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diff --git a/notes/notes.tex b/notes/notes.tex index b820a86..61bc1a8 100644 --- a/notes/notes.tex +++ b/notes/notes.tex @@ -42,7 +42,7 @@ colorlinks=true In 1800s, John Dalton \& Joseph Proust used scientific method to research the atom, developing the first atomic theory (an explanation of the structure of matter in terms of different combinations of very small particles) - Proust discovered that compounds follow the "law of definite proportions:" whole numbers define the ratio of masses of elements found in a compound + Proust discovered that compounds follow the ``law of definite proportions:'' whole numbers define the ratio of masses of elements found in a compound Law of definite proportions allowed Dalton to form atomic theory (which supported law of definite proportions) @@ -85,7 +85,7 @@ colorlinks=true He concluded that an atom is mostly empty space, with a small, positively charged, central region (the nucleus), in which most of the atom's mass is concentrated. \subsection{The Modern Atomic Theory} \subsubsection{Theories of Light} - Newton, in 1704, developed the corpuscular (from Latin for "puny body") theory of light, light as particles. + Newton, in 1704, developed the corpuscular (from Latin for ``puny body'') theory of light, light as particles. Thomas Young in the early 1800s, used the double-slit diffraction experiment to demonstrate light bending around corners and interfering like a wave. @@ -110,14 +110,14 @@ colorlinks=true \item Electrons have a definite radius and momentum, contradicting the Heisenberg Uncertainty Principle. \end{itemize} - The electron cloud model (developed by Schrodinger and others) replaced the Bohr Model, and is the currently accepted model, because it considered the Heisenberg Uncertainty Principle. In this model, electrons are considered to only have probable locations within a "cloud," but the clouds still have different energy levels for the electrons. + The electron cloud model (developed by Schrodinger and others) replaced the Bohr Model, and is the currently accepted model, because it considered the Heisenberg Uncertainty Principle. In this model, electrons are considered to only have probable locations within a ``cloud,'' but the clouds still have different energy levels for the electrons. \subsection{Atomic Spectra} \subsubsection{Bohr's Explanation of Atomic Emission and Absorption} - Electrons aren't strictly in orbits; instead, they rest in discrete \emph{orbitals}, or energy levels. Electrons absorb light ("excitation" of an atom) and rise to higher energy levels and randomly fall to lower energy levels, emitting light. However, the Bohr model can represent this sufficiently. + Electrons aren't strictly in orbits; instead, they rest in discrete \emph{orbitals}, or energy levels. Electrons absorb light (``excitation'' of an atom) and rise to higher energy levels and randomly fall to lower energy levels, emitting light. However, the Bohr model can represent this sufficiently. - This also explains the quantization of atomic spectrum lines (there are a finite number of "jumps" electrons can make between orbitals) + This also explains the quantization of atomic spectrum lines (there are a finite number of ``jumps'' electrons can make between orbitals) \subsubsection{Absorption and Emission Spectra} - Atomic spectra are the frequencies of light at which atoms' electrons "jump" between orbitals. These are visible in "absorption" and "emission" spectra. + Atomic spectra are the frequencies of light at which atoms' electrons ``jump'' between orbitals. These are visible in ``absorption'' and ``emission'' spectra. Absorption spectra is an EM spectrum in which wavelengths of light absorbed by an element show up as dark lines on a visible light background. Emission spectrum is the complement -- brightly colored lines on a black background. These are determined to represent all the possible emission/absorption frequencies of a given atom, respectively. \subsubsection{Spectroscopy} @@ -131,7 +131,7 @@ colorlinks=true \end{itemize} \subsection{The Structure of the Atom} \subsubsection{The Atom's Components} - An atom is the smallest particle of an element that has the same properties as the element. The atom can be divided into two parts, the nucleus (the center that holds protons and neutrons), and the orbitals (regions surrounding the nucleus where electrons sit in "clouds") + An atom is the smallest particle of an element that has the same properties as the element. The atom can be divided into two parts, the nucleus (the center that holds protons and neutrons), and the orbitals (regions surrounding the nucleus where electrons sit in ``clouds'') The atom is made of 3 particles: \begin{itemize} @@ -142,7 +142,7 @@ colorlinks=true In a neutral atom, \# of protons = \# of electrons, but neutrons can vary significantly. Any atom can have any number of these particles, but it's not always stable. \subsubsection{Atomic Mass Unit} - Because atoms' masses are so small, scientists use a unit called an "AMU" to describe weights of subatomic particles. + Because atoms' masses are so small, scientists use a unit called an ``AMU'' to describe weights of subatomic particles. An AMU is defined to be exactly $\frac{1}{12}$ of the mass of a $C_12$ atom, which is equal to $1.66*10^{-24}g$. @@ -191,7 +191,7 @@ colorlinks=true \item Proton: $^1_1p$ \end{itemize} \subsubsection{Fission} - "Nuclear fission is the process in which a heavy nucleus is split into two large fragments of comparable mass to form more stable and smaller nuclei, resulting in the release of great amounts of energy." Nuclear fission works by a neutron hitting a large nucleus and making it into an unstable isotope. Then, the resulting isotope quickly decays to fission products, a large amount of energy, and neutrons. + ``Nuclear fission is the process in which a heavy nucleus is split into two large fragments of comparable mass to form more stable and smaller nuclei, resulting in the release of great amounts of energy.'' Nuclear fission works by a neutron hitting a large nucleus and making it into an unstable isotope. Then, the resulting isotope quickly decays to fission products, a large amount of energy, and neutrons. This isn't a completely clean energy source, however. Nuclear energy processes' large fission products are radioactive waste which needs to be stored far away from humans. These can occur naturally, but they don't occur explosively. In man-made power plants or nuclear bombs, fission reactions self-sustain because the output neutrons from one fission reaction trigger more fission reactions. These reactions only self-sustain if the mass of the reactive material is at or above critical mass, which is different for different nuclei. @@ -651,12 +651,105 @@ colorlinks=true \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. + From Boyle's Law ($V\propto \frac{1}{P}$), Charle's Law ($V\propto T$), and Avogadro's Law ($V\propto n$), the ideal gas law of $V\propto \frac{nT}{P}$ 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{} + \subsubsection{Energy Diagrams and $\Delta G$} + $G$ is the free energy of a system, how much energy is readily available to do work in a system. $\Delta G$ is the change in the free energy over time, and $\Delta G_{rxn}$ is the change in free energy during a reaction. If $\Delta G_{rxn} < 0$, then the reactants have more free energy than the products, and this type of reaction occurs "spontaneously:" if any parts of the chemicals meet the activation energy for the reaction, the reaction is able to continue. The opposite of this type of reaction is nonspontaneous reactions where $\Delta G_{rxn} > 0$. This means that the products have more free energy than the reactants, and energy has to be constantly added to make the reaction continue. + \subsubsection{Activation Energy} + Activation energy ($E_A$) is the minimum amount of energy to initiate a chemical reaction (this is brought on by an increase in free energy of compounds during the reaction---meaning that energy is absorbed by the reaction before the ``hump'' of the activation energy is reached). This is a barrier to the reaction and must be overcome before the reaction will proceed. For all stable compounds, the reaction energy is positive because otherwise they are unstable and decompose readily (the higher the activation energy, the less likely the reaction is to occur and thus more slowly it occurs). + \subsubsection{Chemical Bonds} + Chemical reactions rearrange atoms in molecules by making and/or breaking bonds. Bonds, as mentioned in previous units, are stable electron configurations---implying that energy must be input to start decomposing or making bonds. Note that energy still must be input to start most spontaneous reactions, but they will continue on their own because energy from previous reactions supplies activation energy for other reactant molecules. + \subsubsection{Reaction Rate} + Reaction rate is how quickly reactants convert to products. This depends inversely on activation energy. High activation energies (like in graphite to diamond reaction) mean low reaction rates, and low activation energies (like baking soda and vinegar) mean very high reaction rates. This is completely unrelated to $\Delta G_{rxn}$. + \subsubsection{Collision Theory} + Collision Theory is the model that explains chemical reactions which assumes that chemical reactions' rates are proportional to their collision rate (note that, in reality, orientation and speed of the molecules are important, but the rate is still proportional to the number of collisions). Kinetic molecular theory allows the idea of a Maxwell-Boltzmann Distribution in that molecules have different speeds even at the same temperature. The Maxwell-Boltzmann Distribution describes how many molecules are at a given speed for a given temperature. When graphed, the vertical axis typically represents the count/frequency of particles and the horizontal axis the velocity of the particles. These distributions are typically bell curves, and the "longer" the curve, the higher the temperature + \subsubsection{Effective Collisions} + Effective Collisions, as mentioned in the previous topic, are necessary (as compared to simply collisions where all possible touching of molecules results in a reaction) for chemical reactions to occur. What contrasts these effective collisions is a high enough kinetic energy and the reactants' facing the correct directions to exchange atoms. + \subsubsection{Effect of Concentration on Reaction Rate} + Similar to temperature increasing collision rate by increasing pressure/temperature, concentration causes more frequent collisions---increasing the rate of reaction (concentration meaning number of molecules per volume in an aqueous solution, for example). + \subsubsection{Effect of Pressure on Reaction Rate} + There are 2 other ways to increase pressure other than temperature: increasing the amount of reactants and decreasing volume (which makes sense with the ideal gas law). However, note that increasing the pressure is only useful with reactions exclusively between gases because liquids and solids don't become more dense with higher pressures. + \subsubsection{Effects of Surface Area on Reaction Rate} + Reactions occur at the surface of solids, so decreasing the particle size (such as from one large cube to 8 smaller cubes) will increase the reaction rate. This can also apply to changing the shape (a sphere will have a lower reaction rate than a spiky ball) of the solid reactants. However, the particles are typically too small as for this to be realistic. + \subsection{Reaction Pathways} + \subsubsection{Reaction Pathway Graphs} + A reaction pathway graph is a diagram of the change in energy between reactants and products. This is sometimes called a potential energy diagram because it graphs the Gibbs Free Energy/potential energy over time during a reaction. Energy is typically on the vertical axis, and time/reaction progression is on the horizontal axis (meaning that reactants are to the left and products to the right). + \subsubsection{Exothermic Reactions} + Exothermic Reactions are reactions which release energy. This occurs when the potential energy of the reactants is higher than the potential energy of the products (kinetic energy is released to conserve energy). These include condensation, combustion, dissociation of strong acids, solidification of cement, concrete, and epoxy, and the thermite reaction. These follow the exothermic reaction pathway which is the decrease in potential energy of the materials. + \subsubsection{Endothermic Reaction Pathway} + Endothermic reactions are the opposite of exothermic reactions: they absorb energy. These include melting, photosynthesis, decomposition and dehydration reactions, and the dissociation of some salts. In these, reactants always have lower potential energy than products. For both endothermic and exothermic reactions, the reaction has the property $\Delta H_{rxn}$ --- the change in potential energy of the substances. Endothermic reactions have positive $\Delta H$ because the products have higher potential energy than the reactants. The opposite is true of exothermic reactions. + \subsubsection{Activation Energy and the Activated Complex} + As mentioned in previous lessons, all reactions involving stable compounds have an activation energy---the minimum amount of energy needed to start a chemical reaction (such as heating a match to make it start burning). The activated complex is a ``short-lived, high-energy intermediate between reactants and products,'' which is necessary to complete a reaction and the reason why activation energy is required to bring substances together to form the activated complex. The activation energy is defined as the difference between the activated complex's potential energy and the reactants' potential energy. This is represented as $E_a$. As activation energy increases, reaction rate decreases. + \subsection{Catalysts} + \subsubsection{Catalysts} + Catalysts are substances which increase the rate of a reaction but aren't consumed by the reaction. This is by the creation of an alternate reaction pathway with lower activation energy. As noted in a previous lesson about notation, chemical equations with catalysts have the catalyst written above the arrow. + \subsubsection{How Catalysts Work} + Catalysts decrease the activation energy/increase reaction rate by holding reactants in the right orientation to interact to increase the number of effective collisions. They can also form temporary intermediate substances for a different reaction pathway, and they sometimes weaken or break reactant bonds. + \subsubsection{Heterogenous Catalysts} + Heterogenous catalysts are any catalyst which is in a different state of matter than the reactants---making it easier to remove when the reaction completes. These include platinum in a catalytic converter or iron in ammonia production. + \subsubsection{Enzymes} + Enzymes are complex proteins which are produced biologically and catalyze biochemical reactions at body temperature. Most are specific to particular reactions and substances. Enzymes function by interacting with a substrate (reactants) at the active site, forming a sort of lock and key structure called the enzyme-substrate complex. Then, the reaction occurs and the products are formed. Enzymes are sometimes inhibited by body conditions (different temperatures or acidity can deform proteins) and/or extra compounds interacting with it at the active site (blocking interaction with the actual substrate) or at an allosteric site (deforming the protein). The enzymes can form feedback loops with the body to regulate conditions and limit their deformation. + \subsection{Reversible Reactions and Equilibrium} + \subsubsection{Equilibrium in Reversible Reactions} + Equilibrium is the state where a system is balanced (like boiling water in a closed vessel applying pressure to the liquid part until it stops boiling). A reversible reaction is a reaction where neither the forward ($reactants \rightarrow products$ and $reactants \leftarrow products$ can both occur). Note that reactants and products are always placed in that order regardless of the direction of the arrow. The favored reaction direction can change with environmental conditions like pressure and temperature, so equilibrium is possible with reversible reactions (manifesting as a mixture of reactants and products) + \subsubsection{Forward and Reverse Reaction Rates} + Reactions are constantly happening if the reactants are available and enough kinetic energy is present, so equilibrium with reversible reactions must be dynamic equilibrium---the system stays at the same concentration ratios overall, but any specific part is constantly changing. Forward reaction rates and reverse reaction rates change how much the mixture changes in one way or the other (i.e. are more reactions occuring $reactants \rightarrow products$ or $reactants \leftarrow products$) + \subsubsection{Chemical Equilibrium} + Because chemical reactions' rates are reliant on concentration, equilibrium can occur even when a forward or reverse reaction rate is higher. If the forward reaction rate is higher where reactants and products are the same, then there are more products (products are favored), and the equilibrium lies ``to the right'' on the chemical equation. Similarly, if the reverse reaction rate is higher at a 50/50 mix, there are more reactants, the equilibrium lies ``to the left,'' and reactants are favored. Note that at equilibrium, the reverse reaction rate is always the same as the forward reaction rate by definition. + \subsubsection{The Equilibrium Constant ($K_{eq}$)} + The Equilibrium Constant is $\frac{[C]^c[D]^d}{[A]^a[B]^b}$ for the reversible reaction $cA + cB \leftrightarrow cC + dD$ if [K] is the concentration of substance K in terms of molarity for aqueous solutions and partial pressure for gases, and k is the coefficient of substance k in the chemical equation. + Note that pure solids and pure liquids do not appear in equilibrium constant calculations. + The equilibrium constant can typically be interpreted as: $K<1$means reactants are favored; $K>1$ means products are favored. + \subsection{Shifts in Equilibrium} + \subsubsection{Changes in Reactant or Product Concentration} + Stresses are external changes which disrupt chemical equilibrium. These include: change in pressure, change in temperature, and change in concentration. Le Chatelier's principle states that "if a stress is applied to a chemical system at equilibrium, the system will respond by shifting in a direction to counteract the stress and a new equilibrium will be established. In a chemical system, for example, if a concentration change occurs, then the forward or reverse reaction rate will increase enough to bring back the equilibrium. This is true of any change in chemical concentration: $K_{eq}$ always remains constant as long as no other features of the environment vary. + \subsubsection{Common Ion} + A common ion is the ion which is in both a system's chemical equation (individually like $H^+$) and an external ionic compound (such as $HCl$). For example, adding hydrochloric acid ($HCl$) to a system with Chlorine as a reactant causes the system to respond by shifting the equilibrium further in favor of the forward reaction (to the right). + \subsubsection{Changes in Pressure} + Changes in pressure shift the equilibrium in gaseous mixtures. Equilibrium typically shifts in the direction of lower molecules (e.g. $A \rightarrow 2B$ would shift the equilibrium to the left if pressure increases). + \subsubsection{Changes in Temperature} + Changes in temperature also change the equilibrium because heat is either a reactant or a product (the reaction is necessarily endothermic or exothermic). Because heat acts like a substance on its respective side, an increase in temperature will move the equilibrium away from its position in the location (e.g. $A \leftrightarrow products + heat$ shifts to the left as temperature increases) + \subsubsection{Reaction Quotient} + For non-equilibrium concentrations, applying the equilibrium constant formula gives the reaction quotient, which helps to inform if the forward or reverse reaction is currently preferred. If $Q > K_{eq}$, the reverse is typically preferred. Conversely, if $Q < K_{eq}$, the forward is preferred. +\section{Energy in Chemical Reactions} + \subsection{Energy} + \subsubsection{Basic Definitions} + Energy is ``the ability to do work or cause change.'' The SI unit for energy is the joule or the kilojoule. Other units have also been historically used to represent energy such as calories, kilocalories, BTUs, and kilowatt-hours. Kinetic energy is energy associated with movement. This is related to the amount of work done by an object, and its mass/velocity. Formally, a force consistently applied over a given distance does the work equal to $F*d$. Energy inputted to a system must always be greater than or equal to work done due to the conservation of energy and non-conservative forces like friction. + \subsubsection{Potential Energy} + Potential energy is any energy associated with the position of an object. The most common form is gravitational potential energy because dropping it can generate an equal or lesser amount of kinetic energy from whichever gravitational field it is in. If the field is approximately constant, then $G_{PE} = mgh$ where $m$ is mass, $g$ is gravitational attraction, and $h$ is height. + \subsubsection{Mechanical Energy} + Mechanical Energy is the sum of all kinetic and potential energy of an object. + \subsubsection{Thermal Energy} + Thermal energy is the energy associated with temperature, which can flow as heat. This is dependent on mass and absolute temperature. Heat is "energy that flows from a warmer object or substance to a cooler object or substance." Heat constantly flows until all objects in a system reach equilibrium. + \subsubsection{Electromagnetic and Chemical Energy} + Electromagnetic energy is "energy associated with electric fields, magnetic fields, and electromagnetic radiation." This includes visible light (such as from the sun), X-rays, radio waves, or electricity (like the type which flows through an outlet). Chemical energy is a type of potential energy stored in chemical bonds. Transfers of chemical energy occur in chemical reactions (endothermic = storing, exothermic = releasing energy). + \subsubsection{Law of Conservation of Energy} + Similar to the law of conservation of matter, the law of conservation energy states that "energy cannot be created or destroyed, but it can change from one form to another." These exchanges include, for example, burning gasoline to turn chemical energy into thermal energy. There are two types of systems when talking about the exchange of energy: open systems (can exchange matter and energy) and closed systems (can exchange energy but not matter) + \subsubsection{Energy Transfer and Transformation} + Energy transfer is the movement of energy in the same form. Heat transfer of the type of energy dispersing from a fire is energy transfer. Energy transformation, however, is the change in energy from one form to another like nuclear to thermal energy or electromagnetic to mechanical energy. Note that both follow the law of conservation of energy. + \subsubsection{Sources of Energy} + Energy can't be created or destroyed, so it must come from somewhere. For human use, the earth's interior, the sun, fossil fuels, radioactive elements (like $U^{235}$), moving air/water, and food can be considered sources of energy. + \subsection{Heat} + \subsubsection{Thermal Energy} + Thermal Energy is the same as the kinetic energy of the molecules of a substance. This is a property of all matter. Thermal Energy can be measured with temperature---the average kinetic energy as opposed to the total kinetic energy of a substance. Temeperature can be described with $^{\circ}F$, $^{\circ}C$, and $K$. + \subsubsection{Heat and Conduction} + Heat is "the transfer of kinetic energy between molecules as faster-moving molecules collide with slower-moving molecules. Heat always trends towards equilibrium and thus generally flows from high kinetic energy to low kinetic energy. + Conduction is a type of heat flow which involves direct contact of two substances such as a metal spoon and a hot pot. This, like heat in general, tends towards equilibrium, "taking" energy from the fast molecules and "giving" it to the slow molecules. + \subsubsection{Heat Flow during Chemical Processes} + Exothermic and endothermic chemical reactions decrease and increase the potential energy of the involved substances, respectively. However, in order to maintain conservation of energy (total energy remains the same), the environment either increases its own heat (exothermic) or decreases (endothermic). + \subsection{Calorimetry} + \subsubsection{Specific Heat Capacity} + Heat capacity is ``the quantity of heat needed to raise the temperature of a given sample of a substance by one degree Celsius/Kelvin.'' This is described in units of $\frac{energy}{temperature}$ (ex: $\frac{J}{^{\circ}C}$ or $\frac{cal}{K}$). Note that this is an extensive property because the mass of a sample is relevant (i.e. a larger sample takes more energy to heat by the same amount). Specific heat capacity ($C_p$) is the heat capactiy per gram, so this has the units of $\frac{energy}{mass*K}$. Specific heat can change with temperature, especially in gases. This is related to intermolecular forces. Heat absorbed or released ($q$) can be related, mathematically, as $q=mC_p\Delta T$ where $m$ is mass and $\Delta T$ is the change in temperature. + \subsubsection{Calorimetry Definition} + Calorimetry is ``the use of a calorimeter to measure energy given off or absorbed during a physical or chemical process,'' where a calorimeter is a device designed to do exactly that. + \subsubsection{Bomb Calorimetry} + A bomb calorimeter is a specific type of calorimeter which doesn't use a bath of water (solution) for the reaction. Instead, it has a separated vessel inside of a bath of water to measure more reactions. This are often used to measure combustion heat release. + \subsubsection{The Calorie Content of Foods} + Nutrition information labels give calorie counts (note that a food Calorie is a kilocalorie or $4.184kJ$). These are determined with bomb calorimeters by burning the food and determining heat released during the combustion reaction. + \end{document} |