Hello, I took the 2014 MCAT exam and don't recall being given a separate formula sheet for the chem and physics section. If I remember correctly, most of the formulas we need to answer the questions are given in the passage. Does anyone know if it will be the same for the MCAT 2016? Or will we be given a separate formula sheet? Thank you!!
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MCAT 2016 formula sheet?
- Thread starter pch
- Start date
There's no formula sheet. But from what I've seen in AAMC materials, rote memorization of formulas is de-emphasized on the new MCAT. You should still be familiar with the formulas but there will be very little "plug-and-chug" and more of how variables relate to one another (e.g. increasing cross-sectional area of an artery would affect pressure how?). Sometimes, the equations are given in the passage as well.
Thank you aldol16!There's no formula sheet. But from what I've seen in AAMC materials, rote memorization of formulas is de-emphasized on the new MCAT. You should still be familiar with the formulas but there will be very little "plug-and-chug" and more of how variables relate to one another (e.g. increasing cross-sectional area of an artery would affect pressure how?). Sometimes, the equations are given in the passage as well.
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It is important to understand the equations to understand the relationships between different variables. They sometimes test that on the exam. But like aldol16 said, plug-and-chug is not tested.
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The attached PDF might help. Certainly not comprehensive, but maybe useful. The process of deciding how to organize the different sections was more useful that simply trying to memorize it. I tried out a lot of different organization schemes and this was the one I ended up with at test day.
Sadly SDN will not allow my to upload my Lyx file or even a text file with Latex Code. But for anyone so inclined, this might be helpful:
Sadly SDN will not allow my to upload my Lyx file or even a text file with Latex Code. But for anyone so inclined, this might be helpful:
%% LyX 2.2.0 created this file. For more info, see LyX | LyX – The Document Processor.
\documentclass[12pt,twocolumn]{article}
\usepackage[utf8]{inputenc}
\usepackage[a4paper]{geometry}
\geometry{verbose,tmargin=3cm,bmargin=3cm}
\usepackage{fancyhdr}
\pagestyle{fancy}
\usepackage{amsmath}
\usepackage{amssymb}
\usepackage{setspace}
\onehalfspacing
\makeatletter
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% LyX specific LaTeX commands.
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%%% PAGE DIMENSIONS
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% or letterpaper (US) or a5paper or....
% support the \includegraphics command and options
%%% PACKAGES
%\usepackage{booktabs}% for much better looking tables
%\usepackage{array}% for better arrays (eg matrices) in maths
%\usepackage{paralist}% very flexible & customisable lists (eg. enumerate/itemize, etc.)
% adds environment for commenting out blocks of text & for better verbatim
%\usepackage[framestyle=fbox, framefit=yes, heightadjust=all, framearound=all]{floatrow}
%\usepackage{floatrow}\usepackage{caption}\usepackage{subcaption}% make it possible to include more than one captioned figure/table in a single float
%\usepackage{float}\floatstyle{boxed}
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%\usepackage{sidecap}\allowdisplaybreaks[1]
%\usepackage{lineno}
%\linenumbers
%%% HEADERS & FOOTERS
% Header/footer
%\usepackage{endnotes}
%\let\footnote=\endnote %place "\theendnotes" in document where you want them
%\usepackage{fancyhdr}
%\fancyhead{}
%\fancyfoot{}
%\fancyhead[C]{\includegraphics[width=0.07\textwidth]{/Users/austinr2222/Dropbox/Eco_Milfoil_Management/Presentations/FOVLAP/Pamphlet/logo.png} Milfoil Management $\bullet$ October 2012}
%\fancyfoot[RO,LE]{\thepage}
\usepackage{fancyhdr}
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\lhead{}
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\rhead{}
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%\lhead{%\includegraphics[width=0.07\textwidth]{/Users/austinr2222/Dropbox/Eco_Milfoil_Management/Presentations/FOVLAP/Pamphlet/logo.png}}
%\chead{Burr Pond Weevil Stocking Project Description}
%\rhead{%October 2012}
%\setlength{\headrulewidth}{1pt}
%\fancyhead[C]{\includegraphics[width=0.07\textwidth]{/Users/austinr2222/Dropbox/Eco_Milfoil_Management/Presentations/FOVLAP/Pamphlet/logo.png} Milfoil Management $\bullet$ October 2012}
%\fancyfoot[RO,LE]{\thepage}
%\usepackage[firstpage]{draftwatermark}
%\SetWatermarkScale{5}
%%% SECTION TITLE APPEARANCE
%\usepackage{sectsty}\sectionfont{\Large\sffamily\mdseries\upshape} % (See the fntguide.pdf for font help)
%\subsectionfont{\large\sffamily\mdseries\upshape}
%%% The "real" document content comes below...
\makeatother
\begin{document}
\title{MCAT Formula Sheet}
\maketitle
\tableofcontents{}
\newpage
\section{Mechanics }
\subsection{Translational Motion}
\textcompwordmark{}
$x=x_{0}+v_{0}t+\frac{1}{2}at^{2}$
$v_{f}=v_{0}+at$
$v_{f}^{2}=v_{0}^{2}+at$
\subsection{Force}
\textcompwordmark{}
\textbf{Center of Mass}
$com=\frac{m_{1}x_{1}+m_{2}x_{2}}{x_{1}+x_{2}}$
\textcompwordmark{}
\textbf{Newtons 1st Law}
inertia, momentum, impluse
\textcompwordmark{}
\textbf{{*}Newtons Second Law }
$F=ma$
$Weight=F_{g}=mg$
\textcompwordmark{}
\textbf{Frictional Force}
$f_{max}=\mu N$
$\mu_{k}<\mu_{s}$...always
\textcompwordmark{}
\textbf{Uniform Circular Motion}
$F_{c}=ma_{circ.}=\frac{mv^{2}}{r}$
$a_{circ.}=\frac{v^{2}}{r}$
\textcompwordmark{}
\textbf{Inclined Plan}
$F_{normal}=mg\,cos\theta$
\subsection{Equilibrium}
\textcompwordmark{}
\textbf{Torque Forces}
$\mathbf{\tau}=\mathbf{F\cdot d}$
\textcompwordmark{}
\textbf{Tension on Pendulum }
$T=mg\,cos\theta$
\subsection{Work}
\textcompwordmark{}
\textbf{{*} Work}
$W=F\,d\,cos\theta$
$W_{total}=\Delta E$
\textcompwordmark{}
\textbf{{*}Kintic Energy}
$KE=\frac{1}{2}mv^{2}$
Units: Joules=N{*}m
\textcompwordmark{}
\textbf{{*}Potential Energy}
$U_{gravity}=mgh$
$U_{spring}=\frac{1}{2}kx^{2}$
\textcompwordmark{}
\textbf{Conservation of Energy}
$E_{total}=KE+U$
$\Delta E=\Delta K+\Delta U=0$
$E=mc^{2}$
\textcompwordmark{}
\textbf{Power}
$P=\frac{\Delta W}{\Delta t}$
Units:watt = J/s
\textcompwordmark{}
\textbf{{*}Spring Force and Work}
$F=-kx$
$W=\frac{1}{2}kx^{2}$
\newpage
\section{Fluids}
\subsection{Hydrostatics}
\textcompwordmark{}
\textbf{Specific Gravity}
SG=\%object submergerd
$SG=\frac{\rho_{substance}}{\rho_{water}}=\frac{height\,above\,surf}{total\,height}$
$\rho_{water}=\frac{1g}{cm^{3}}=\frac{10^{3}kg}{m^{3}}$
\textcompwordmark{}
\textbf{Archimedes Principle}
$F_{buoy}=\rho_{fluid}gV_{submerged}$
=weight of volume of displaced fluid
$V_{submerged\,object}=V_{displaced\,fluid}$
\textcompwordmark{}
\textbf{Pressure}
$P=\frac{F}{A}$
units: Pa = $\frac{N}{m^{2}}$
\textcompwordmark{}
\textbf{Static Pressure}
- pressure of object submerged in fluid
$P_{fluid}=\rho gh$
h is height of fluid above object
\textcompwordmark{}
\textbf{Absolute Pressure}
-adds atm pressure for open container
$P_{total}=P_{atm}+P_{fluid}=P_{atm}+P_{guage}$
$=P_{atm}+\rho gh$
\textcompwordmark{}
\textbf{Gauge Pressure}
- pressure due to liquid alone
$P_{guage}=P_{total}-P_{atm}=P_{fluid}$
\textcompwordmark{}
\textcompwordmark{}
\textbf{Weight}
$F_{g}=\rho gV=mg$
\textcompwordmark{}
\textbf{Pascals Principle}
$P=\frac{F_{1}}{A_{1}}=\frac{F_{2}}{A_{2}}$ (equal pressure)
$A_{1}d_{1}=A_{2}d_{2}$(same $\Delta V$)
$W=F_{1}d_{1}=F_{2}d_{2}$ (energy conserved)
small force, small area, big distance
–\textgreater{}large force, large area, small distance
\textcompwordmark{}
\textbf{Float or Sink?}
$\rho_{fluid}V_{disp}g=mg$
$\Rightarrow\rho_{fluid}V_{disp}=\rho_{obj}V_{obj}$
$\Rightarrow\frac{V_{disp}}{V_{obj}}=\frac{\rho_{obj}}{\rho_{fluid}}$
\textcompwordmark{}
\subsection{Flow}
\textcompwordmark{}
\textbf{Viscose Force}
$F_{viscosity}=\eta A\frac{V}{d}$
Unit of $\eta=\frac{F\,d}{A\,V}=Pa\cdot s$
1 Poise = $\frac{1}{10}Pa\cdot s$
\textcompwordmark{}
\textbf{Posieulle Flow}
$\frac{V}{t}=\frac{\Delta P\pi R^{4}}{8\eta L}$
\textcompwordmark{}
\textbf{{*} Continuity Eqn}
$A\,v=constant$
$\rho Av=constant$
$A_{1}V_{a}=A_{2}V_{2}$
\textcompwordmark{}
\textbf{Turbulence}
$V_{critical}=\frac{R\eta}{2\rho r}$
\textcompwordmark{}
\textbf{Surface Tension}
\textcompwordmark{}
\textbf{Bernoulli's Equation}
$p+\frac{1}{2}\rho V^{2}+\rho gh=constant$
\textcompwordmark{}
\textbf{Venturi Effect}
\newpage
\subsection{Gas Phase}
\textcompwordmark{}
\textbf{Kelvin Scale}
\textcompwordmark{}
\textbf{STP}
0C or 273K, 1 atm
1mole @STP = 22.4L
\textcompwordmark{}
\subsubsection{Ideal }
\textcompwordmark{}
\textbf{{*} Ideal Gas Law}
$PV=nRT$
\textcompwordmark{}
\textbf{{*} Avagadros Principle}
$\frac{n}{V}=k$
\textcompwordmark{}
\textbf{{*} Boyles Law}
$PV=k$
$P_{1}V_{1}=P_{2}V_{2}$
\textcompwordmark{}
\textbf{{*} Charles Law}
$\frac{V}{T}=k$
$\frac{V_{1}}{T_{1}}=\frac{V_{2}}{T_{2}}$
\textcompwordmark{}
\textbf{G-L Law}
$\frac{P}{T}=k$
\textcompwordmark{}
\textbf{Combined Gas Law}
$\frac{P_{1}V_{1}}{T_{1}}=\frac{P_{2}V_{2}}{T_{2}}$
\subsubsection{Non-ideal}
\textcompwordmark{}
\textbf{Vanderwalls Eqn of State}
$(P+\frac{n^{2}a}{V^{2}})(V=nb)=nRT$
$P_{1}=P_{o}+a\left[\frac{n}{v}\right]^{2}$
$V_{1}=V_{c}-nb$
n is \# of moles
a is a +/- constant
b is a constant
\subsubsection{Partial Pressure}
\textcompwordmark{}
\textbf{Mole Fraction}
$X_{A}=\frac{n_{A}}{n_{T}}=\frac{moles\,A}{mole\,total}$
\textcompwordmark{}
\textbf{Daltons Law of Partial Pressures}
$P_{T}=P_{A}+P_{B}+P_{c}+..$
$P_{A}=P_{T}X_{A}$
\textcompwordmark{}
\textbf{Henrys Law?}
\subsubsection{KineticMT}
\textcompwordmark{}
\textbf{Average Molecular Speed}
$k=\frac{1}{2}mv^{2}=\frac{3}{2}k_{B}T$
\textcompwordmark{}
\textbf{Root Mean Square}
$U_{rms}=\sqrt{\frac{sRT}{M}}$
\newpage
\section{Electromagnetism}
\subsection{Electrostatics}
\textcompwordmark{}
\textbf{Coulombs Law}
$F=k_{e}\frac{q_{1}q_{2}}{r^{2}}$
\textbf{\textcompwordmark{}}
\textbf{Electric Field}
$E=\frac{F_{e}}{q}=\frac{kQ}{r^{2}}$
Q is source charge of E field
q is the charge feeling the E field
Units: $\frac{N}{C}$ or $\frac{V}{m}$
\textcompwordmark{}
\textbf{Electric Potential Energy}
$U=q\Delta V=qEd=k_{e}\frac{qQ}{r}$
``work to move to point from $\infty$''
\textcompwordmark{}
\textbf{Electric Potential}
$V=\frac{U}{q}$
Units: J/C
\newpage
\subsection{Magnetism}
\textcompwordmark{}
Definition of magnetic field B
Motion of charged particles in magnetic fields; Lorentz force
\newpage
\subsection{Circuits}
\textcompwordmark{}
\textbf{{*}Current }
$I=\frac{Q}{\Delta t}$
Units:Amps=C/s
\textcompwordmark{}
\textbf{Potential Difference (Voltage)}
$\Delta V=\frac{W}{q}=\frac{kQ}{r}$
Units: J/c
Same as \textbf{EMF }in batteries
\textcompwordmark{}
\textbf{Kirchoff's Laws}
???????? what do these mean
\textcompwordmark{}
\textbf{Conductivity: Metallic}
\textcompwordmark{}
\textbf{Conductivity: Electrolytic }
\textbf{\textcompwordmark{}}
\textbf{Meters}
\subsubsection{Resistance}
\textcompwordmark{}
\textbf{Resistivity}
$R=\frac{\rho L}{A}$, where $\rho$ is some constant
\textcompwordmark{}
\textbf{{*} Ohms Law}
$V=IR$
\textcompwordmark{}
\textbf{Serial Resistors}
$R_{equiv}=R_{1}+R_{2}+...$
\textcompwordmark{}
\textbf{Parallel Resistors}
$\frac{1}{R_{equiv}}=\frac{1}{R_{1}}+\frac{1}{R_{2}}+...$
\textcompwordmark{}
\textbf{Power Dissipated by Resistors}
$P=IV=\frac{V^{2}}{R}=I^{2}R$
\textcompwordmark{}
\subsubsection{Capacitance}
\textcompwordmark{}
\textbf{Capacitance}
$C=\frac{Q}{V}$
\textcompwordmark{}
\textbf{Parallel Plates}
$V=Ed$
\textcompwordmark{}
\textbf{Energy Storage }
$U=\frac{1}{2}QV=\frac{1}{2}CV^{2}=\frac{1}{2}\frac{Q^{2}}{C}$
\textbf{\textcompwordmark{}}
\textbf{Parallel Capacitors}
$C_{eq}=C_{1}+C_{2}+....$
\textcompwordmark{}
\textbf{Serial Capacitors}
$\frac{1}{C_{eq}}=\frac{1}{C_{1}}+\frac{1}{C_{2}}+...$
\textcompwordmark{}
\textbf{Dialectrics?}
\newpage
\subsection{Electrochemistry}
\textcompwordmark{}
\textbf{Galvanic vs Electrolytic}
\begin{tabular}{|c|c|c|}
\hline
& Galvanic & Electrolytic\tabularnewline
\hline
\hline
$\Delta G^{\circ}$ & (-) & (+)\tabularnewline
\hline
EMF & (+) & (-)\tabularnewline
\hline
Sign of an & (-) & (+)\tabularnewline
\hline
Sign of cat & (+) & (-)\tabularnewline
\hline
\end{tabular}
For both types, ``AnOx RedCat''
= Ox @ an, Red@ cat
$\Rightarrow e^{-}$ flow from an to cat
\textcompwordmark{}
\textbf{Standard Reduction Potential}
$\uparrow E^{\circ}\Rightarrow\uparrow Probabilty\,its\,reduced$
(see Gibbs Free Energy below)
\textcompwordmark{}
\textbf{Standard EMF (induced voltage)}
$E_{cell}^{\circ}=E_{red}^{\circ}+E_{cat}^{\circ}$
measured under standard conditions
\textcompwordmark{}
\textbf{Gibbs Free Energy}
$\Delta G^{\circ}=-nFE^{\circ}$
$\Delta G^{\circ}=-RTlnK_{eq}$
$\Rightarrow E^{\circ}=\frac{RT}{nF}lnK_{eq}$
F=Faradays Constant \textasciitilde{}=10\textasciicircum{}5
R=gas constant \textasciitilde{}=8
n=moles of $e^{-}$transfered
RT/F has units of volts
\textcompwordmark{}
\textbf{Nernst Equation}
$E=E^{\circ}-\frac{RT}{nF}lnQ$
(comes from: $\Delta G=\Delta G^{\circ}+RTlnQ$)
$\uparrow Q\Rightarrow\downarrow E$
\textcompwordmark{}
\textbf{Faradays Law of Electrolysis}
$I\,t=nF$
n = moles of $e^{-}$
\textcompwordmark{}
\textbf{Oxidations Rules}
- Elemental forms are always zero.
- Number given in table below are overridden when combined with an element of higher electonegativity
-dont confuse with formal charge
\begin{tabular}{|c|c|}
\hline
Element & ox \#\tabularnewline
\hline
\hline
G 1A & +1\tabularnewline
\hline
G 2A & +2\tabularnewline
\hline
H & +1(w/ non-metal)\tabularnewline
\hline
& -1 (w/ metal)\tabularnewline
\hline
O & -1 (in peroxides $O_{2}^{-}$)\tabularnewline
\hline
& -2 (everything else)\tabularnewline
\hline
G 7A & -1 \tabularnewline
\hline
Cl & -1 (except w/ O of F)\tabularnewline
\hline
S & -2??\tabularnewline
\hline
\end{tabular}
\textbf{\textcompwordmark{}}
\textbf{Common Oxidizing Agents}
-oxidizing agents almost always contain oxygen
-reducing often contain metal ions of hydrides
\begin{tabular}{|c|c|}
\hline
Ox & Red\tabularnewline
\hline
\hline
$O_{2}$ & CO\tabularnewline
\hline
$H_{2}O_{2}$ & C\tabularnewline
\hline
Halogens & B5H6\tabularnewline
\hline
H2SO4 & Sn2+ \tabularnewline
\hline
HNO3 & Hydrazine\tabularnewline
\hline
NaClO & Zn(Hg)\tabularnewline
\hline
KMnO4 & Lindlars\tabularnewline
\hline
CrO3, Na2Cr2O7 & NaBH4\tabularnewline
\hline
PCC & LiAlH4\tabularnewline
\hline
NAD+, FADH & NADH, FADH\tabularnewline
\hline
\end{tabular}
\textcompwordmark{}
\newpage
\section{Periodic Motion}
\subsection{Oscillatory Motion}
\textcompwordmark{}
\textbf{Angular Frequency}
$\omega=\frac{\pi}{t}$
for SHM: $\omega=\sqrt{\frac{k}{m}}$
units: radians/sec
\textcompwordmark{}
\textbf{Amplitude}
-max displacement from equilibrium
$A=\frac{x(t)}{cos(\omega t)}$
\textcompwordmark{}
\textbf{Period}
$T=\frac{2\pi}{\omega}$
- the time it takes motion to repeat itself
\textcompwordmark{}
\textbf{Frequency}
$f=\frac{1}{T}$
Unit: Hz =1 oscillation/sec
\textcompwordmark{}
\textbf{Phase}
$x(t)=A\,cos(\omega t+\phi)$
$\phi=$phase constant
$\phi>0\Rightarrow left\,shift$
$\phi<0\Rightarrow right\,shift$
$\phi$ doesnt effect \emph{A} or \emph{f}
\newpage
\subsection{Wave Motion}
\textcompwordmark{}
\textbf{General definition of waves}
a traveling disturbance that transports energy but not matter
\textcompwordmark{}
\textbf{Longitudinal Wave}
oscillation in same direction as propagation (e.g., sound)
\textcompwordmark{}
\textbf{Transverse Wave }
oscilation perpendicular direction of propogation (e.g., a stadium wave)
\textbf{\textcompwordmark{}}
\textbf{Period}
\emph{time }over which wave pattern repeats
\textcompwordmark{}
\textbf{Wavelength}
\emph{distance }over which pattern repeats
\textcompwordmark{}
\textbf{Propagation Speed}
$v=\frac{\lambda}{T}=\lambda\,f$
\subsubsection{Sound }
\textcompwordmark{}
\textbf{Intensity}
$dB=10\,log_{10}(\frac{I}{I_{0}})$
\textcompwordmark{}
\textbf{Doppler Effect{*}}
can actually apply to any wave
\newpage
\section{Optics}
\subsection{Physical Optics}
\textcompwordmark{}
\textbf{Properties of electromagnetic radiation:}
Velocity equals constant c, in vacuo
Electromagnetic radiation consists of perpendicularly oscillating electric and magnetic fields; direction of propagation is perpendicular to both
\textcompwordmark{}
\textbf{Polarization of light: linear and circular }
\textcompwordmark{}
\subsubsection{Interf and Diffrac}
\textcompwordmark{}
\textbf{Interference Maxima}
$dsin\theta=m\lambda$
d=distance btwn slits
m=1,2,3....
\textcompwordmark{}
\textbf{Diffraction Limit (Rayleigh Criterion)}
$\theta_{d}=\frac{1.22\lambda}{D}$
D=diamter of circular apature
theta =angle of seperation
\textcompwordmark{}
\textbf{X-ray diffraction}
$2d\,sin\theta=m\,\lambda$
\textcompwordmark{}
\textbf{Diffraction Grating}
$\frac{\lambda}{\Delta\lambda}=mN$
\subsubsection{EMR Spectrum}
\textcompwordmark{}
Classification of electromagnetic spectrum
Visual spectrum, color
\textcompwordmark{}
\textbf{Photon Energy}
$E=hf$
\newpage~\newpage
\subsection{Spectroscopy}
\textcompwordmark{}
\textbf{Infared}
\textbf{}%
\begin{tabular}{|c|c|c|}
\hline
Vibration & Peak (cm-1) & Shape\tabularnewline
\hline
\hline
O-H & 3100-3500 & broad\tabularnewline
\hline
N-H & 3100-3500 & sharp\tabularnewline
\hline
C=O & 1700-1750 & sharp\tabularnewline
\hline
\end{tabular}
{*}Peaks given in wave numbers
{*}Fingerprint: region below 1400
$Wave\#=\frac{1}{\lambda}\,\propto\,f=\frac{c}{\lambda}$
$Abs=2-log(\%\,Transmitance)$
$\Rightarrow\downarrow\%T\Rightarrow\uparrow Abs$
\textcompwordmark{}
\textbf{NMR Spectroscopy}
\begin{tabular}{|c|c|}
\hline
Group & $\delta(ppm)$\tabularnewline
\hline
\hline
Alky & 0-3\tabularnewline
\hline
Alkynes & 2-3\tabularnewline
\hline
Alkenes & 4.6-6\tabularnewline
\hline
Aromatics & 6-8.5\tabularnewline
\hline
Aldehydes & 9-10\tabularnewline
\hline
COOH & 10.5-12\tabularnewline
\hline
\end{tabular}
$\#\,peaks=n+1$, where n is the number of non-identical protons less than 3 bonds away
$area\,under\,peak(s)\propto\#\,identical\,H^{+}$
\textcompwordmark{}
\textbf{UV-Vis}
$\downarrow\left|HOMO-LUMO\right|\Rightarrow\downarrow f_{absorption}$
$\uparrow conjugation\Rightarrow\downarrow f_{absorption}$
\newpage
\subsection{Geometrical Optics}
applies when object size \textgreater{}\textgreater{} $\lambda$
\subsubsection{Reflec and Refrac}
\textcompwordmark{}
\textbf{Refractive Index}
$n=\frac{c}{v}$
\textcompwordmark{}
\textbf{{*} Snell's Law}
{\Large{}$\frac{sin\theta_{1}}{sin\theta_{2}}=\frac{v_{1}}{v_{2}}=\frac{n_{2}}{n_{1}}=\frac{\lambda_{1}}{\lambda_{2}}$}{\Large \par}
\newpage
\subsubsection{Thin Lenses}
\textcompwordmark{}
\textbf{{*} Spherical Lense Eqn}
$\frac{1}{f}=\frac{1}{o}+\frac{1}{i}$
\textcompwordmark{}
\textbf{Power}
$P=\frac{1}{f}$
units: diapters, D=$m^{-1}$
\textcompwordmark{}
\textbf{Magnification}
$M=\frac{-i}{o}$
\textbf{\textcompwordmark{}}
\textbf{Image hieght}
$\frac{o}{i}=\frac{h_{o}}{h_{i}}$
\textbf{\textcompwordmark{}}
\textbf{Radius of Curvature}
$R=2f$
\subsubsection{Spherical Mirrors}
\textcompwordmark{}
\textbf{Eqn}
$\frac{1}{f}=\frac{1}{i}+\frac{1}{o}=\frac{2}{R}$
\newpage
\section{Thermodynamics}
\subsection{Heat Eqns }
\textcompwordmark{}
\textbf{First Law of Thermodynamics}
$\Delta U=Q-W$
\begin{tabular}{|c|c|}
\hline
Q = 0 & Adiabtic\tabularnewline
\hline
W = 0 & Isovolumetric/Isochoric\tabularnewline
\hline
$\Delta U=0$ & Isothermal\tabularnewline
\hline
$\Delta P=0$ & Isobaric\tabularnewline
\hline
\end{tabular}
\textcompwordmark{}
\textbf{Specific Heat}
$c=\frac{Q/\Delta T}{m}$
\textbf{\textcompwordmark{}}
\textbf{Heat Capacity}
$mc=\frac{Q}{\Delta T}$
\textcompwordmark{}
\textbf{Heat of Absorption}
$Q=mc\Delta T$
\textcompwordmark{}
\textbf{Heat of Transformation}
$Q=mL$
\textcompwordmark{}
\textbf{Heat Transfer}
Conduction = molec collisions
Convection = fluid motion
Radiation = electromag waves
\textcompwordmark{}
\textbf{Thermal Expansion}
$\Delta L_{linear}=\alpha L_{0}\Delta T$
$\Delta A_{area}=??$
$\Delta V_{volume}=\beta V_{0}\Delta T$
\textcompwordmark{}
\textbf{Entropy}
$\Delta S=\frac{Q_{rev}}{T}$
Qrev=heat lost in reverse rxn
T=temp in kelvin
\textcompwordmark{}
\textbf{PV Diagrams}
W=-area on PV graph
$W=\int_{path}\mathbf{F}\cdot d\mathbf{s}=\int P\,dv$
\newpage
\subsection{Chemical Equilibria}
\textcompwordmark{}
\textbf{General Rxn}
$aA+bB\rightarrow cC+dD$
\textcompwordmark{}
\textbf{Equilibrium Constant}
$rate_{forward}=rate_{reverse}$
$K_{c}=K_{eq}=\frac{K_{forw}}{K_{rev}}=\frac{[C]^{c}[D]^{d}}{[A]^{a}^{b}}$
\textcompwordmark{}
\textbf{Reaction Quotient}
$Q_{c}=\frac{[C]^{c}[D]^{d}}{[A]^{a}^{b}}$
\newpage
\subsection{Isobaric Rxns}
\textcompwordmark{}
\textbf{Standard Conditions ($^{\circ}$)}
25C or 298 K, 1 atm, 1 M concentration
\textcompwordmark{}
\textbf{Physiological Conditions}
....
\textcompwordmark{}
\textbf{Heat of Reaction}
$\Delta H_{rxn}^{\circ}=\Sigma_{i}\Delta H_{f\,products}^{\circ}$
$\;\;\;\;\;\;\;\;\;\;\;\;\;\;-\Sigma_{i}\Delta H_{f\,reactants}^{\circ}$
- same applies for entropy and all other state functions (e.g. pressue, density, temperature, volume, enthalpy, internal energy, free energy; see Hess's Law)
\textcompwordmark{}
\textbf{Bond Enthalpy}
$\Delta H_{rxn}^{\circ}=\Sigma_{i}\Delta H_{broken}-\Sigma_{i}\Delta H_{formed}$
\textcompwordmark{}
\textbf{Gibbs Free Energy}
$\Delta G=\Delta H-T\Delta S$
$\Delta G^{\circ}=-R\,T\,ln(K_{eq})$
$\Delta G=\Delta G^{\circ}+RT\,ln\frac{Q}{K_{eq}}=ln\frac{Q}{K_{eq}}$
T is in Kelvin!
\subsection{Isovolumetric Calorimetry}
\newpage
\section{Kinetics}
\textcompwordmark{}
\textbf{General Rxn}
$aA+bB\rightarrow cC+dD$
\textcompwordmark{}
\textbf{Definition of Rate}
$rate=\frac{\Delta[A]}{a}=-\frac{\Delta}{b\Delta t}=\frac{\Delta[C]}{c\Delta t}=\frac{\Delta[D]}{c\Delta t}$
for simplicity i will say rate = dP/dt, where P={[}Products{]}
units:$\frac{mol}{l\cdot s}=\frac{M}{s}$
\textcompwordmark{}
\textbf{General Rate Law}
$\frac{dP}{dt}=k[A]^{x}^{y}$
k=rate constant of rxn
x and y must be determines experimentally for a given rxn at a given temp
example:
\begin{tabular}{|c|c|c|}
\hline
{[}A{]} & {[}B{]} & rate\tabularnewline
\hline
\hline
1.0 & 1.0 & 2.0\tabularnewline
\hline
1.0 & 2.0 & 8.1\tabularnewline
\hline
2.0 & 2.0 & 15.9\tabularnewline
\hline
\end{tabular}
$\Rightarrow rate=k[A]^{1}^{2}$
$(\Delta[reactants])^{x}=(\Delta rate)$
\textcompwordmark{}
\textbf{Zero Order}
$\frac{dP}{dt}=k[A]^{0}^{0}=k$
\textcompwordmark{}
\textbf{First Order}
$\frac{dP}{dt}=k[A\,or\,B]$
\textcompwordmark{}
\textbf{Second Order}
$\frac{dP}{dt}=k[A]^{1}^{1}$
$\frac{dP}{dt}=k[A\,or\,B]^{2}$
\textbf{\textcompwordmark{}}
\textbf{Broken Order}
fractional exponents
\textcompwordmark{}
\textbf{Mixed Order}
rate constants vary over time
\textcompwordmark{}
\textbf{Collision Theory}
$rxn\,rate=Z\times f$
Z = total \# collisions per time
f = fraction of effective collisions
\textcompwordmark{}
\textbf{Arrhenius Eqn}
$k=Ae^{\frac{-E_{a}}{RT}}$
k = rate constant of rxn
A = frequency of collisions (s-1)
$E_{a}$= activation energy
R = ideal gas constant
T = temperature IN KELVIN
\textcompwordmark{}
\textbf{M-M Eqn}
\newpage
\section{Solution Chemistry}
\subsection{Definitions and Rules}
\textcompwordmark{}
\textbf{Dilutions}
$M_{i}V_{i}=M_{f}V_{f}$
\textcompwordmark{}
\textbf{Mole Fraction}
$X_{A}=\frac{mole\:A}{total\,moles\,of\,all\,specieis}$
\textcompwordmark{}
\textbf{Molarity (M)}
$M=\frac{moles\,solute}{liters\,soltuion}$
\textcompwordmark{}
\textbf{Molality (m)}
$m=\frac{mole\,solute}{kg\,solvent}$
\textcompwordmark{}
\textbf{Normality}
$N=\frac{\#\,equivs\,of\,interest}{liters\,soln}$
? or is it ``\# g equivalent weights?''
``molarity of the 'stuff' of interest''
\textcompwordmark{}
\textbf{Osmolality}
$Osmoles=\frac{\#\,seperate\,molecules}{L_{solution}}$
\textcompwordmark{}
\textbf{Solubility Rules}
1. Water soluble IF \emph{cation} = alkali metal (G1) or ammonium (NH4+)
2. Water soluble IF \emph{anion} = nitrate (NO3-) or acetate (CH3COO-)
Refer to Kaplan text for additional rules to know...
\textcompwordmark{}
\textbf{Equivalents}
amnt of substance that will produce or react with 1 mole of H+ or OH- ions
\newpage
\subsection{Colligative Properties}
\textcompwordmark{}
\textbf{Vapor Pressure Depression (Raoults Law)}
$P_{A}=X_{A}P_{A}^{\circ}$
\textcompwordmark{}
\textbf{Boiling Point Elevation}
$\Delta T_{b}=iK_{b}m$
i = \# of particles into which compound dissasociates
m=molalility of soln
\textcompwordmark{}
\textbf{Freezing Point Depression}
$\Delta T_{f}=iK_{f}m$
``amount that normal freezing point is lowered''
\textcompwordmark{}
\textbf{Osmotic Pressure}
$\Pi=iMRT$
R = ideal gas constant
\textcompwordmark{}
\textbf{Diffusion}
$\frac{r_{1}}{r_{2}}=\sqrt{\frac{M_{2}}{M_{1}}}$
r = diffusion rate
M = molar masses of gasses
\textcompwordmark{}
\textbf{Henrys Law?}
\newpage
\subsection{Acids and Bases}
\textcompwordmark{}
\textbf{Estimation}
$log(n\times10^{m})\approx m+0.n$
\vspace{0.2cm}
$k_{a}=\frac{[X]^{2}}{[IC]-X}\approx x^{2},$when acid is weak
\textcompwordmark{}
\textbf{pH and pOH}
$pH+pOH=14$
\textcompwordmark{}
\textbf{Acid Disassociation}
$k_{a}=\frac{[H^{+}][A^{-}]}{[HA]}$
\textcompwordmark{}
\textbf{Base Disassociation}
\textbf{$k_{b}=\frac{[OH^{-}][HA]}{[A^{-}]}$}
\textcompwordmark{}
\textbf{Water Autoionization}
$k_{w}=[H^{+}][OH^{-}]$
$=k_{a}k_{b}$
$=\left(10^{-7}\right)\left(10^{-7}\right)=10^{-14}$
\textcompwordmark{}
\textbf{Henderson-Hasselbalch}
$pH=pK_{a}+log\frac{\left[A^{-}\right]}{\left[HA\right]}$
\vspace{0.2cm}
$pOH=pK_{b}+log\frac{\left[HA\right]}{\left[A^{-}\right]}$
\vspace{0.2cm}
- HA=weak acid and HB=weak base
- can only be used in buffer region
\textcompwordmark{}
\textbf{Neutralization w/ reactants 1:1}
$M_{a}V_{a}=M_{b}V_{b}$
\textcompwordmark{}
\textbf{Equivalence Point for acidic (negative?) AA }
$\frac{pKa_{R-group}+pKa_{COOH}}{2}\approx\frac{pKa_{R-group}+9}{2}$
\textcompwordmark{}
\textbf{Equivalence Point for basic (positive?) AA}
$\frac{pKa_{R-group}+pKa_{NH2}}{2}\approx\frac{pKa_{R-group}+2}{2}$
\textcompwordmark{}
\textbf{pH approximation}
$log(m\times10^{n})\approx n+\frac{m}{10}$
$\Rightarrow pH=-log([H^{+}])\approx-n-\frac{m}{10}$
\newpage
\section{Atomic Physics}
\textcompwordmark{}
\textbf{Atomic Structure}
$E_{electron}=\frac{-R_{H}}{n^{2}}$
\textcompwordmark{}
$E_{photon}=\frac{hc}{\lambda}$
\textcompwordmark{}
\textbf{Electronic Configuration}
??? n+l rule
\textcompwordmark{}
\textbf{Exponential Decay Formula}
$n=n_{o}=e^{-\lambda t}$
\textcompwordmark{}
\textbf{Alpha Decay}
$_{92}^{238}U\rightarrow_{90}^{234}Th+_{2}^{4}He$
\textcompwordmark{}
\textbf{Beta-minus Decay}
$_{53}^{137}Cs\rightarrow_{56}^{137}Ba+_{-1}^{0}e^{-}+\overline{V_{e}}$
\textcompwordmark{}
\textbf{Beta-plus Decay}
$_{11}^{22}Na\rightarrow_{10}^{22}Ne+_{+1}^{0}e^{+}+\overline{V_{e}}$
\newpage
\subsection{Periodic Table}
\textcompwordmark{}
\textbf{Left to Right}
$\uparrow Z_{eff}$
$\downarrow Atomic\,Radii$
$\uparrow IE\,\&\,EA$
$\downarrow Ionic\,Radii$ (except no $\Delta$ for metaloids)
\textcompwordmark{}
\textbf{Top to Bottom}
slight$\downarrow Z_{eff}$
$\uparrow Atomic\,Radii$
$\uparrow IE\,\&\,EA$
$\uparrow Ionic\,Radii$ (including metaloids)
\newpage
\section{Genetics}
\textcompwordmark{}
\textbf{Recombination Frequency}
\textcompwordmark{}
\textbf{Hardy Weinberg Equilibrium}
\textcompwordmark{}
\textbf{Mendelian Inheritance}
\newpage
\section{SI Units}
\textcompwordmark{}
\textbf{SI Prefixes}
\begin{tabular}{|c|c|c|}
\hline
\emph{Symbol} & \emph{Prefix} & \textbf{\emph{$10^{x}$}}\tabularnewline
\hline
\hline
T & tera & 12\tabularnewline
\hline
k & kilo & 3\tabularnewline
\hline
– & – & 0\tabularnewline
\hline
c & centi & -2\tabularnewline
\hline
m & milli & -3\tabularnewline
\hline
$\mu$ & micro & -6\tabularnewline
\hline
n & nano & -9\tabularnewline
\hline
p & pico & -12\tabularnewline
\hline
f & femto & -15\tabularnewline
\hline
\end{tabular}
\textcompwordmark{}
\newpage
\section{Orgo Nomenclature}
\begin{tabular}{|c|c|c|}
\hline
{\scriptsize{}Group} & {\scriptsize{}Prefix} & {\scriptsize{}Suffix}\tabularnewline
\hline
\hline
{\scriptsize{}COOH} & {\scriptsize{}carboxy-} & {\scriptsize{}-oic acid}\tabularnewline
\hline
{\scriptsize{}Anhydrides} & {\scriptsize{}-alkanoyloxy} & {\scriptsize{}anhydride}\tabularnewline
\hline
& {\scriptsize{}-carbonyl} & \tabularnewline
\hline
{\scriptsize{}Esters} & {\scriptsize{}alkoxycarbonyl-} & {\scriptsize{}-oate}\tabularnewline
\hline
{\scriptsize{}Amides} & {\scriptsize{}carbomoyl-} & {\scriptsize{}-amide}\tabularnewline
\hline
{\scriptsize{}nitrile} & {\scriptsize{}cyano-} & {\scriptsize{}-nitrile}\tabularnewline
\hline
{\scriptsize{}Aldehydes} & {\scriptsize{}oxo-} & {\scriptsize{}-al}\tabularnewline
\hline
{\scriptsize{}Ketones} & {\scriptsize{}oxo- ket-} & {\scriptsize{}-one}\tabularnewline
\hline
{\scriptsize{}Alcohols} & {\scriptsize{}hydroxy-} & {\scriptsize{}-ol}\tabularnewline
\hline
{\scriptsize{}thiol} & {\scriptsize{}mercapto-} & {\scriptsize{}-thiol}\tabularnewline
\hline
{\scriptsize{}amine} & {\scriptsize{}amino-} & {\scriptsize{}-amine}\tabularnewline
\hline
{\scriptsize{}alkene} & {\scriptsize{}alkenyl} & {\scriptsize{}-ene}\tabularnewline
\hline
{\scriptsize{}alkyne} & {\scriptsize{}alkynyl} & {\scriptsize{}-yne}\tabularnewline
\hline
{\scriptsize{}alkane} & {\scriptsize{}alkyl} & {\scriptsize{}-ane}\tabularnewline
\hline
{\scriptsize{}ether} & {\scriptsize{}alkoxy} & {\scriptsize{}-ane}\tabularnewline
\hline
{\scriptsize{}alkyl halide} & {\scriptsize{}halo-} & {\scriptsize{}-ane}\tabularnewline
\hline
{\scriptsize{}nitro} & {\scriptsize{}nitro} & {\scriptsize{}-ane}\tabularnewline
\hline
\end{tabular}
\textcompwordmark{}
groups are in order of priority from top (highest) to bottom (lowest priority)
\end{document}
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