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% Document Info
\author{mjb}
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  /Title (chapter-9-gases.pdf)
  /Creator (Cheatography)
  /Author (mjb)
  /Subject (Chapter 9 - Gases Cheat Sheet)
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        \hspace*{-6pt}\includegraphics[width=5.8cm]{/web/www.cheatography.com/public/images/cheatography_logo.pdf}}
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\begin{tabulary}{11cm}{L}
    \vspace{-2pt}\large{\bf{\textcolor{DarkBackground}{\textrm{Chapter 9 - Gases Cheat Sheet}}}} \\
    \normalsize{by \textcolor{DarkBackground}{mjb} via \textcolor{DarkBackground}{\uline{cheatography.com/128288/cs/25374/}}}
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  \mymulticolumn{2}{p{5.377cm}}{\bf\textcolor{white}{Cheatographer}}  \\
  \vspace{-2pt}mjb \\
  \uline{cheatography.com/mjb} \\
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  \mymulticolumn{1}{p{5.377cm}}{\bf\textcolor{white}{Cheat Sheet}}  \\
   \vspace{-2pt}Published 23rd November, 2020.\\
   Updated 23rd November, 2020.\\
   Page {\thepage} of \pageref{LastPage}.
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  Measure your website readability!\\
  www.readability-score.com
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\begin{multicols*}{3}

\begin{tabularx}{5.377cm}{x{2.28942 cm} x{2.68758 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{Gas Laws}}  \tn
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Boyle's Law & P\textasciicircum{}initial\textasciicircum{}V\textasciicircum{}initial\textasciicircum{}=P\textasciicircum{}final\textasciicircum{}V\textasciicircum{}final\textasciicircum{} \tn 
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Charles's Law & V\textasciicircum{}i\textasciicircum{}÷T\textasciicircum{}i\textasciicircum{} = V\textasciicircum{}f\textasciicircum{}÷T\textasciicircum{}f\textasciicircum{} \tn 
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Combined Gas Law & P\textasciicircum{}i\textasciicircum{}V\textasciicircum{}i\textasciicircum{}÷T\textasciicircum{}i\textasciicircum{} = P\textasciicircum{}f\textasciicircum{}V\textasciicircum{}f\textasciicircum{}÷T\textasciicircum{}f\textasciicircum{} \tn 
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Avogadro's Law & V\textasciicircum{}i\textasciicircum{}÷n\textasciicircum{}i\textasciicircum{}=V\textasciicircum{}f\textasciicircum{}÷n\textasciicircum{}f\textasciicircum{} \tn 
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Ideal Gas Law & PV=nRT \tn 
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Dalton's Law of Partial Pressure & P\textasciicircum{}total\textasciicircum{}=P\textasciicircum{}1\textasciicircum{}+P\textasciicircum{}2\textasciicircum{}+P\textasciicircum{}3\textasciicircum{}... \tn 
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\mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{Dalton's Law of Partial Pressure}}  \tn
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Partial Pressure & P\textasciicircum{}gas\textasciicircum{}(atm)=(total pressure x moles\textasciicircum{}gas\textasciicircum{})÷total moles \tn 
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PP when volumes are different & P\textasciicircum{}total\textasciicircum{}=P\textasciicircum{}1\textasciicircum{}(atmxV\textasciicircum{}1\textasciicircum{}÷V\textasciicircum{}total\textasciicircum{})+P\textasciicircum{}2\textasciicircum{}(atmxV\textasciicircum{}2\textasciicircum{}÷V\textasciicircum{}total\textasciicircum{})... \tn 
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Mole fraction & moles of gas ÷ total moles \tn 
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Wet Gas & P\textasciicircum{}wet gas\textasciicircum{}=P\textasciicircum{}total\textasciicircum{}-P\textasciicircum{}H2O\textasciicircum{} \tn 
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 & then use PV=nRT to solve for variables \tn 
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\mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{Real Gases}}  \tn
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Van der waal's equation & P={[}(nRT)÷(V-nb){]} - {[}(a*n\textasciicircum{}2\textasciicircum{})÷(V\textasciicircum{}2\textasciicircum{}){]} \tn 
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When comparing real gases & a gas with a larger "a" value will require the largest correction to account for intermolecular forces \tn 
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 & a gas with a smaller "b" value will behave most ideally at high pressures \tn 
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 & If Vdw's pressure is lower than the ideal pressure, attractive forces dominate \tn 
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 & If Vdw's pressure is higher than ideal pressure, repulsive forces dominate \tn 
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Real Gas Behavior & attractive forces between molecules cause a decrease in pressure \tn 
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 & As molecules increase in size deviations from ideal behavior become apparent at relatively HIGH temps \tn 
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 & In general, most gases behave most ideally at HIGH temps and LOW pressures \tn 
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1 atm= & 1 atm (R= .08206) \tn 
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 & 760 mmHg (R= 62.364) \tn 
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 & 760 torr \tn 
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 & 1.013x10\textasciicircum{}5\textasciicircum{} Pa \tn 
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 & 101.3 kPa \tn 
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 & 29.92 inches Hg \tn 
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 & 14.69 psi \tn 
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 & 1.01325 bar \tn 
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\mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{Stoichiometry and Gases}}  \tn
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Mole ratio = Volume ratio & 2A+3B=AB \tn 
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 & 2A:3B \tn 
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 & 2mL A:3mL B \tn 
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\mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{Kinetic Molecular Theory}}  \tn
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\seqsplit{Temperature} & If temperature is increased, Pressure and KE increase by a factor of T\textasciicircum{}f\textasciicircum{}÷T\textasciicircum{}i\textasciicircum{} and rms increases by a factor of √T\textasciicircum{}f\textasciicircum{}÷T\textasciicircum{}i\textasciicircum{} \tn 
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Volume & If volume is increased, Pressure increases by a factor of V\textasciicircum{}i\textasciicircum{}÷V\textasciicircum{}f\textasciicircum{} while KE and rms increase by a factor of 1 (because they are not affected)) \tn 
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Moles & If moles are increased, pressure increases by a factor of n\textasciicircum{}f\textasciicircum{}÷n\textasciicircum{}i\textasciicircum{}, while KE and rms increase by a factor of 1 (no change) \tn 
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\mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{Using Ideal Gas Law to Calculate Gas Properties}}  \tn
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Ideal Gas Law & PV=nRT \tn 
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STP & 0 degrees celcius, 273 degrees Kelvin, 1 atm, 22.4 L/mol \tn 
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Density & d=MP÷RT    where M is molar mass \tn 
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Volume & When not given volume, but told to assume ideal gas behavior, use V=1L \tn 
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\mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{Diffusion and Effusion}}  \tn
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G1=gas 1 & G2=gas 2 \tn 
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Average Kinetic Energy & KE\textasciicircum{}G1\textasciicircum{} = KE\textasciicircum{}G2\textasciicircum{} when T\textasciicircum{}G1\textasciicircum{}=T\textasciicircum{}G2\textasciicircum{} \tn 
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Molecular Speed & √u\textasciicircum{}2\textasciicircum{} = √3RT÷M where M is the molar mass \tn 
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 & √u\textasciicircum{}2\textasciicircum{}G1 ÷ √u\textasciicircum{}2\textasciicircum{}G2 = √M\textasciicircum{}G2\textasciicircum{} ÷ √M\textasciicircum{}G1\textasciicircum{} \tn 
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Rate & d/dx \textasciicircum{}G1\textasciicircum{} ÷ d/dx \textasciicircum{}G2\textasciicircum{} = √M\textasciicircum{}G2\textasciicircum{} ÷ √M\textasciicircum{}G1\textasciicircum{} \tn 
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Time & t\textasciicircum{}G2\textasciicircum{} ÷ t\textasciicircum{}G1\textasciicircum{} = √M\textasciicircum{}G2\textasciicircum{} ÷ √M\textasciicircum{}G1\textasciicircum{} \tn 
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\end{tabularx}
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% That's all folks
\end{multicols*}

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