Blueprint Fl-1 Review

Volume Units

1 L = 10^3 mL = 10^3 cm^3

Units of Pressure

1 atm= 760 mmHg= 760 torr=10^5 Pa (N/m^2)

mM (millimolar) or mM/L

1 × 10-3 M

Analyte

A substance that is being identified or measured in a laboratory test.

KE (kinetic energy)

1/2mv^2 Mass (kg) velocity (m/s)

Ionic Radius

A concept that relates closely to atomic radius is ionic radius, or the radius of a charged species (for example, F_). It is important to understand that cations (positive ions) tend to have smaller ionic radii than the atomic radii of their corresponding uncharged elements. This is because an uncharged atom must lose one or more electrons to become positively charged. On the other hand, for anions (negative ions), the ionic radius is typically larger than the corresponding atomic radius, since these species must gain electrons, and thus become slightly larger, to take on their negative forms. The most common ionic configuration of an atom often relates to the number of electrons it must gain or lose to obtain the same electron configuration as its nearest noble gas. For example, fluorine needs to gain only a single electron to obtain the same electron configuration as neon, so its preferred ionic form is F_.

Chiral Carbon

Chirality, or chemical "handedness," occurs when an atom is connected to four unique groups. Such molecules are not superimposable upon their own mirror images. Atoms within a molecule that connect to four unique groups are known as chiral centers, and a molecule with n chiral centers will have 2n stereoisomers. Compounds that produce clockwise (+) rotation of plane-polarized light are dextrorotatory (d), and compounds that produce counterclockwise (-) rotation are levorotatory (l). The specific rotation of a chiral compound in solution can be calculated according to the equation [α] =α/cl, where α is the observed rotation, c is the concentration in g/mL, and l is the length of the polarimeter tube in decimeters (dm).

Capacitor concept

Circuits on the MCAT contain batteries, resistors, and/or capacitors. Capacitors have several medical applications (e.g. defibrillators) and are used to store charge and electrical potential energy, precluding the need for large batteries in electrical components. A basic capacitor consists of two metal plates separated by a layer of insulating material called a dielectric. Capacitance is the ability to store charge and is calculated as C = ɛ0A/d, where A is the area of the plates and d is the distance between them. When two conducting plates are connected to a battery, electrons move towards one plate. The positive plate loses electrons as well, and both plates eventually have equal and opposite charge, +Q and -Q. When a capacitor is fully charged, the capacitor has charge Q. We can relate the charge, capacitance, and voltage across the plates using the equation Q = VC (remember the home shopping network?). The voltage in this equation is the maximum potential difference that can be applied before the insulation of the dielectric breaks down. The electrical potential energy stored in the capacitor can also be related via the equations E = ½ QV = ½ CV2. Once fully charged, the capacitor can discharge a current across the circuit until the capacitor is "emptied" of all the stored charge. The MCAT may ask you to compare the difference in terms of charging when a battery is connected (V is constant) or disconnected (Q is constant). Finally, capacitors can be combined in series (common path) or in parallel (common origin and destination, different path). Capacitors in series combine like resistors in parallel (1/Ceq = 1/C1 + 1/C2...) while capacitors in parallel combine like resistors in series (Ceq = C1 + C2...).

Circuits/Resistors Concepts

Circuits, as tested on the MCAT, are combinations of one or more resistors and/or capacitors connected by a conductive wire to which a battery is attached. The voltage differential of the battery (or "electromotive force") pushes current through the circuit. The three quantities of current, voltage, and resistance are linked together in Ohm's law, which is essential knowledge: V = IR. Power, which is conceptually equivalent to work over time, can be expressed as P = IV. Circuits can contain multiple resistors, which can be connected either in parallel or in series. For a circuit with resistors R1, R2, ... Rn wired in series, Itotal = I1 = I2 = ... = In, Vtotal = V1 + V2 + ... + Vn, and Rtotal = R1 + R2 + ... + Rn. If the resistors are wired in parallel, Itotal = I1 + I2 + ... + In, Vtotal = V1 = V2 = ... = Vn, and 1/Rtotal = 1/R1 + 1/R2 + ... + 1/Rn. Circuits can also contain capacitors, which store charge in two physically separated components. The charge stored by a capacitor is a function of its capacitance and voltage, as expressed by the equation Q = VC. When capacitors are connected in series, their capacitance adds reciprocally, like how resistance adds for resistors in parallel. When capacitors are connected in parallel, their capacitance adds directly, like resistors in series.

Zeff trends

Due to the presence of protons, the nucleus of an atom is always positive. The attractive force of this positively-charged nucleus on the atom's negatively-charged valence electrons is termed the effective nuclear charge (Zeff). As the number of protons in the nucleus increases from left to right across a period (or row) of the table, Zeff also increases, since each additional proton adds positive charge to the nucleus. However, Zeff is not synonymous with the number of protons held by an atom. Moving down a group, the principal quantum number of the outermost energy level increases, which effectively means that more shells of electrons are added between the nucleus and the outermost, or valence, electrons. These layers of core electrons partially shield the valence electrons from the effects of the positive charge in the nucleus. Thus, Zeff decreases as one moves down a group.

Water is a rare substance in that the solid is less dense than the liquid at the freezing point, resulting in a solid form that floats on top of the liquid. Which of the following best explains this phenomenon?

For most substances, the liquid becomes more dense as the average kinetic energy (temperature) decreases, and the solid is more dense than the liquid due to close-packing solid-state structures, resulting in the formation of the solid at the bottom of the liquid. However, as stated in the question, solid water (ice) is significantly less dense than the liquid form at 0°C (the melting/freezing point). Remember, the water molecule is bent (shown below), with a bond angle of approximately 104.5°. This, combined with the degree of hydrogen bonding that can occur between water molecules, yields a solid crystalline structure with relatively large amounts of empty space. As a result, solid water is less dense than its liquid form.

Reduction

Gain of bonds to hydrogens or loss of bonds to oxygen (or other electron withdrawing species)

ETC concept

In the electron transport chain, electrons are passed from species with less positive reduction potential to those with more positive reduction potential. O2 serves as the final electron acceptor of the electron transport chain and must possess a standard reduction potential that is more positive than any other acceptor in the chain. Of the standard reduction potentials mentioned in the passage, the greatest is that of Fe3+/Fe2+ in cytochrome c, for which E° = +0.22 V. Only choice A exceeds this value.

Thermodynamics concepts

In thermodynamics, a key distinction is made between enthalpy (heat energy in a system) and entropy (energy in a closed system that is unavailable to do work). The enthalpy (H) of a reaction is the heat energy it contains. The most important law when looking at enthalpy is Hess's law: ΔHrxn = Σ∆Hproducts - ΣΔHreactants. This equation illustrates that enthalpy, like entropy, is a state function. This means that the ∆H accompanying a chemical reaction is independent of the mechanism by which the reaction occurs. That is, when reactants are converted into products, the overall enthalpy change is the same whether it is done as one step or multiple steps. The third law of thermodynamics allows us to calculate absolute entropy, but not absolute enthalpy. The enthalpy of a substance can only be calculated relative to other substances, and therefore enthalpy does not approach 0 as temperature approaches 0 K (known as "absolute zero"). The change in entropy (∆S) of a system is commonly understood as the change in the degree of randomness or disorder the system contains. Entropy, like enthalpy, increases with temperature and as a material changes phase from solid to liquid to gas. On the MCAT, there are several ways by which you can estimate the entropy of a system: Reactions that increase the number of moles of substances in the system (or produce more gas particles) typically increase the entropy of the system. Entropy generally increases when a solid or liquid is dissolved in a solvent. Entropy increases when the solubility of a gas decreases and it escapes from a solvent. Entropy generally increases as molecular complexity increases (KOH vs. Ca(OH)2) due to the increased movement of electrons.

Newton's Law

Newton's first law is a statement about inertia. It states that within a reference frame, an object remains at rest or at a constant velocity unless an external force acts upon it. Essentially, this law captures the insight that forces of resistance and friction make moving objects slow down and stop. It can be summarized as Fnet = 0 at equilibrium. Newton's second law defines force. It states that the total sum of forces acting on an object is equivalent to its mass times its acceleration. This is the familiar equation Fnet = ma. Newton's third law is about how forces come in pairs. It states that when body A exerts a force on body B, body B exerts an equal and opposite force on body A: FAB = -FBA. For example, the earth exerts a gravitational force on your body, which is responsible for your weight, but your body also exerts a gravitational force on the earth. In contrast to a common misconception, weight (caused by a gravitational force) and the normal force do not form a Newton's third law pair, because they are caused by different underlying forces and do not always have to be equal.

vacuum distillation

Next, remember that boiling occurs when the Pvap of the substance in question equals the Patm. Typically, we boil substances by increasing the temperature, thereby increasing Pvap. Alternatively, however, we can lower boiling point by reducing Patm, which can be accomplished through the introduction of a vacuum. Vacuum distillation is often used when components have very high boiling points and would otherwise be difficult to distill.

Important cm^-1 for spectroscopy

OH- broad peak from 2800-3500cm^-1. (C=O) is 1700-1750cm^-1. (C=C) is 1580-1640cm^-1

6 primary enzyme classes

Oxidoreductases catalyze oxidation-reduction reactions where electrons are transferred. In metabolism, these electrons are usually in the form of hydride ions or hydrogen atoms. When a substrate is being oxidized, it is the hydrogen donor. Examples include reductases, oxidases, and dehydrogenases. Transferases catalyze transfer of a chemical group from one molecule (donor) to another (acceptor). Most of the time, the donor is a cofactor that is charged with the group about to be transferred. Examples include kinases and phosphorylases. Lyases catalyze reactions where functional groups are added to break bonds in molecules or they can be used to form new double bonds or rings by the removal of functional group(s). Decarboxylases are examples of lyases. Isomerases catalyze reactions that transfer functional groups within a molecule so that a new isomer is formed to allow for structural or geometric changes within a molecule. Hydrolases catalyze reactions that involve cleavage of a molecule using water (hydrolysis). This cases usually involves the transfer of functional groups to water. Hydrolases include amylases, proteases/peptidases, lipases, and phosphatases. Ligases are used in catalysis where two substrates are stitched together (i.e., ligated) via the formation of C-C, C-S, C-N or C-O bonds while giving off a water (condensation) molecule. Every enzyme you will ever see on the MCAT will fit under one of these labels. The test makers will not expect you to learn a bunch of random enzymes, but they will expect you to match an enzyme's name to the clues given about its function, or vice versa. Luckily, most enzymes are named for exactly what they do (e.g., pyruvate decarboxylase) and for the substrate they act upon (e.g., DNA ligase).

Power (in terms of Ohm's Law)

P = IV, P = I^2R, or P = V^2/R

Terpenes

Precursors of steroids. Steroids generally end with "one" "en" or "ol" Cholesterol, estrogen, testosterone

Nuclear Decay

Radioactive decay is the spontaneous transformation of one atomic nucleus into another. Often, this involves a change from one element into a different element. The only way this transformation can happen is by changing the number of protons (and often neutrons) in the nucleus, since atomic identity is defined by the number of protons. There are a number of ways that this can happen, and when it does, the atom is forever changed. There is no going back - the process is irreversible. There are four primary types of decay: alpha decay, beta decay (β+ and β-), gamma decay, and electron capture. In alpha decay, an alpha particle, containing two protons, two neutrons, and a +2 charge, is emitted. In beta-minus decay, a neutron is converted into a proton in the nucleus, and a β- particle (an electron) is ejected to maintain charge balance. In beta-plus decay, a proton is converted into a neutron, and a β+ particle (a positron) is emitted to preserve charge. Gamma decay involves the emission of a gamma ray, which is a high-energy photon, from an excited nucleus. Finally, in electron capture, a nucleus "grabs" an electron, which changes a proton into a neutron.

Vapor Pressure

Remember that boiling point is defined as the temperature at which the vapor pressure of a solution is equal to the atmospheric pressure. A decrease in vapor pressure makes this point more difficult to achieve, resulting in a higher boiling temperature.

Important Concepts in Ochem

Separation techniques are widely used in organic chemistry to prepare purified substances for analysis or reaction. The best technique for a given scenario often depends on the phases of the substances being separated. If all are liquids, one may be able to utilize distillation, which aims to separate liquids by utilizing the difference between their boiling points. The liquids are initially held in the same round-bottom flask, termed the distilling flask. This flask is positioned above a heat source, typically a Bunsen burner. The top of the flask is connected to a column, which leads to a downward-sloping glass condenser over a receiving flask. The condenser is held within a glass casing through which cold water is pumped. As the round-bottom flask is heated, the liquid with the lower boiling point will begin to vaporize, and its vapor will travel up the column and re-condense to fall into the receiving flask. The eventual result is a receiving flask that is rich in the lower-BP liquid, while the distilling flask will still contain the liquid(s) with the higher BP. If boiling points are very high, a vacuum may also be used to lower atmospheric pressure, which lowers the boiling points of all substances involved. Recrystallization is used to purify a solid product that contains impurities. This process involves the dissolution of the solid in a solvent and subsequent heating. The solid then dissolves and is cooled, causing it to solidify (crystallize) again. As the lattice structures of solids tend to exclude impurities, each subsequent recrystallization results in a progressively purer compound. Chromatography is a broad set of separatory techniques based on relative affinity, or tendency for a compound to attract to a certain solvent or structure. Specifically, sample molecules vary in their affinities for a mobile (moving, typically solvent-based) phase versus a stationary (static) phase. In column chromatography, the stationary phase is a vertical column packed with an adsorbent with carefully chosen properties. This adsorbent can attract sample molecules based on charge, size, or affinity for specific ligands. Finally, centrifugation utilizes a rapidly spinning apparatus to separate particles by density. More dense particles, such as cells, gravitate toward the bottom of the spun tube, while less dense substances remain at the top in a liquid termed the supernatant. This liquid can then be poured off, and further separation or analysis can be conducted.

SO4

Sulfate always has a negative 2 charge.

Elemental Nitrogen

The MCAT will expect you to be familiar with N2 as a very inert gas. It makes up approximately 80% of the air you breathe, yet has no significant chemical reactions with your lungs - or with anything other than nitrogen-fixing plants. This information implies that nitrogen is very inert (unreactive). As such, it would serve as a good artificial atmosphere when working with reagents that might react with oxygen or other gases.

Conduction/Convection

The anterior hypothalamus serves as the body's "thermostat" to maintain body core temperature. Heat exchange is determined by convection, conduction, evaporation, and radiation. Radiation, conduction, and convection are determined by the difference between the skin temperature and the ambient temperature. The rate of heat body heat loss depends primarily on the surface temperature of the skin, which is in turn a function of cutaneous blood flow. The body can lose heat by increasing cutaneous blood flow and sweating, or by decreasing the basal metabolic rate through thyroid signaling. It can gain heat by decreasing cutaneous blood flow, increasing muscular activity (through movement and shivering), increasing the basal metabolic rate through thyroid signaling, metabolizing brown adipose (in infants only), or triggering piloerection of the hair on the body (goosebumps). A forced change in body temperature results when an environmental stress is sufficient to overcome the thermoregulatory systems of the body. For example, prolonged time in cold water results in forced hypothermia, while prolonged time in hot water results in hyperthermia. A regulated change in body temperature occurs when the hypothalamic "temperature setting" is shifted, as when a fever results from infection by a pathogen.

Structural Protein

The most common function of proteins in the body is not enzymatic, but structural. Structural proteins are fibrous proteins that have an elongated shape and provide structural support for cells and organ tissues. The first type of fibrous proteins are keratins, which form the skin, hair, and nails. Keratins are classified as soft or hard according to their sulfur content (i.e. the relative number of cysteine residues in their polypeptide chains). The low-sulfur keratins of the skin are much more flexible than the high-S, hard keratins. The second type of fibrous proteins you must know are the actin and myosin proteins of muscle tissue. Actin and myosin interact to form cross-linkages that allow the sliding of the filaments over each other in muscle contraction, which takes place through the contraction and relaxation of the sarcomere, the fundamental unit of all muscle fibers. When muscle contracts, the actin and myosin filaments slide over each other and the H-zone (myosin-only region), Z-lines (sarcomere boundaries), and I-band (actin-only region) all shrink, while the A-band (the entire myosin region) remains the same size. The opposite occurs upon muscle relaxation. A third type of structural protein you should know for test day is collagen, which is found in tendons, forms connective ligaments within the body, and gives extra support to the skin. Collagen is a triple helix formed by three proteins that wrap around one another. Many collagen molecules are cross-linked together in the extracellular space to form collagen fibrils to provide structural support for the cell. Elastin polypeptide chains are cross-linked together to form flexible, elastic fibers that give stretched tissues flexibility and the ability to recoil spontaneously as soon as the stretching force is relaxed.

More Snell's law concepts

The propagation speed of a wave is specific to the medium that it is traveling through. This is true both for sound and for electromagnetic waves, including light. This means that when a light wave goes from one medium to another, it changes speed. Since the speed of light in a vacuum (c) is the maximum speed at which normal matter can travel in the universe, it is convenient to define the speed at which light passes through a medium with reference to the speed of light in a vacuum. More specifically, the refractive index (n) of a given material is defined as follows: n = c/vmaterial. This value is 1 for a vacuum and is approximated as 1 for air. For all other materials, n is greater than 1; for instance, window glass has a refractive index of 1.52. When light passes from one medium to another and changes speed, it bends. Snell's law relates the refractive index—that is, how much the speed of a light wave changes—to how much the light bends upon entering the new medium. Snell's law is expressed as n1sin(θ1) = n2sin(θ2). It is important to keep in mind that θ is defined with reference to the normal, or a line that runs perpendicular to the surface on which the wave is incident. An important special case occurs when light moves into a medium with a smaller index of refraction (that is, when n2 > n1). A classic example of this is when light is moving from water to air. As this happens, the angle θ with the normal will increase—in other words, the ray of light will bend further away from the normal. As the angle of the incident ray (θ1) increases, there will come a point where the angle of the refracted ray (θ2) reaches 90°. This is known as the critical angle. If we increase the angle beyond the critical angle, the light can no longer refract at all. Instead, all the light rays are reflected within the original medium. This is known as total internal reflection.

Reduction Potential Concepts

The tendency for a species to spontaneously become reduced is measured using a parameter called the standard reduction potential. Reduction potentials (E°) are measured in volts and are defined relative to the standard hydrogen electrode (2 H+ (aq) + 2 e- → H2(g)), which is set at 0 V. Greater (more positive) reduction potentials indicate that a substance 'wants' to be reduced more, while smaller (more negative) reduction potentials indicate that a substance is not prone to reduction. Redox reactions can be carried out in special devices known as electrochemical cells. These cells must have two electrodes, which are where the redox half-reactions occur. The electrode where oxidation happens is known as the anode, while the electrode where reduction happens is known as the cathode. Therefore, a surplus of electrons is generated at the anode (because electrons are lost during oxidation), and they travel to the cathode. In a galvanic (or voltaic) cell, a spontaneous redox reaction is used to generate a positive potential difference that can drive current. The total standard potential generated by a cell, Ecell, can be calculated from the standard reduction potentials of the half-reactions. The simplest way of defining Ecell is presented below: Ecell = E°cathode - E°anode In contrast to a galvanic cell, an electrolytic cell uses a connected power source to conduct a nonspontaneous redox reaction. While galvanic cells have positive Ecell values (indicating spontaneity), electrolytic cells are characterized by negative Ecell values.

Cancer Defintion

The term "tumor" describes any abnormal proliferation of cells. Benign tumors remain localized, whereas malignant tumors (which are what the term "cancer" properly refers to) can invade other organs and tissues in the body in a process called metastasis. The first step in oncogenesis, tumor initiation, involves changes that allow a single cell to proliferate abnormally. This means that the cell must develop the ability to bypass regulatory steps of the cell cycle that normally help to limit mitotic proliferation. Tumor progression occurs as a cell develops the ability to proliferate even more aggressively, such that its descendants are selected for and come to predominate the growing tumor. In addition, malignant cells often undergo mutations that promote their own growth and the development of blood vessels to feed them (angiogenesis). Oncogenesis is most often associated with mutations that occur by random chance (and elude the normal DNA repair machinery in the cell) or as a result of mutagenic compounds known as mutagens or carcinogens. (Examples of mutagens include ultraviolet light and certain chemicals, such as reactive oxygen species.) These mutations alter the functionality of crucial genes in the cell. However, oncogenesis is also associated with dysregulation of gene expression, as the abnormally elevated expression of genes involved in growth and proliferation can help contribute to the development of a tumor. The genes involved in oncogenesis can be divided into two groups: oncogenes and tumor suppressor genes. The basic difference between them is that oncogenes function to promote abnormal growth and proliferation, leading to cancer, while tumor suppressor genes function to prevent tumorigenic properties. Oncogenes can arise from the mutation of other genes, termed proto-oncogenes. If not mutated, proto-oncogenes do not promote cancer, but certain mutations or inappropriately elevated gene expression can effectively turn them into oncogenes.

Reactivity Trends

There are several important oxygen-containing functional groups: alcohols (RC-OH), aldehydes (RC(=O)H), ketones (RC(=O)R'), and carboxylic acids (R(C=O)OH). Due to hydrogen bonding, alcohols and carboxylic acids have higher melting/boiling points than aldehydes and ketones and can function as organic weak acids. Carbonyl (C=O) carbons have a significant partial positive charge and therefore often act as electrophiles. The -OH group of carboxylic acids can be replaced by other functional groups to form carboxylic acid derivatives, the most notable are amides (R(C=O)NR'R''), esters (R(C=O)OR'), acid anhydrides (R(C=O)O(C=O)R'), and acid halides (R(C=O)X), in increasing order of reactivity. Amines (R-NH2, R-NHR', or R-NR'R"), imines (R=NH or R=NR'), and enamines (C=C-NH2, C=C-NHR, or C=C-NRR') are nitrogen-containing compounds with medium melting/boiling points that can act as weak bases. Sulfur-containing functional groups contain the root "thio" and generally act similarly to the corresponding oxygen-containing groups.

Torque

Torque (τ) is the rotational analog of force. Specifically, torque is caused by force applied to a lever arm at a certain distance from an object capable of rotating, known as a fulcrum. Torque can be defined as τ = F∙d∙sin(θ), where F (n*m) is the force applied, d (m) is the distance that the force is applied from the fulcrum, and θ is the angle between the lever arm and the force that is applied. Thus, there are three ways to increase the torque applied to an object: (1) increasing the force, (2) increasing the distance at which the force is applied from the fulcrum, and (3) adjusting the angle at which the force is applied to make it as close as possible to perpendicular to the lever arm.

colligative properties

Vapor pressure refers to the pressure of the vapor phase that exists (to some degree) immediately above the surface of any liquid. A higher vapor pressure indicates that a larger number of solvent particles were able to escape the liquid and enter the gas phase. When vapor pressure is equal to the atmospheric pressure exerted on the liquid's surface, the liquid will boil. Knowing this, the fact that adding more solute particles causes a reduction in vapor pressure is actually logical. Imagine the surface of an aqueous solution with a lot of solutes in it. Some of the solutes will be at the surface of the solution, so the space they take up is unavailable for the liquid-gas phase transition that is at the core of vapor pressure. This causes vapor pressure reduction. Boiling point elevation directly follows from vapor pressure reduction. The lower the vapor pressure, the more energy that will be required to increase that vapor pressure to a level that matches the atmospheric pressure. In other words, the more solute particles present, the lower the vapor pressure, and the higher the boiling point. The extent of this elevation can be calculated using the formula ∆Tb = iKbm, where ∆Tb refers to the amount by which the boiling point is elevated, i refers to the ionization or van't Hoff factor, which refers to the number of ions each solute molecule dissociates into in solution, and m refers to solute molality. A similar equation exists for the third colligative property: freezing point depression. This property stems from the idea that solute molecules disrupt the lattice structure of the frozen solvent, so more added solute corresponds to more "difficulty" freezing and a lower freezing point. The equation for freezing point depression is ∆Tf = iKfm. Finally, osmotic pressure is discussed much more often in a biological context, but it does also have an associated equation: π = iMRT, where π represents osmotic pressure, M refers to molarity, R is the ideal gas constant, and T is the temperature in Kelvin.

Gas Laws

Volume is the size of the space a gas occupies. Volume can be related to pressure using Boyle's law, which states that for an ideal gas at a constant temperature, PV = constant. Thus, we can see there is an inverse relationship between P and V. Volume and temperature are related in Charles's law: T/V = constant if P is constant, indicating a direct relationship between T and V. Volume can be expressed as any unit of distance cubed or as any standard unit of volume, but the most common units are mL, L, or cm3, where 1 L = 103 mL = 103 cm3.

Light with a denser medium will

bend more toward the normal

inert

chemically inactive

Boiling Chip

is a tiny, unevenly shaped piece of substance added to liquids to make them boil more calmly. Boiling chips are frequently employed in distillation and heating. When a liquid becomes superheated, a speck of dust or a stirring rod can cause violent flash boiling. Boiling chips provide nucleation sites (places to start forming bubbles so the liquid boils smoothly without becoming superheated or bumping).

PE (potential energy)

mgh mass (kg)(10m/s^2)(m)

Snell's Law

n1sinθ1 = n2sinθ2

Normality

number of equivalents of reactive species per liter of solution, for which we must define the reactive species. For example, hydrochloric acid (HCl) generates one equivalent of H+ ions and one equivalent of Cl- ions per mole, while sulfuric acid (H2SO4) generates two equivalents of H+ ions and one equivalent of SO42- ions per mole.

The angle of incidence always equals

the angle of reflection

Spontaneity is attributed to

∆G < 0, Keq > 1, and E° > 0.