MCAT General Chemistry Podcast
Episode 21: This is a General Chemistry 101 overview for the MCAT. Get ready for more specific and detailed podcasts on a WEEKLY basis.
Conservation of Mass
The Law of Conservation of Mass state that there are no detectable changes in mass in any chemical reaction. This indicates that there are the same number of atoms of each types present after a chemical reaction as there were before the reaction. A balanced equation shows equal numbers of each type of atom on each side of the equation and is, thereby, consistent with the Law of Conservation of Mass.
MCAT Equations (download complete list of MCAT equations)
Equations are balanced by placing coefficients in front of the chemical formulas for the substances involved in the reactions. It is possible to predict the products of simple reactions by analogy to known reactions and by use of the periodic table. Among the reactions, there are the followings:
One; combustion in oxygen in which an organic compound reacts with oxygen forming carbon dioxide, water and possibly other products depending on the composition of the compound.
Two; neutralization reaction in which an acid plus a base react to form water or another neutral compound and a salt. There are precipitation reactions in which one of the products over reaction between two substances in solution is insoluble in the solution. The coefficient in a balanced equation can be interpreted as either the relative number of formula units involved in the reaction or the relative number of moles.
A mole of any substance is Avogadro’s number, which is 6.02 x 1023 of formula units of that substance. The mass of a mole of atoms, molecules or ions is the formula weight expressed in grams. For example, a single molecule of water, H2O, weighs 18 amu, which are atomic mass units. A mole of water weighs 18 grams. The empirical formula, or simplest formula, of a substance expresses the composition in terms of the smallest possible set of whole number subscripts denoting the relative number of atoms. The mole concept can be used to determine the empirical formula of a compound and calculate the quantities involved in chemical reactions. In dealing with reactions between substances and solutions, it is convenient to employ the concept of solution concentration.
Molarity is defined as the number of moles of solute per liter of solution. Molarity serves as a conversion factor for interconverting solution volume and number of moles of solute.
Chemical equations and energy
We will look specifically at the energy and the first law of thermodynamics. Energy can be measured in terms of the ability to accomplish work or transfer heat. An object may possess potential energy because of its position relative to another object or because of its composition. Thus, chemical energy is potential energy which can be released when the object undergoes a chemical change. An object may possess kinetic energy because if it’s relative motion to another object. The first law of thermodynamics also referred to as the law of conservation of energy states that in any change that occurs in nature, the total energy of the universe remains constant.
It is often convenient to consider one portion of nature called the system as separate from all the rest called the surroundings. According to the first law of thermodynamics any energy gained by the system in a change must equal the energy lost from the surroundings. Any process in which heat energy is lost to the surroundings is termed “exothermic”. On the other hand, when heat energy is absorbed by the system from the surroundings, the process is termed “endothermic”.
Heat changes occurring at constant pressure are of special interest. The heat gained or lost by the system in a process occurring at constant pressure is termed the enthalpy change, represented by the symbol delta H. This quantity is negative for an exothermic process and positive for an endothermic process.
Enthalpy is a state function, which means that the enthalpy of a system is determined by specifying its present condition and not by the details of how it came to be in that state. If a particular overall change can be described as the sum of several individual changes then enthalpy change for the overall process is equal to the sum of the enthalpy changes associated with the individual steps.
Hess’ Law of Constant Heat Summation
This statement is known as Hess’s law of constant heat summation. In applying Hess’s law, it is useful to define the standard heat of formation of a substance, which is the heat change in the formation of a substance from the elements, all in the states in which they are most stable at the temperature of interest. This is usually 25 degrees Celsius.
Using Hess’s law, the enthalpy change in any reaction can be described as the sum of the heat of formation of all the products, less the heat of formation of all reactants. In solving problems dealing with enthalpy changes, it is important to keep the following points in mind.
First, the enthalpy change in a reaction, delta-H, is directly proportional to the amount of substance that reacts or is produced. Secondly, delta-H for any reaction is equal in magnitude but opposite in sign to the value of delta-H for the reverse reaction. Thirdly, the heat of formation for any element in its standard state is zero.
Now, we shall look at the quantum numbers. According to quantum mechanics, the state of an electron in an atom is specified by four quantum numbers-n, l, ml and ms. The principle quantum number, n, can take any integer value-one, two, three, etc. l, the orbital quantum number can take on values from zero up to n-1. ml the magnetic quantum number can take on integer values from -l to +l. And ms, the magnetic spin quantum number can be either + ½ or – ½.
The energy levels in the hydrogen atom depend on n whereas in other atoms, they depend on n and l. When an external magnetic field is applied, the spectral lines are split, indicating that the energy depends also on ml. Even in the absence of a magnetic field, precise measurements of spectral lines show a tiny splitting of the lines called fine structure, whose explanation is that the energy depends very slightly on the spin quantum number ms.
Pauli Exclusion Principle
The arrangement of electrons in multi-electron atoms is governed by the Pauli Exclusion Principle, which states that no two electrons can occupy the same quantum state. That is, they cannot have these same set of quantum numbers n, l, ml and ms. The electrons as a result are grouped into shells according to the value of n and subshells according to the value of l. This shell structure gives rise to a periodicity in the properties of the elements.
Now, we shall look at chemical bonds. Ionic bonding results from the complete transfer of electrons from one atom to another with formation of a three dimensional lattice of charged particles. The stabilities of ionic substances result from the powerful electrostatic attractive forces between an ion and all these surrounding ions of opposite charge. They call anions are negative ions, while cations are positive. These interactions are measured by the lattice energy.
Covalent bonding results from the sharing of electron between atoms. The rules that govern this sharing are based on the stability of the noble gas electron configuration. This is called the Octet Rule. We can represent shared electron pair structures of molecules by means of Lewis structures, which show the sharing of electron pairs between atoms.
The sharing of one pair of electron produces a single bond. The sharing of two or three pairs of electrons between atoms produces double and triple bonds, respectively. It sometimes happens that a single Lewis structure is inadequate to represent a particular molecule. But then an average of two or more Lewis structures does form a satisfactory representation.
Lewis Structures and Resonance Forms
In these cases, the Lewis structures are referred to as Resonance Forms. It also sometimes happens that the Octet Rule is not obeyed. This situation occurs mainly when a large atom is surrounded by small electronegative atoms, like fluorine, oxygen or chlorine. In such instances, the large atom often has more than an octet of electrons.
The strength of covalent bonds increase with the number of electron pairs shared between two atoms. In single bonds, the bond strings are generally higher between atoms of smaller size. It is important to recognize that even in covalent bonding electrons may not be shared equally between two atoms.
Electronegativity is a measure of the ability of an atom to compete with other atoms for the electrons shared between them. Highly electronegative elements strongly attract electrons. The electronegativities of the elements which show regular periodic relationship are an important guide to chemical behavior. The difference in electronegativities of bonded atoms is used to determine of the polarity of the bond.
Another application of electronegativity is in the assignment of oxidation numbers which are formal whole number charges assigned to atoms in molecules and ions. Although the oxidation numbers do not represent the real charges on atoms except in simple ionic substances, they are of great value in helping us to organize chemical facts and are in aid in balancing equations and in the naming of compounds.
Oxidation may be defined as the process in which an atom undergoes an increase in oxidation number. Reduction is a process in which an element undergoes a decrease in oxidation number. In an oxidation-reduction reaction, both oxidation and reduction occur in such a manner as to balance the total increases and decreases in oxidation numbers.
Chemical bonds and shapes. The three dimensional structures of molecules are determined by the distances between bonded atoms and by the directions of chemical bonds with the respect to one another around a particular atom. The Valence shell electron pair repulsion model explains these relative directions in term of the repulsions that exist between electron pairs.
According to this model, electron pairs around an atom orient themselves so as to minimize electrostatic repulsions. That is, they remain as far apart as possible. By recognizing the unshared electron pair take up more space, i.e. they exert greater repulsive forces then shared electron pairs, it is possible to account for the departures of bond angles from the ideal-like values and to explain many other aspects of molecular structure. The shape of a molecule and the bond polarities determine whether or not a molecule will be polar. The degree of polarity of a molecule is measured by its dipole moment.
The Lewis model for covalent bonding can be extended to account very nicely for the geometrical properties of molecules. We can imagine that the atoms in a molecule are bonded to one another by electron pairs that occupy pairs of overlapping atomic orbitals. The extent to which the atomic orbitals share the same region of space, called overlap, is important in determining the amount of stability that results from bond formation.
Sigma (Single) Bonds
The bonds directed along the internuclear axes are called sigma bonds, sigma bonds or single bonds. It is possible to formulate orbitals on an atom that are directed toward each of the other atoms surrounding it by forming a hybrid orbital. These orbitals are made up of mixtures of the familiar SPND atomic orbitals. Depending on the particular number of other atoms bonded to an atom and their arrangement in space, a particular set of hybrid orbitals can be formulated that has the necessary directional characteristics.
For example, SP3 hybrid orbitals are directed towards the corners of a tetrahedron. In addition to the sigma bonds which determine the geometry of the bonding around a particular atom, there are also pi bonds constructed from remaining unhybridized atomic orbitals. Thus, double bonds consisting of a sigma and a pi bond, or triple bonds consisting of a sigma and two pi bonds may be formed. In some molecules, the pi bond may extend or be delocalized over several atoms.
Delocalization of the pi electron in a cyclic structure, such as in benzene or throughout a plane, leads to a special stability. The coming together of atoms to form molecules may be viewed also as the coming together of the atomic orbitals to from molecular orbitals. Atomic orbitals may combine with one another in various ways. The rules for combining atomic orbitals on atoms to form molecular orbitals allow us to account very well for the observed properties of the diatomic molecules formed by the first several elements of the periodic table.
Properties of gases
To describe the state or condition of a gas, it is necessary to specify four variables-pressure, temperature, volume, and the quantity of the gas. Volume is usually measured in liters and temperature in the Kelvin scale. Pressure is defined as the force per unit area. It is expressed in the SI unit as Pascals, where one Pascal is equal to one Newton per meter squared, which in turn is equal to one kilogram per meter second squared. Pressure can also be defined in millimeters of mercury. One standard atmosphere of pressure equals 101.3 kilopascals or 760 millimeter of mercury. A barometer is often used to measure the atmospheric pressure.
The ideal gas equation
Where P is the pressure, V is the volume, n is the number of moles, R is the gas constant, and t is the Temperature in Kelvin.
Most gases at pressures of about one atmosphere and temperatures of 300 Kelvin and above obey the ideal gas equation reasonably well. We can use the ideal gas equation to calculate variations in one variable when one or more of the others are changed.
For a constant quantity of gas at constant temperature, the pressure of the gas is inversely proportional to the volume. That is Boyle’s law.
Similarly for a constant quantity of gas at constant pressure, the volume of a gas is directly proportional to temperature. That is Charles’ law.
Dalton’s Law of Partial Pressures
In gas mixtures, the total pressure is the sum of the partial pressures that each gas would exert if it were present alone under the same conditions. That is the Dalton’s law of partial pressures. In all applications of the ideal gas equation, we must remember to convert temperature to the absolute temperature scale, in Kelvin. It is important to be able to use the ideal gas equation to solve problems involving gases as reactants or products in chemical reactions.
Molecular Weight of Gas
From the gas density, rho, under given conditions of pressure and temperature, it is possible to calculate the molecular weight of the gas, where molecular weight will, therefore, be equal to rho rt/p, this can be derived from PV=nRT. As long as you remember that the density is equal mass divided by volume.
Density = Mass / Volume
In calculating the quantity of gas collected over water, correction must be made for the partial pressure of water vapor in the container.
Kinetic Molecular Theory (analagous to Brownian Motion)
The kinetic molecular theory accounts for the properties of an ideal gas in terms of a set of assumptions about the nature of gases. Briefly, these assumptions are that molecules are in ceaseless, chaotic motion, that the volume of gas molecule is negligible in relation to the volume of their container, that the gas molecules have no attracted forces for one another, and finally, that the average kinetic energy of the gas molecules is proportional to absolute temperature.
The molecules of a gas do not all have the same kinetic energy at a given instance. Their speeds are distributed over a wide range. The distribution varies with the molecular weight of the gas and with the temperature. The root mean square speed varies in proportion to the square root of absolute temperature and inversely with the square root of molecular weight. It follows that the rate at which a gas escapes or effuses through a tiny hole is inversely proportional to the square root of its molecular weight.
Molecules in a real gas posses finite volume and, thus, undergo frequent collisions with one another. These frequent collisions will limit the rate at which a gas molecule can diffuse through a space occupied by other gas molecules and determine the thermal conductivity of the gas. The extent of non ideality of a real gas can be seen by examining the quantity PV over RT for one mole of a gas as a function pressure. This quantity is exactly equal to one for an ideal gas at all pressures.
Real gas will depart from ideal behavior because the molecules possess finite volume or because the molecules experience attractive forces from one another upon collision. The van der Waals equation is an equation of state for gases that attempts to correct the ideal gas equation to take into account the two properties of real gases.
Solutions-solutions are homogenous mixtures of atoms, ions, or molecules. The relative amounts of solute and solvent in a solution can be described qualitatively-dilute or a concentrated solution, or quantitatively, as in weight percentage; molarity, which is moles per liter; molality, which is moles solute per kilogram solvent; normality, equivalence per liter; or mole fraction. Mole fraction is the ratio of the number of moles of one component of a solution to the total number of moles of all substances present.
The extent to which a solute will dissolve in a particular solvent depends on the relative magnitudes of solute-solute or solute-solvent, and solvent-solvent attractive forces, as well as the – it depends on the changes in disorder accompanying the mixing. The rule, like dissolves like is found to be useful in rationalizing solubilities. It is possible to chain the solubility of a solute by changing temperature and pressure. If the solution process is endothermic, an increase in temperature promotes solubility. With a gas, an increase in pressure promotes solubility.
Le Chatelier’s Principle
These effects can be understood in terms of Le Chatelier’s principle. Substances that exist in solution as ions are called electrolytes. Those substances that are completely ionized in solution are called strong electrolytes. Reactions occur between electrolytes if an insoluble substance, a gas or a non-electrolyte conforms. Net ionic equations focus attention on the particular species that actually undergo some change during the reaction.
The presence of a solute in a solvent lowers the vapor pressure and the freezing point, and increases the boiling point of the solvent. These changes are termed colligative properties. The magnitude of the change depends on the total concentration of solute particles in solution, and not on there characteristics.
Acids and Bases
Acids and bases-an acid solution is created when a substance reacts with water in such a way as to increase the concentration of solvated hydrogen ions, which are represented as H+ or H3O+. The concentration of H+ is often expressed on the pH scale, where pH equals negative log concentration of hydrogen ions. Solutions of pH less than seven are acidic. Those with pH greater than seven are basic.
Ionization of Water
Water spontaneously ionizes to a slight degree, forming H+ and OH-. The extent of ionization is expressed by the ion product constant for water, which is Kw, which is equal to a concentration of a H+ times the concentration of OH-, which is equal to 10 to the minus 14. This relationship describes not only pure water but aqueous solution as well. Because the concentration of water is effectively constant in dilute solutions, the concentration of water is omitted from this equilibrium constant expression as well as from others associated with reactions in aqueous solutions.
One can rely on the Bronsted-Lowry theory of acids and bases. According to this theory, an acid is a proton donor, or a base is a proton acceptor. Reaction of an acid with water results in the formation of H+ and the conjugate base of the acid. Strong acids have conjugate bases that are weaker than water. Such acids are strong electrolytes, ionizing completely in solution. The common strong acids are HCl, HBr, HI, HNO3, HClO4, and H2SO4. Weak acids are substances for which the reaction with water is incomplete and equilibrium is established.
The extent to which the reaction proceed is expressed by the acid dissociation constant Ka. Polyprotic acids are acids such as H2SO3 that have more than one ionizable proton. Aside from the ionic hydroxides, such as NaOH, base is produced an increase of OH- by reaction with water. Strong bases have conjugate acids that are no stronger than water. The common strong bases are the hydroxides and oxides of the alkali metals and alkaline earth. Weak bases include H2O, NH3, amines, and the anions of weak acids. The extent to which a weak base reacts with water to generate OH- and a conjugate acid of the base is measured by the base dissociation constant, Kb.
Tags: acids and bases, avagadro's number, boyle's law, charles' law, chemical bonds, chemical equations and energy, conservation of mass, dalton's law of partial pressures, electronegativity, electrostatic repulsion, enthalpy, hess' law of constant heat summation, ideal gas equation, le chatelier's principle, lewis structures, mcat equations, molarity, molecular weight of gases, oxidation number, pauli exclusion principle, properties of gases, quantum numbers, resonance forms, sigma bonds, stoichiometry