Formal Charges: The Not-So-Mathematical Way

Formal Charges...how do they work?

A formal charge is a charge assigned to an electron in a molecule.  This is the sum of the electrons and protons associated with the atom.  If the atom has more electrons than protons, it will have a negative charge.  When the opposite is true, the atom will have a positive charge.   Formal charges help keep track of electrons.

That being said, formal charges aren't the actual charge of the atom; they are used as a guide to help draw the different resonance structures of the molecule which will ultimately lead to the resonance hybrid structure.  The resonance hybrid structure is the best 'real' representation of a molecule.  For now I'll just talk about an easy way to determine those formal charges.

My textbook uses a formal for calculating hybrid structures.  It looks something like this:

Formal Charge=Group Number - nonbonding electrons - 1/2(shared electrons)

Group Number:  The group number the atom belongs to on the periodic table.  For example, carbon is in group four (fourth column from the right...don't count the columns between element 21 and 30).  Oxygen is in group six.

Nonbonding Electrons:  The number of electrons that are not shared with other atoms in the moledule.

Shared Electrons:  The number of electrons that are shared with other atoms in the molecule.

This works, but it takes time to count up all of the electrons and figure out what's being shared and what's not.  It would be much easier to just look at an atom and know what the formal charge is.  Here's how!  I'm going to assume that you know how to draw Lewis structures.

Lets use carbon as our example.  Carbon is a very important element.

 

In this photo, carbon has four single bonds.  It's not important where they go.

1.  As I've said previously, carbon is in group four.  It has four valence electrons in its outer shell.  In this drawing, it's sharing all of them.  For the purpose of determining formal charge quickly, just know that it's in group four, so keep the number four in mind.

2. We must now determine how many electrons are in carbon's OWN POSESSION.  This 'own possession' thing is important.  You might be tempted to say eight, but this is not true.  It's sharing electrons; we can pretend that for one of single bond, carbon has one electron and the other atom has the other one.  Since we have four single bonds on this carbon, we'll say that it has four electrons in its own posession.

3.  Very easy math.  Take the number of electrons in carbon's own poession (four) and subtract it from the group number (four).  That equals zero.  This carbon has no charge.

Easy...but what if carbon doesn't feel like sharing.  See the drawing below.

 

This carbon only has three single bonds.  How does that work?  Lets figure it out.

1.  Carbon is still and always will be in group four.  Make note of that number.

2.  In this case, carbon has three single bonds and a pair of unshared electrons.  We only care about the electrons in carbon's own possession.  In this case, we'll count one electron for each single bond another two electrons for the ones that are unshared.  The unshared pair of electrons belong to carbon and no one else.

3.  Do the math.  The group number is 4 and the number of electrons in carbon's own possession is 5. 4-5 = -1.  This carbon atom has a negative charge!

 

Lets do it quickly one more time with another atom.  Lets use nitrogen.

 

1.  Nitrogen is in group five.

2.  Nitrogen has two single bonds and two pairs of unshared electrons.  That equals to six electrons in its own possession.

3.  5-6 = -1  This nitrogen atom has a negative charge.

 Here is a photo from my textbook (which I have referenced in this post) of some important atoms in organic chemistry.  It shows common bonding patterns and their charges.  You'll start to recognize the patterns and know right away what charges the atoms.

 

 Wade, Leroy G. "Chapter 1-8." Organic Chemistry. Upper Saddle River [etc.: Prentice Hall, 2010. Print.

Thanks goes out to my O-Chem professor/advisor and to Dmitri  Mendeleev.

First Day Back At University

Today is the first day of the 2011 Spring semester.  This semester includes classes like Calculus II, Geography of Europe, and Organic Chemistry.

I'll see you in the lab!

How To Draw A Heart On Your Graphing Calculator

As Valentine's Day approaches, we are bombarded with hearts, candy, and fluffy stuffed animals.  A slightly more geeky approach to Valentine's Day is this shirt with a heart plotted on the Cartesian coordinate plane. When I see something like this, I can't make myself think, 'Oh, cute!' and move on.  I need to know how it works and that means being able to recreate it myself.

Unable to let this go, I immediately messaged my friend who has a master's degree in mathematics.  We shall call him Mr. Mathematic.  The short answer is that, yes, it works.  However, the equation given needs to be manipulated so that it can be entered into a graphing calculator.

The equation on the shirt is

There are two variables on one side of the equation, but y must be by itself on one side so that it can be correctly entered into a graphing calculator.  This requires moving  to the right side and then taking the square root of both sides.  Lastly, move the  over to the right side.  This can also be written as .

What's important here is that when you take the square root of something, you must consider both positive and negative values.  For example, the square root of 4 can be both 2 and -2.  As a result, our equation manipulation has left us with two separate equations.

1.  

2.  

The first equation will plot the bottom of the heart and the second equation will plot the top.  Grab your graphing calculator and follow these steps to draw your own.  I'm going with the assumption that you know how to use the graphing feature on your graphing calculator of choice.

1.  In the 'Y=' screen, enter in the first equation like so:

 2.  This is what the graph should look like for this equation. Don't forget to resize your graph!  The standard graph on my calculator is when the x and y axis are displaying -10 to 10.  This makes the heart look very small.  I change it so that they both display -2 to 2.

3.  Enter in the second equation like so:

4.  This is what the graph should look like with both equations!  Congratulations!

I know that the heart appears to be broken (hah..?), but that is just a limitation of the graphing calculator.  They can't seem to make circular objects seamless.  If you zoom in, you'll see the lines are pretty close.

So, there you have it!  Show your significant other how much of a geek you really are by expressing your love on your graphing calculator!  Or, keep it simple and more stylish and get the shirt.

Thanks to ThinkGeek, R. Becker (who brought the shirt to my attention), and Mr. Mathematic.

Asking For the Unlikely...and Getting It.

I've learned over time that if you want something, the best strategy is to just ask for it.  It sounds simple enough, but I find that many people come up with all kinds of excuses as to why they can't achieve something.  Here is a recent example!

Cal State is experiencing the wonders of budget cuts.  That translates to decreased availability of classes for a growing population of students.  I was afraid that I wouldn't get the calculus professor I wanted for spring.  I couldn't register the class until my final grade for my previous math class was posted...and who knows how quickly that would be.  Here is what I did.

1.  A week before finals, I emailed the teacher expressing my desire to take his class and asking for advice in case his class filled up before I could register.  He said to not worry about it now, but to email him again if his class was full after my grade was posted.  No promises.

Naturally...that's exactly what happens.

2.  I emailed the professor again, letting him know I didn't get a chance to sign up for his class.  He responded with "That was fast" and gave me a permission number that let me into his class even though it was officially full and closed.

That's it!  Not even three steps.  When I mentioned what I did to other students, most looked surprised. I had broken some unspoken rule about The Process.  Well, screw The Process.

I did the same thing to get into another class that was full.  I needed this class to get into Cal State.  If I didn't get in, I'd have to wait an entire year to apply again.  I explained this to the professor teaching the class and she let me take it. I've found that if I show even a hint of a caring and desire to succeed towards a professor, he'll usually go out of his way for me.  Really, it works!

Have any of you asked for something that you were certain you wouldn't get or achieve?  Did it work?