Chemistry Articles

Article / Updated 03-20-2024

Chemists aren’t satisfied with measuring length, mass, temperature, and time alone. On the contrary, chemistry often deals in calculated quantities. These kinds of quantities are expressed with derived units, which are built from combinations of base units. Here are some examples: Area (for example, catalytic surface). and area has units of length squared (square meters, or m2, for example). Volume (of a reaction vessel, for example). You calculate volume by using the familiar formula Because length, width, and height are all length units, you end up with or a length cubed (for example, cubic meters, or m³). Density (of an unidentified substance). Density, arguably the most important derived unit to a chemist, is built by using the basic formula Density = Mass / Volume. Pressure (of gaseous reactants, for example): Pressure units are derived using the formula Pressure = Force / Area. The SI units for force and area are newtons (N) and square meters (m²), so the SI unit of pressure, the pascal (Pa), can be expressed as N/m². Let’s try an example. A physicist measures the density of a substance to be 20 kg/m³. His chemist colleague, appalled with the excessively large units, decides to change the units of the measurement to the more familiar grams per cubic centimeter. What is the new expression of the density? The answer is 0.02 g/cm³. A kilogram contains 1,000 (10³) grams, so 20 kg equals 20,000 g. Well, 100 cm = 1 m; therefore, (100 cm)³= (1 m)³. In other words, there are 100³ (or 106) cubic centimeters in 1 cubic meter. Doing the division gives you 0.02 g/cm³. You can write out the conversion as follows:

Article / Updated 07-10-2023

Chiral molecules usually contain at least one carbon atom with four nonidentical substituents. Such a carbon atom is called a chiral center (or sometimes a stereogenic center), using organic-speak. Any molecule that contains a chiral center will be chiral, with the exception of a meso compound (see below for how to identify these). For example, the compound shown here contains a carbon atom with four nonidentical substituents; this carbon atom is a chiral center, and the molecule itself is chiral, because it's nonsuperimposable on its mirror image. A chiral center You need to be able to quickly spot chiral centers in molecules. All straight-chain alkyl group carbons (CH3 or CH2 units) will not be chiral centers because these groups have two or more identical groups (the hydrogens) attached to the carbons. Neither will carbons on double or triple bonds be chiral centers because they can't have bonds to four different groups. When looking at a molecule, look for carbons that are substituted with four different groups. See, for example, if you can spot the two chiral centers in the molecule shown here. A molecule with two chiral centers Because CH3 and CH2 groups cannot be chiral centers, this molecule has only three carbons that could be chiral centers. The two leftmost possibilities, identified in the next figure, have four nonidentical groups and are chiral centers, but the one on the far right has two identical methyl (CH3) groups and so is not a chiral center. The chiral centers in a long molecule How to identify molecules as meso compounds A meso compound contains a plane of symmetry and so is achiral, regardless of whether the molecule has a chiral center. A plane of symmetry is a plane that cuts a molecule in half, yielding two halves that are mirror reflections of each other. By definition, a molecule that's not superimposable on its mirror image is a chiral molecule. Compounds that contain chiral centers are generally chiral, whereas molecules that have planes of symmetry are achiral and have structures that are identical to their mirror images. The plane of symmetry in meso compounds For example, cis-1,2-dibromocyclopentane (shown in the first figure) is meso because a plane cuts the molecule into two halves that are reflections of each other. Trans-1,2-dibromocyclopentane, however, is chiral because no plane splits the molecule into two mirror-image halves. Now look at the mirror images of these two molecules in the second figure to prove this generality to yourself. The mirror images of achiral (meso) and chiral molecules Even though the cis compound has two chiral centers (indicated with asterisks), the molecule is achiral because the mirror image is identical to the original molecule (and is, therefore, superimposable on the original molecule). Molecules with planes of symmetry will always have superimposable mirror images and will be achiral. On the other hand, the trans stereoisomer has no plane of symmetry and is chiral. In organic chemistry, you need to be able to spot planes of symmetry in molecules so you can determine whether a molecule with chiral centers will be chiral or meso. For example, can you spot the planes of symmetry in each of the meso compounds shown in the last figure? Some meso compounds How to Identify the Diastereomers of a Molecule When more than one chiral center is present in a molecule, you have the possibility of having stereoisomers that are not mirror images of each other. Such stereoisomers that are not mirror images are called diastereomers. Typically, you can only have diastereomers when the molecule has two or more chiral centers. The maximum number of possible stereoisomers that a molecule can have is a function of 2n, where n is the number of chiral centers in the molecule. Therefore, a molecule with five chiral centers can have up to 25 or 32 possible stereoisomers! As the number of chiral centers increases, the number of possible stereoisomers for that compound increases rapidly. For example, the molecule shown here has two chiral centers. A molecule with two chiral centers Because this molecule has two chiral centers, it can have a total of 22, or 4, possible stereoisomers, of which only one will be the enantiomer of the original molecule. Enantiomers are stereoisomers that are mirror images of each other. Because both chiral centers in this molecule are of R configuration, the enantiomer of this molecule would have the S configuration for both chiral centers. All the stereoisomers of this molecule are shown in the next figure. Those molecules that are not enantiomers of each other are diastereomers of each other. The four stereoisomers of a molecule with two chiral centers

Step by Step / Updated 07-05-2023

When elements combine through chemical reactions, they form compounds. When compounds contain carbon, they’re called organic compounds. The four families of organic compounds with important biological functions are

Article / Updated 05-03-2023

Acid-base reactions and their associated calculations play a primary role in many chemical, biological, and environmental systems. Whether you’re determining hydrogen ion concentration, [H+]; hydroxide ion concentration, [OH˗]; pH; or pOH, an equation and a calculator are important tools to have in your toolbox. Following are some handy formulas for solving acid/base problems. Calculating hydrogen or hydroxide ion concentration The following equation allows you to calculate the hydrogen ion concentration, [H+], at 25°C if you know the hydroxide ion concentration, [OH–]; you can also find [OH–] if you know [H+]. Just divide 1 × 10–14 by the concentration given, and you get the concentration that you need. Tip: To use scientific notation on your calculator, use the EE or EXP key (followed by the exponent) rather than the × 10^ keys. Calculating hydrogen or hydroxide ion concentration from the pH or pOH Be familiar with how to solve for [H+] or [OH–] when given the pH or pOH (or vice versa). Use the following formulas: Many scientific and graphing calculators differ in how they handle inputting values and taking logarithms, so know the proper keystroke order for your calculator. Be sure to review your calculator manual or look online. Calculating pH when given the pOH Calculating pH when you know the pOH (or vice versa) is probably the easiest of the acid-base calculations. Here’s the formula: pH + pOH = 14 Simply subtract the given value from 14 (keeping significant digits in mind) to get the value that you need. Doing titration calculations with a 1:1 acid-to-base ratio When you’re given titration calculations where the acid and base are reacting in a 1:1 ratio according to the balanced equation, the following equation offers a quick and easy way to solve for either the concentration of one of the substances or the volume necessary to complete the titration: MAVA = MBVB If the acid and base aren’t reacting in a 1:1 ratio, use stoichiometry (or dimensional analysis) to solve for your unknown quantity. By the way, stoichiometry works for the 1:1 ratio questions, too; it just takes one or two more steps. Remember: Keep track of your units! Cancel what you need to get rid of and make sure that you still have the units you need in your final answer.

Article / Updated 05-03-2023

The hyperbolic functions are certain combinations of the exponential functions ex and e–x. These functions occur often enough in differential equations and engineering that they’re typically introduced in a Calculus course. Some of the real-life applications of these functions relate to the study of electric transmission and suspension cables.

Article / Updated 04-14-2023

A conversion factor uses your knowledge of the relationships between units to convert from one unit to another. For example, if you know that there are 2.54 centimeters in every inch (or 2.2 pounds in every kilogram or 101.3 kilopascals in every atmosphere), then converting between those units becomes simple algebra. It is important to know some common conversions of temperature, size, and pressure as well as metric prefixes. Conversion factor table The following table includes some useful conversion factors. Using conversion factors example The following example shows how to use a basic conversion factor to fix non-SI units. Dr. Geekmajor absentmindedly measures the mass of a sample to be 0.75 lb and records his measurement in his lab notebook. His astute lab assistant, who wants to save the doctor some embarrassment, knows that there are 2.2 lbs in every kilogram. The assistant quickly converts the doctor’s measurement to SI units. What does she get? The answer is 0.34 kg. Let’s try another example. A chemistry student, daydreaming during lab, suddenly looks down to find that he’s measured the volume of his sample to be 1.5 cubic inches. What does he get when he converts this quantity to cubic centimeters? The answer is 25 cm3. Rookie chemists often mistakenly assume that if there are 2.54 centimeters in every inch, then there are 2.54 cubic centimeters in every cubic inch. No! Although this assumption seems logical at first glance, it leads to catastrophically wrong answers. Remember that cubic units are units of volume and that the formula for volume is Imagine 1 cubic inch as a cube with 1-inch sides. The cube’s volume is Now consider the dimensions of the cube in centimeters: Calculate the volume using these measurements, and you get This volume is much greater than 2.54 cm3! To convert units of area or volume using length measurements, square or cube everything in your conversion factor, not just the units, and everything works out just fine.

Cheat Sheet / Updated 01-09-2023

Organic Chemistry II is one of the toughest courses you can take. Surviving isn’t easy — you probably know that from your Organic Chemistry I class. Preparation is key: If you study the basics of organic chemistry the right way, prepare for your tests, and know your aromatic systems, you’re off to a great start!

Cheat Sheet / Updated 11-08-2022

Chemistry covers all kinds of stuff. Sometimes you might not be sure where to start when you are first given a set of problems and told to go forth and succeed. Sometimes it’s converting metric units, writing ionic formulas, naming covalent compounds, balancing reactions, or dealing with extensive and intensive properties. This Cheat Sheet is designed to give you some help on a few of the trickier things you might encounter so that when you are done looking it over you can go forth and succeed!

Article / Updated 09-27-2022

Studying the elements of the periodic table is vital for understanding organic chemistry. So that you don't have to memorize each element, they're grouped together by their properties.

Cheat Sheet / Updated 04-08-2022

Chemistry II is more than fires and smelly explosions. Chemistry II is more about solving calculations. In fact, Chemistry II has a lot more calculations and math than your Chemistry I class did. In your Chemistry II class, you need to master several formulas so you can calculate different mathematical problems, ranging from kinetics, different types of equilibrium, thermochemistry, and electrochemistry. This Cheat Sheet can serve as a quick reference to how to solve kinetics, thermodynamics, and different types of equilibrium problems.