General Chemistry Equations and Concepts Flashcards

Flashcards for General Chemistry equations and concepts.

Dilutions

𝑀1𝑉1 = 𝑀2𝑉2 or 𝐶1𝑉1 = 𝐶2𝑉2. M or C = concentration. V = volume.

Percent Error

(𝐴 − 𝑇) / 𝑇 × 100. T = theoretical. A = actual.

Absorbance (Spectrophotometer)

𝐴𝑏𝑠 = 𝜀𝑐𝑙. 𝜀 = molar extinction coefficient (molar absorptivity). c = sample's concentration. l = path length.

Energy of a Photon

𝐸𝑝ℎ𝑜𝑡𝑜𝑛 = ℎ𝑓 = ℎ𝑐 / 𝜆. h = Planck's constant (6.63 × 10−34 J ∙ s). f = photon's frequency. c = speed of light (3.0 × 108 m/s). λ = photon's wavelength.

Absorption/Emission Line Spectra

Δ𝐸 = 𝐸𝑝ℎ𝑜𝑡𝑜𝑛

Molarity

𝑀 = moles solute / L solution

Molality

𝑚 = moles solute / kg solvent

Henry's Law

𝑃𝐴 = 𝑘𝐻[𝐴]. 𝑃𝐴 = partial pressure of gas A. 𝑘𝐻 = Henry's Law constant (varies per problem). [A] = conc. of gas A

Freezing Point Depression

Δ𝑇𝐹 = −𝑖𝐾𝐹𝑚. i = van't Hoff factor. 𝐾𝐹 = F.P. depression constant. m = molality

Boiling Point Elevation

Δ𝑇𝐵 = 𝑖𝐾𝐵𝑚. i = van't Hoff factor. 𝐾𝐵 = B.P. elevation constant. m = molality

Vapor Pressure Depression (Raoult's Law)

𝑃𝑠𝑜𝑙𝑛 = 𝜒𝑠𝑜𝑙𝑣𝑃𝑠𝑜𝑙𝑣 0. 𝑃𝑠𝑜𝑙𝑛 = VP of solution. 𝜒𝑠𝑜𝑙𝑣 = mol fract of solvent. 𝑃𝑠𝑜𝑙𝑣 0 = VP of pure solvent

Osmotic Pressure (𝝅)

𝜋 = 𝑖𝑀𝑅𝑇. M = molarity of solute. i = van't Hoff factor. 𝑅 = 0.0821 L⋅atm/mol⋅K. T = temp. in Kelvin

Pressure

𝑃 = 𝐹 / 𝐴. F = force. A = area.

Average Kinetic Energy

𝐾𝐸𝑎𝑣𝑔 = (3/2) 𝑅𝑇. 𝑅 = 8.314 J / mol ∙ K

Root-Mean-Square Speed (𝒗)

𝑣 = √3𝑅𝑇 / 𝑀𝑚. 𝑅 = 8.314 J / mol ∙ K. 𝑀𝑚 = molar mass

Ideal Gas Law

𝑃𝑉 = 𝑛𝑅𝑇. n = # of moles. 𝑅 = 0.0821 L⋅atm / mol⋅K

Boyle's Law

𝑉 ∝ 1 / 𝑃

Charles' Law

𝑉 ∝ 𝑇

Avogadro's Law

𝑉 ∝ 𝑛

Combined Gas Law

𝑃1𝑉1 / 𝑛1𝑇1 = 𝑃2𝑉2 / 𝑛2𝑇2

Standard Temperature & Pressure (STP)

P = 1 atm. T = 273 K. 1 mol of gas = 22.4 L at STP

Density

[𝑃(𝑀𝑀)] / 𝑅𝑇 = 𝑚 / 𝑣. 𝑀𝑀 = molar mass. 𝑅 = 0.0821 L⋅atm/mol⋅K. m = mass. v = volume.

Dalton's Law of Partial Pressures

𝑃𝑡𝑜𝑡𝑎𝑙 = 𝑃𝐴 + 𝑃𝐵 + ⋯

Partial Pressure (Dalton's Law)

𝑃𝐴 = 𝜒𝐴𝑃𝑡𝑜𝑡𝑎𝑙. 𝜒𝐴 = mol fraction of gas A

Graham's Law of Effusion

𝑟1 / 𝑟2 = √𝑀𝑚2 / 𝑀𝑚1. r = rate of effusion. M = molar mass.

General Rate Law

A + B → C + D; rate = 𝑘[𝐴]𝑚[𝐵]𝑛. k = rate constant. m & n = determined experimentally.

Rate Constant Units (0 order)

𝑘 = 𝑀1 ∙ 𝑠 −1

Rate Constant Units (1st order)

𝑘 = 𝑠 −1

Rate Constant Units (2nd order)

𝑘 = 𝑀−1 ∙ 𝑠 −1

Rate Constant Units (3rd order)

𝑘 = 𝑀−2 ∙ 𝑠 −1

Arrhenius Equation

𝑘 = 𝐴𝑒^(−𝐸𝑎 / 𝑅𝑇). k = rate constant. A = unique to each rxn. 𝐸𝑎 = act. energy. 𝑅 = 8.314 J/mol∙K. T = temp. in Kelvin.

Equilibrium Constant Expressions

𝐾𝑐 = [products] / [reactants], 𝐾𝑒𝑞 = 𝑘𝑓𝑜𝑟𝑤𝑎𝑟𝑑 / 𝑘𝑟𝑒𝑣𝑒𝑟𝑠𝑒, 𝐾𝑃 = 𝑃𝑝𝑟𝑜𝑑𝑢𝑐𝑡𝑠 / 𝑃𝑟𝑒𝑎𝑐𝑡𝑎𝑛𝑡𝑠. k = rate constant, P = pressure

Reaction Quotient (Q)

𝑄 = [products] / [reactants]. Q > K = shift left. Q < K = shift right. Q = K = equilibrium.

Solubility Product Constant (𝑲𝒔𝒑)

𝐾𝑠𝑝 = [products]

Ionization Constant of Water

𝐾𝑤 = [𝐻3𝑂+][ 𝑂𝐻−] = 1 × 10−14 @ 25 °C

pH & pOH

𝑝𝐻 = −log [𝐻+], 𝑝𝑂𝐻 = −log [𝑂𝐻−], 𝑝𝐻 + 𝑝𝑂𝐻 = 14. [𝐻+] = conc. of protons, [𝑂𝐻−] = conc. of hydroxide

[H+] & [OH-]

[𝐻+] = 10−𝑝𝐻, [𝑂𝐻−] = 10−𝑝𝑂𝐻, [𝐻+][𝑂𝐻−] = 1 ∗ 10−14

Weak Acids

𝐻𝐴 + 𝐻2𝑂 ⇌ 𝐻3𝑂+ + 𝐴−, 𝐾𝑎 = [𝐻3𝑂+][𝐴−] / [𝐻𝐴], [𝐻+] = √𝐾𝑎[𝐻𝐴]. 𝐾𝑎 = acid dissociation constant

Weak Bases

𝐴− + 𝐻2𝑂 ⇌ 𝐻𝐴 + 𝑂𝐻−, 𝐾𝑏 = [𝑂𝐻−][𝐻𝐴] / [𝐴−], [𝑂𝐻−] = √𝐾𝑏[𝐴−]. 𝐾𝑏 = base dissociation constant

pKa & pKb

𝑝𝐾𝑎 = −𝑙𝑜𝑔 [𝐾𝑎], 𝑝𝐾𝑏 = −𝑙𝑜𝑔 [𝐾𝑏], 𝑝𝐾𝑎 + 𝑝𝐾𝑏 = 14, 𝐾𝑤 = 𝐾𝑎 × 𝐾𝑏 = 1 ∗ 10−14

Neutralization Reaction

𝑛𝐴𝑀𝐴𝑉𝐴 = 𝑛𝐵𝑀𝐵𝑉𝐵. 𝑛𝐴 = # of moles 𝐻+, 𝑛𝐵 = # of moles 𝑂𝐻−

Buffers

𝑝𝐻 = 𝑝𝐾𝑎 + 𝑙𝑜𝑔 [𝐴−] / [𝐻𝐴]. [𝐴−] = conc. of base, [𝐻𝐴] = conc. of acid

Enthalpy (H)

(Δ𝐻 > 0): endothermic, (Δ𝐻 < 0): exothermic

Enthalpy of Formation

Δ𝐻𝑓 = Σ𝑛Δ𝐻°𝑓(𝑝𝑟𝑜𝑑𝑢𝑐𝑡) − Σ𝑛Δ𝐻°𝑓(𝑟𝑒𝑎𝑐𝑡𝑎𝑛𝑡𝑠). n = coefficient from balanced rxn

First Law of Thermodynamics

Δ𝐸 = 𝑞 + 𝑤. Δ𝐸 = change in internal energy, q = heat, w = work

Pressure-Volume Work

𝑤 = −𝑃Δ𝑉. P = external pressure, Δ𝑉 = change in volume

Calorimetry - Thermal Energy (q)

𝑞 = −𝐶𝑐𝑎𝑙𝑜𝑟𝑖𝑚𝑒𝑡𝑒𝑟Δ𝑇. 𝐶𝑐𝑎𝑙𝑜𝑟𝑖𝑚𝑒𝑡𝑒𝑟 = specific heat of calorimeter, Δ𝑇 = change in temp.

Heat Curves & Thermal Energy (q)

𝑞 = 𝑚𝐶Δ𝑇, 𝑞 = 𝑚Δ𝐻𝑓𝑢𝑠𝑖𝑜𝑛, 𝑞 = 𝑚Δ𝐻𝑣𝑎𝑝𝑜𝑟𝑖𝑧𝑎𝑡𝑖𝑜𝑛. +q: heat gained by system, -q: heat lost from system, m = mass, C = specific heat

Entropy (S)

Δ𝑆 = Σ𝑛𝑆𝑝𝑟𝑜𝑑𝑢𝑐𝑡𝑠 − Σ𝑛𝑆𝑟𝑒𝑎𝑐𝑡𝑎𝑛𝑡𝑠, 𝑆𝑔𝑎𝑠 > 𝑆𝑙𝑖𝑞𝑢𝑖𝑑 > 𝑆𝑠𝑜𝑙𝑖𝑑, 𝑆𝑎𝑞 > 𝑆𝑠𝑜𝑙𝑖𝑑

Bond Dissociation Energy

Δ𝐻 = ΣΔ𝐻𝑟𝑒𝑎𝑐𝑡𝑎𝑛𝑡𝑠 − ΣΔ𝐻𝑝𝑟𝑜𝑑𝑢𝑐𝑡𝑠 = ΣΔ𝐻𝑏𝑟𝑜𝑘𝑒𝑛 − ΣΔ𝐻𝑓𝑜𝑟𝑚𝑒𝑑; making bonds = exothermic (−Δ𝐻), breaking bonds = endothermic (+Δ𝐻)

Gibb’s Free Energy (𝜟𝑮)

Δ𝐺° = Δ𝐻° − 𝑇Δ𝑆°. Δ𝐺° = standard conditions, Δ𝐻° = enthalpy, T = temp. in Kelvin, Δ𝑆° = entropy

Gibb's Free Energy (𝜟𝑮)

Δ𝐺 = Δ𝐺° + 𝑅𝑇ln𝑄, Δ𝐺° = −𝑅𝑇ln𝐾𝑒𝑞. Δ𝐺 = nonstandard conditions, 𝑅 = 8.314 J/mol∙K, Q = reaction quotient, 𝐾𝑒𝑞 = equilibrium constant

Kinetics (Nuclear Reactions)

𝑁 = 𝑁0𝑒^(−𝑘𝑡), ln 𝑁 = ln 𝑁0 − 𝑘𝑡, 𝑡1/2 = 0.693 / 𝑘. N = amt of radioisotope after time t, 𝑁0 = initial amt, k = rate constant, t = time, 𝑡1/2 = half life (independent of concn for 1st order rxns)

Nuclear Binding Energy

𝐸 = Δ𝑚𝑐^2. m = mass (MUST be in kg), c = speed of light (3.0 × 10^8 m/s)

Standard Cell Potential

𝐸° = 𝐸°𝑟𝑒𝑑𝑢𝑐𝑡𝑖𝑜𝑛 + 𝐸°𝑜𝑥𝑖𝑑𝑎𝑡𝑖𝑜𝑛 = 𝐸°𝑐𝑎𝑡ℎ𝑜𝑑𝑒 + 𝐸°𝑎𝑛𝑜𝑑𝑒

Nernst Equation

𝐸𝑐𝑒𝑙𝑙 = 𝐸° − (0.0592 / 𝑛) log 𝑄. 𝐸𝑐𝑒𝑙𝑙 = nonstandard cell potential, n = # of electrons transferred, Q = reaction quotient

Faraday's Law (mass of product)

mass of product = (𝐼 ∗ 𝑡𝑠 ∗ 𝑀𝑊) / (𝑛 ∗ 𝐹). MW = molec. weight, I = current (Amps), ts = time (seconds), n = # of electrons transferred, 𝐹 = Faraday's constant (96485 coulombs/mol e-)

Faraday's Law (moles of product)

moles of product = (𝐼 ∗ 𝑡𝑠) / (𝑛 ∗ 𝐹). I = current (Amps), ts = time (seconds), n = # of electrons transferred, 𝐹 = Faraday's constant (96485 coulombs/mol e-)