑀𝐵...

Ē =

2

ū =

𝑚 𝑉

𝑝2𝑉2 𝑇2

Partial Pressure

𝑛𝐴

𝑝𝐴 = 𝑋𝐴 • 𝑝𝑇

𝑛𝑇

Avg. Molecule Speed

𝐾

1 2

=

2

𝑚ū

3𝑅𝑇 𝑀

Root Mean-Square Speed of Gas Molecule

𝑢𝑟𝑚𝑠(𝐴)

3𝑅𝑇 𝑀

𝑢𝑟𝑚𝑠 =

Root Mean-Square Speed of 2 Diff. Gas Molecules

𝑢𝑟𝑚𝑠(𝐵)

=

𝑀𝐵 𝑀𝐴

**heavier M in numerator**

Graham’s Law

𝑒𝑛𝑟𝑖𝑐ℎ𝑚𝑒𝑛𝑡 𝑓𝑎𝑐𝑡𝑜𝑟 (𝑓) =

𝑟𝑒𝑓𝑓(𝐴) 𝑟𝑒𝑓𝑓(𝐵)

=

𝑀𝐵 𝑀𝐴

Constants & Conversions 𝑅 = 8. 314 𝐽/𝐾 • 𝑚𝑜𝑙 (for Kpa) bars) 1 bar

=

100Kpa

=

0.9869atm

𝑅 = 0. 082507 𝐿 • 𝑎𝑡𝑚/𝐾 • 𝑚𝑜𝑙 (for atm)

=

750torr

=

750mmHg

=

14.5psi

𝑅 = 0. 08314 𝐿 • 𝑏𝑎𝑟/𝐾 • 𝑚𝑜𝑙(for

Chapter Two: Thermodynamics & Thermochemistry Formula Sheet Work

Internal Energy

W = P ext ΔV 

Heat

ΔE = q + w

Enthalpy

q = C ΔT

Molar Enthalpy

ΔH = ΔE + P ΔV

ΔH x =

ΔH °rxn = ΣH °(prod.) qsol = msolc solΔT sol

Calorimeter Calibration: Option One

Calorimeter Calibration: Option Two

q water = q cal  mH2Oc H 2OΔT H 2O = (C calΔT cal)  C cal =

q cal = C calΔT cal = q rxn  q C cal = ΔTrxn  cal



Bomb Calorimeter Heat

q rxn =

ΣH °(reac.) 

Heat Exchanged By Solvent w.r.t c

q rxn = (q sol + q cal) 

mH2O cH2O ΔT H 2O ΔT cal

q = mcΔT

Standard Enthalpy Change

ΔH n

Simple Calorimetry Heat Exchange

q surr = q sys 

Heat

Bomb Calorimeter Enthalpy

( qcal + q H2O  ) = (C cal + cH2Om H 2O)ΔT 

ΔH = ΔE + Δngases RT

Hess’s Law For Reaction: aA + bB →cC + dD

Δ H °rxn = [ cΔH °f (C) + dΔH °f (D)]

[aΔH ° f(A) + bΔH ° f(B)] 

Total Bond Enthalpy

T BE = ΔH°rxn = ΣH°(prod.)

ΣH°(reac.) 

Enthalpy Change of Gas Phase Reactions

ΔH°rxn = ΣT BE (reac.) ΣT BE (prod.)  ΔH°rxn = Σenthalpiesof bondsbroken enthalpiesof bondsf ormed  Boltzmann Equation (W=# of microstates)

S=k

l n(W ) 

Entropy Contributions

ΔS univ = ΔS sys + ΔS surr > 0

Standard Molar Entropies

ΔS°rxn = ΣnS °f (prod.)

ΣnS ° f (reac.) 

Entropy & Heat Flow

ΔS surr =

ΔH surr T or

Entropy & Heat Flow of System Only

=

ΔH sys T



Entropy of Dissolution

ΔH sys T

> 0

Entropy & Gases

S solution > (S solvent + S solute) Gibbs Free Energy

Δ G = Σ G(prod.)

ΔS sys =

ΔS = S A+Bmixed

(S A(g) + S B(g)) > 0 

Gibbs Equation

ΣG(reac.) 

ΔG = Δ H

T ΔS 

Chapter Two: Thermodynamics & Thermochemistry Formula Sheet Melting Point Temperature

ΔH f us = T mΔS f us Standard Free Energy Change

ΔG° = ΔH°

T ΔS° 

Δ G Under Standard Conditions

ΔG° = RT lnK 

Boiling Point Temperature

ΔH evap = T bΔS evap Standard Free Energy of Formation

ΔG°rxn = ΣG°f (prod.) Δ G Under Non-Standard Conditions

ΔG = ΔG° + RT lnQ

ΣG° f (reac.) 

Chapter Three: Chemical Equilibrium Equilibrium Constant K for: aA + bB c

K=

cC + dD

Reversing Equilibrium Reaction

d

[C] [D ] [A]a [B]b

K =

Combining Equilibria

K = K1

Multiplying & Dividing Equilibrium Reaction

m

K = K , m = division/multiplicationf actor 

K2 

Reaction Quotient Q: aA + bB c

Q=

Relationship Between ᅀG°and K

cC + dD

d

[C] [D ] [A]a [B]b

ΔG = ΔG° + RT lnK

Entropy, Enthalpy & K Relationship

ΔH° R

lnK =

1 K

Van’t Hoff Equation

K

(T1 ) + ΔS° R 

ln K 2 = 1

ΔH° R

(

1 T1

1 T2

)

y = mx + b Solubility Product K sp : AxB y(s)

xA a+(aq) + y Bb

(aq)

Reaction Quotient/Ion Product: A2B (s)



K sp = [Aa+ ]x[B b ]y

+ 2 2A + B 

Q = [A+ 2 ][B 2 ]

PH AND PK STUFF

p H = l og[H + ]  [H + ] = 1 0

pH

pOH = l og[OH ]  [OH ] = 1 0

pOH

Acid Ionization

H +(aq)

H A(aq)

pK b = logK b 

p Ka = logK a  Base Ionization

+A

B (aq) + H 2O (aq)

(aq) 

Weak Acid Equilibrium Constant

Ka =

pH + pOH = 14

BH + (aq) + OH

(aq) 

Weak Base Equilibrium Constant

[H+ ][A ] [HA]

Kb =

[BH ][OH ] [B ]

Percent Ionization

=

x(thisisamountionized) c(thisis[initial])

100% 

Conjugate Base (A-) Equilibrium Reaction

A

(aq)

Conjugate Base Equilibrium Constant

+ H 2O (l) HA (aq) + OH

(aq) 

Conjugate Acid (BH+) Equilibrium Reaction

B H +(aq)

+ H 2 O(l)

+ H 3 O (aq)

K w = [H ][OH ] = 1.0

[HA][OH ] [A ]

Conjugate Acid Equilibrium Constant +

+ B (aq) 

Equilibrium Constant K w

+

Kb = Ka =

[H 3 O ][B ] [BH+ ]

Equilibrium Constant K w of Conjugate Acid-Base Pair

10

14



K w = K a

K b 

Chapter Three: Chemical Equilibrium Salts

For amphoteric species compare K a&K b , if K a > K b then salt is acidic, if K a < K b then salt is basic Henderson-Hasselbalch Equation

[n

]

[A ] pH = pK a + l og( [HA] ) or  pH = pK a + l og( [n A ] ) HA Acid-Base Indicator Equilibrium

H In (aq)

H 3 O+(aq)

+ In

Indicator Equilibrium Constant

(aq) 

K HIn =

[H3 O + ][In ] [HIn]

Chapter Four: Electrochemistry Oxidation States

If C is bonded to an atom more electronegative than itself, that bond contributes +1 to C’s oxidation state.

of Carbon

If C is bonded to an atom less electronegative than itself, that bond contributes -1 to C’s oxidation state.

Standard Cell Potential

𝐸°𝑐𝑒𝑙𝑙 = 𝐸°𝑟𝑒𝑑 + 𝐸°𝑜𝑥

or

𝐸°𝑐𝑒𝑙𝑙 = 𝐸°𝑟𝑒𝑑 − 𝐸°𝑟𝑒𝑑

-

Species with more +𝐸°

-

Species with more -𝐸°𝑟𝑒𝑑 values are strong reducing agents and are more easily oxidized.

𝑟𝑒𝑑

values are strong oxidizing agents and are more easily reduced.

Cell Diagram

𝑎𝑛𝑜𝑑𝑒 | 𝑝𝑟𝑜𝑑𝑢𝑐𝑡 𝑜𝑓 𝑜𝑥𝑖𝑑𝑎𝑡𝑖𝑜𝑛(𝑎𝑞, 𝑥𝑀)| |𝑝𝑟𝑜𝑑𝑢𝑐𝑡 𝑜𝑓 𝑟𝑒𝑑𝑢𝑐𝑡𝑖𝑜𝑛(𝑎𝑞, 𝑦𝑀) | 𝑐𝑎𝑡ℎ𝑜𝑑 Relationship Between 𝐸°𝑐𝑒𝑙𝑙& ΔG°

or

∆𝐺° =− 𝑛𝐹𝐸°𝑐𝑒𝑙𝑙 Nernst Equation

𝐸𝑐𝑒𝑙𝑙 = 𝐸°𝑐𝑒𝑙𝑙 − (

𝐸°𝑐𝑒𝑙𝑙 =

𝑅𝑇 𝑛𝐹

Nernst Equation @ T=298.15K

𝑅𝑇 𝑛𝐹

)𝑙𝑛𝑄

𝐸𝑐𝑒𝑙𝑙 = 𝐸°𝑐𝑒𝑙𝑙 − (

Quantitative Determination Of Electrons

𝑄 = 𝑛𝑒𝐹 = 𝐼𝑡

𝑙𝑛𝑄

or

𝑛𝑒𝐹 = 𝐼𝑡

0.0257 𝑛𝐹

)𝑙𝑛𝑄

Chapter Five: Chemical Kinetics Reaction Rate for aA +bB → cC + dD

r ate =

1 Δ[A] a ( Δt )

=

1 Δ[B] b ( Δt )

1 Δ[D] = c1 ( Δ[C] Δt ) = d ( Δt )

Rate Law for aA +bB→products

r ate = k [A]x [B]y Number of Elapsed Half-Lives (n)

n=

timeelapsed lengthof half lif e

Order of Reactions & Their Associated Equations

Activation Energy

E a (f orward)

E a (reverse) = ΔG rxn 

Molecularity

Rate

rate = #of coll.

probability f actor(stericf actor)

Arrhenius Equation

k = Ae

Determining E a Graphically with Arrhenius’s Equation

Ea RT

lnk =

Rate Enhancement Factor

l n( rate2 rate1 ) =

Effect of Temperature on Rate

l n( rate2 rate1 ) =

Ea 1 ( ) R T

=

+ lnA 

Comparing Rates

k cat k uncat k ln k2 1

f ractionof coll.wE > E A 

Ea 1 ( R T1

E a2 RT 2

(

E a1 RT 1 ) 

Effect of A Catalyst on Rate

1 ) T2

k

2 l n( rate2 rate1 ) = ln k 1 =

1 RT (E a1

E a2) ...