DAT General Chemistry Equation Sheet

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Chapter 0: General and Lab Concepts Review

Dilutions

𝑀1𝑉1=𝑀2𝑉2 or

𝐶1𝑉1=𝐶2𝑉2

𝑀 𝑜𝑟 𝐶= 𝑐 𝑜𝑛𝑐𝑒𝑛𝑡𝑟𝑎𝑡𝑖𝑜𝑛

𝑉=𝑣𝑜𝑙𝑢𝑚𝑒

Percent Error

(𝐴−𝑇)

𝑇×100

𝑇=𝑡ℎ𝑒𝑜𝑟𝑒𝑡𝑖𝑐𝑎𝑙

𝐴=𝑎𝑐𝑡𝑢𝑎𝑙

Absorbance

(Spectro-

photometer)

𝐴𝑏𝑠=𝜀𝑐𝑙

𝜀 =𝑚𝑜𝑙𝑎𝑟 𝑒𝑥𝑡𝑖𝑛𝑐𝑡𝑖𝑜𝑛

𝑐𝑜𝑒𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑡 (𝑚𝑜𝑙𝑎𝑟

𝑎𝑏𝑠𝑜𝑟𝑝𝑡𝑖𝑣𝑖𝑡𝑦)

𝑐=𝑠𝑎𝑚𝑝𝑙𝑒′𝑠 𝑐𝑜𝑛𝑐𝑒𝑛𝑡𝑟𝑎𝑡𝑖𝑜𝑛

𝑙=𝑝𝑎𝑡ℎ 𝑙𝑒𝑛𝑔𝑡ℎ

Chapter 2: Atomic and Electronic Structure

Energy of a

photon

𝐸𝑝ℎ𝑜𝑡𝑜𝑛 =ℎ𝑓=ℎ𝑐

𝜆

ℎ=𝑃𝑙𝑎𝑛𝑐𝑘′𝑠 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡

(6.63×10−34𝐽∙𝑠)

𝑓=𝑝ℎ𝑜𝑡𝑜𝑛′𝑠 𝑓𝑟𝑒𝑞𝑢𝑒𝑛𝑐𝑦

𝑐 =𝑠𝑝𝑒𝑒𝑑 𝑜𝑓 𝑙𝑖𝑔ℎ𝑡

(3.0×108𝑚𝑠

⁄)

𝜆=𝑝ℎ𝑜𝑡𝑜𝑛′𝑠

𝑤𝑎𝑣𝑒𝑙𝑒𝑛𝑔𝑡ℎ

Absorption/

Emission Line

Spectra

𝛥𝐸=𝐸𝑝ℎ𝑜𝑡𝑜𝑛

Kinetic Energy

of an electron

(Photoelectric

Effect)

𝐾𝐸𝑒− =𝐸𝑝ℎ𝑜𝑡𝑜𝑛 −𝜙

𝜙 =𝑤𝑜𝑟𝑘 𝑓𝑢𝑛𝑐𝑡𝑖𝑜𝑛

(𝑚𝑖𝑛𝑖𝑚𝑢𝑚 𝑒𝑛𝑒𝑟𝑔𝑦 𝑛𝑒𝑒𝑑𝑒𝑑

𝑡𝑜 𝑖𝑜𝑛𝑖𝑧𝑒 𝑒𝑙𝑒𝑐𝑡𝑟𝑜𝑛)

Chapter 7: Chemical Solutions

Molarity

𝑀=𝑚𝑜𝑙𝑒𝑠𝑠𝑜𝑙𝑢𝑡𝑒

𝐿𝑠𝑜𝑙𝑢𝑡𝑖𝑜𝑛

Molality

𝑚=𝑚𝑜𝑙𝑒𝑠𝑠𝑜𝑙𝑢𝑡𝑒

𝑘𝑔𝑠𝑜𝑙𝑣𝑒𝑛𝑡

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.𝑑 𝑒𝑝𝑟𝑒𝑠𝑠𝑖𝑜𝑛 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡

𝑚=𝑚𝑜𝑙𝑎𝑙𝑖𝑡𝑦

Vapor

Pressure

Depression

(Raoult’s

Law)

𝑃𝑠𝑜𝑙𝑛 =𝜒𝑠𝑜𝑙𝑣𝑃𝑠𝑜𝑙𝑣0

𝑃𝑠𝑜𝑙𝑛 = 𝑉𝑃 𝑜𝑓 𝑠𝑜𝑙𝑢𝑡𝑖𝑜𝑛

𝜒𝑠𝑜𝑙𝑣 = 𝑚𝑜𝑙 𝑓𝑟𝑎𝑐𝑡 𝑜𝑓 𝑠𝑜𝑙𝑣𝑒𝑛𝑡

𝑃𝑠𝑜𝑙𝑣0= 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

Chapter 5: Gases

Pressure

𝑃=𝐹

𝐴

𝐹=𝑓𝑜𝑟𝑐𝑒

𝐴=𝑎𝑟𝑒𝑎

Average Kinetic

Energy

𝐾𝐸𝑎𝑣𝑔 = 32

⁄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 Temp.

& Pressure (STP)

P=1 atm

T=273 K

*1 mol of gas = 22.4 L

at STP

Standard

Conditions

All aqueous species @ 1M

All gaseous species @1 atm

T=298 K

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+⋯

Dalton’s Law of

Partial Pressures

𝑃𝐴=𝜒𝐴𝑃𝑡𝑜𝑡𝑎𝑙

𝜒𝐴= 𝑚𝑜𝑙 𝑓𝑟𝑎𝑐𝑡𝑖𝑜𝑛

𝑜𝑓 𝑔𝑎𝑠 𝐴

Graham’s Law of

Effusion

𝑟1

𝑟2=√𝑀𝑚2

𝑀𝑚1

𝑟 =𝑟𝑎𝑡𝑒 𝑜𝑓 𝑒𝑓𝑓𝑢𝑠𝑖𝑜𝑛

𝑀 =𝑚𝑜𝑙𝑎𝑟 𝑚𝑎𝑠𝑠

Real Gas

Equation

(𝑃+𝑎𝑛2

𝑉2)(𝑉

−𝑛𝑏)=𝑛𝑅𝑇

𝑎 & 𝑏 =𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡𝑠

𝑠𝑝𝑒𝑐𝑖𝑓𝑖𝑐 𝑡𝑜 𝑒𝑎𝑐ℎ 𝑔𝑎𝑠

𝑎𝑛2

𝑉2 𝑐𝑜𝑟𝑟𝑒𝑐𝑡𝑠 𝑓𝑜𝑟

𝐼𝑀𝐹𝑠

−𝑛𝑏 𝑐𝑜𝑟𝑟𝑒𝑐𝑡𝑠 𝑓𝑜𝑟

𝑣𝑜𝑙𝑢𝑚𝑒

Chapter 8: Chemical Kinetics

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

1𝑠𝑡 𝑜𝑟𝑑𝑒𝑟: 𝑘 =𝑠 −1

2𝑛𝑑 𝑜𝑟𝑑𝑒𝑟: 𝑘=𝑀−1∙𝑠−1

3𝑟𝑑 𝑜𝑟𝑑𝑒𝑟: 𝑘=𝑀−2∙𝑠−1

𝑘 =𝑟𝑎𝑡𝑒 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡

𝑀=𝑚𝑜𝑙𝑎𝑟𝑖𝑡𝑦

s=𝑠𝑒𝑐𝑜𝑛𝑑𝑠

Arrhenius

Equation

𝑘=𝐴𝑒−𝐸𝑎𝑅𝑇

⁄

𝑘 =𝑟𝑎𝑡𝑒 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡

𝐴 = 𝑢𝑛𝑖𝑞𝑢𝑒 𝑡𝑜 𝑒𝑎𝑐ℎ 𝑟𝑥𝑛

𝐸𝑎=𝑎𝑐𝑡.𝑒𝑛𝑒𝑟𝑔𝑦

𝑅=8.314 𝐽

𝑚𝑜𝑙∙𝐾

𝑇=𝑡𝑒𝑚𝑝.𝑖𝑛 𝐾𝑒𝑙𝑣𝑖𝑛

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DAT General Chemistry Equation Sheet

www.datbootcamp.com

Chapter 0: General and Lab Concepts Review

Dilutions 𝑀 1 𝑉 1 = 𝑀 2 𝑉 2 or

Percent Error (𝐴^ −^ 𝑇)

× 100

Absorbance

(Spectro-

photometer)

𝐴𝑏𝑠 = 𝜀𝑐𝑙 𝜀^ =^ 𝑚𝑜𝑙𝑎𝑟^ 𝑒𝑥𝑡𝑖𝑛𝑐𝑡𝑖𝑜𝑛

Chapter 2: Atomic and Electronic Structure

Energy of a

photon

( 6. 63 × 10 −^34 𝐽 ∙ 𝑠)

( 3. 0 × 108 𝑚⁄^ 𝑠^ )

Absorption/

Emission Line

Spectra

Kinetic Energy

of an electron

(Photoelectric

Effect)

𝐾𝐸𝑒− = 𝐸𝑝ℎ𝑜𝑡𝑜𝑛 − 𝜙 𝜙^ =^ 𝑤𝑜𝑟𝑘^ 𝑓𝑢𝑛𝑐𝑡𝑖𝑜𝑛

Chapter 7: Chemical Solutions

Molarity

Molality

Henry’s

Law

𝑃𝐴 = 𝑘𝐻 [𝐴] 𝑃𝐴^ =^ 𝑝𝑎𝑟𝑡𝑖𝑎𝑙^ 𝑝𝑟𝑒𝑠𝑠𝑢𝑟𝑒^ 𝑜𝑓^ 𝑔𝑎𝑠^ 𝐴

Freezing

Point

Depression

𝛥𝑇𝐹 = −𝑖𝐾𝐹 𝑚 𝑖^ =^ 𝑣𝑎𝑛′𝑡^ 𝐻𝑜𝑓𝑓^ 𝑓𝑎𝑐𝑡𝑜𝑟

Boiling

Point

Elevation

𝛥𝑇𝐵 = 𝑖𝐾𝐵 𝑚 𝑖^ =^ 𝑣𝑎𝑛′𝑡^ 𝐻𝑜𝑓𝑓^ 𝑓𝑎𝑐𝑡𝑜𝑟

Vapor

Pressure

Depression

(Raoult’s

Law)

𝑃𝑠𝑜𝑙𝑛 = 𝜒𝑠𝑜𝑙𝑣 𝑃𝑠𝑜𝑙𝑣 0 𝑃𝑠𝑜𝑙𝑛^ =^ 𝑉𝑃^ 𝑜𝑓^ 𝑠𝑜𝑙𝑢𝑡𝑖𝑜𝑛

𝑃𝑠𝑜𝑙𝑣^0 = 𝑉𝑃 𝑜𝑓 𝑝𝑢𝑟𝑒 𝑠𝑜𝑙𝑣𝑒𝑛𝑡

Osmotic

Pressure

𝜋 = 𝑖𝑀𝑅𝑇 𝑀^ =^ 𝑚𝑜𝑙𝑎𝑟𝑖𝑡𝑦^ 𝑜𝑓^ 𝑠𝑜𝑙𝑢𝑡𝑒

Chapter 5: Gases

Pressure

Average Kinetic

Energy

𝐾𝐸𝑎𝑣𝑔 = 3 ⁄^2 𝑅𝑇 𝑅 = 8. 314 𝐽

Root-Mean-

Square Speed

Ideal Gas Law 𝑃𝑉 = 𝑛𝑅𝑇 𝑛^ =^ #^ 𝑜𝑓^ 𝑚𝑜𝑙𝑒𝑠

Boyle’s Law

Charles’ Law 𝑉 ∝ 𝑇

Avogadro’s Law 𝑉 ∝ 𝑛

Combined Gas

Law

Standard Temp.

& Pressure (STP)

P=1 atm

T=273 K

Standard

Conditions

All aqueous species @ 1M

All gaseous species @1 atm

T=298 K

Density 𝑃(𝑀𝑀)

Dalton’s Law of

Partial Pressures

Dalton’s Law of

Partial Pressures

𝑃𝐴 = 𝜒𝐴𝑃𝑡𝑜𝑡𝑎𝑙 𝜒𝐴 =^ 𝑚𝑜𝑙^ 𝑓𝑟𝑎𝑐𝑡𝑖𝑜𝑛