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diff --git a/notes/notes.tex b/notes/notes.tex index 63cc519..b820a86 100644 --- a/notes/notes.tex +++ b/notes/notes.tex @@ -375,7 +375,7 @@ colorlinks=true \section{States and Properties of Matter} \subsection{Gases} \subsubsection{Kinetic-Molecular Theory} - Kinetic-molecular theory is a model of gases "as a large number of constantly and randomly moving particles that collide with eachother and the walls of the container. + Kinetic-molecular theory is a model of gases ``as a large number of constantly and randomly moving particles that collide with eachother and the walls of the container.'' The model postulates that: \begin{itemize} @@ -620,5 +620,43 @@ colorlinks=true Stoichiometry is the relationship between the relative quantities of substances taking part in a reaction or forming a compound, typically a ratio of whole integers. Stoichiometry is typically used in chemistry to determine the ratios between substances in which they react. For example, $H_2$ and $N_2$ react to form $NH_3$ in a ratio of $H:N=3:1$. However, if there are 5mol of $H_2$ and 1mol of $N_2$, then there is left 2mol of $H_2$, called the excess reactant. Because more nitrogen would allow continued reaction, nitrogen is called the limiting reactant. In general, the limiting and excess reactants in a reaction with uneven proportions can be determined with a similar calculus. Stoichiometry also extends to comparisons between reactants and products. If $2O_2 + H_2O \rightarrow H_2O_5$, 10 fully reacted moles of oxygen form 5 moles of the substance on the right (note that the substance makes no sense and isn't real). \subsubsection{Theoretical Yield and Percent Yield} Theoretical yield is ``the ideal maximum amount of a product that can be produced during a reaction, calculated from stoichiometric relationships.'' All examples above assumed that reactions occurr perfectly, consuming all of the reactants and creating the correct amount of product and nothing else. The amount of product created was the theoretical yield. However, real life doesn't usually have the same yield (actual yield) as predicted. Actual yield is almost always less than theoretical yield due to suboptimal reactant conditions and random factors. Percent yield is the ratio between actual yield and theoretical yield. +\section{Stoichiometry and the Gas Laws} + \subsection{Molar Masses} + \subsubsection{Moles and Avogadro's Number} + Moles (mol) are the SI unit for the amount of a substance, one mol being the same number of particles of a given substance as there are atoms in 12g of C-12, or $6.02*10^{23}$. Avogadro's number is that number of particles in a mol, and it is calculable from basic units of a carbon-12 atom, namely its atomic mass of $12amu$ and the fact that $1amu=1.66*10^{-24}g$ + \subsubsection{Molar Mass and Average Atomic Mass} + The mole and Avogadro's number relate average atomic mass and molar mass. Average atomic mass is the statistic displayed on the periodic table below a given element, in $\frac{amu}{atom}$. This is extensible to any arbitrary molecule, still in units $\frac{amu}{particle}$. Note that for a given substance, the molar mass (units $\frac{g}{mol}$) is equal to the average particle mass by definition of the mol. + \subsection{Introduction to Stoichiometry} + \subsubsection{Stoichiometry and Ratios} + Stoichiometry is based on ratios, such as $Reactant:Product$, $Reactant:Reactant$, or $Product:Product$. In the previous lesson, this was explored as the way to determine theoretical yield, so the foundation should already be set. Note that these ratios are molar ratios calculated from the ratios of the coefficients next to each compound in a balanced chemical equation. These ratios represent the amount of any two given substances in a balanced chemical reaction, ignoring total amount, and can be used to calculate the amounts of byproducts, amount of reactant required to react completely, limiting reactants, storage requirements, and how much product is created with a certain amount of reactant. + \subsection{Stoichiometric Calculations} + \subsubsection{Molar Mass and Mass-to-Mole Ratio} + Molar mass is in units of grams of element per mol. For example, $\frac{58.44g NaCl}{mol NaCl}$. This can be expanded to a given number of moles or a mass using dimensional analysis (note that dimensional analysis permits inversion of a ratio such as $\frac{mol NaCl}{58.44g NaCl}$). Also, for clarity's sake, the element formula next to each unit is necessary, and doesn't cancel. + \subsubsection{Interchemical Calculations} + Becuase of stoichiometric ratios as mentioned in the previous lesson, such as $\frac{mol NaCl}{mol Cl^+}$ in a table salt decomposition reaction, dimensional analysis can be further used to determine the mass of product created by a given chemical reaction. + \subsection{Gas Laws} + \subsubsection{Boyle's Law} + All gas laws are merely extensions of the ideal gas law mentioned in Unit II Topic 1.1. The ideal gas law is $\frac{P_1V_1}{N_1T_1}=\frac{P_2V_2}{N_2T_2}$ (N is number in moles, T is temperature in Kelvin, P is pressure, V is volume, and this holds for any two ideal gases according to Avogadro's Law). The first of these derivative laws is Boyle's Law: where quantity and temperature remain constant, pressure is inversely related to volume. This allows simple calculations relating changing volume and/or pressure of a gas. + \subsubsection{Other Laws} + \begin{tabular}{|c|c|} + \hline + Law & Relation \\ \hline + Boyle's Law & Volume and Pressure are inversely related \\ \hline + Charle's Law & Volume and Temperature are directly related \\ \hline + Gay-Lussac's Law & Pressure and Temperature are directly related \\ \hline + \end{tabular} + \subsubsection{Partial Pressure} + Partial pressure is "the fraction of the total pressure exerted by a mix of gases that is contributed by an individual gas." (i.e. the pressur of one gas in a mixture). $Partial pressure = \frac{Pressure if there were only the one gas}{Actual pressure}$. Dalton's Law states that the total pressure is equal to the sum of the partial pressures. Note that the fraction which the partial pressure makes up of the total pressure is equal to the molar fraction by the ideal gas law and the fact that temperature and volume are the same for all gases. + \subsection{The Ideal Gas Law} + \subsubsection{Avogadro's Law} + Avogadro's Law states that "the volume of a gas is proportional to the moles of the gas when pressure and temperature are kept constant." This is the $N$ term in the ideal gas law mentioned in last lesson. Note that this is unrelated to the gas's makeup. + \subsubsection{Derivation of the Ideal Gas Law} + From Boyle's Law ($V\ispropto \frac{1}{P}$), Charle's Law ($V\ispropto T$), and Avogadro's Law ($V\ispropto n$), the ideal gas law of $V\ispropto \frac{nT}{P}$ can be derived. This is equivalent to $V=R(\frac{nT}{P})$ or $PV=nRT$ where $R$ is the gas constant. Because the ideal gas law is independent from the gas's identity, $R$ has only one value. However, ideal gases can diverge from real gases significantly in high pressure or low temperature environments. + \subsection{Gas Stoichiometry} + \subsubsection{Implications of Molar Volume: Avogadro's Principle} + As stated repeatedly in the previous two lessons, the volume of a mole of gas is irrelevant to its composition. This is exemplified by molar volume: one mole of any ideal gas at standard temperature and pressure ($0^{\circ}C=273K$ and $1atm = 101.3kPa = 760 torr$) always has a molar volume of $22.4L$. Molar volume varies with temperature and pressure but is consistent between substances. Molar volume implies Avogadro's Principle: ``if two gas samples contain the same number of particles, they will have the same volume at a given temperature and pressure.'' Avogadro's Principle implies that in stoichiometry (ratios of coefficients in chemical reactions), the numbers can represent ratios of particles, moles, or volumes. +\section{Reaction Rates and Equilibrium} + \subsection{Reaction Rate} + \subsubsection{} \end{document} |