Tuesday, October 05, 2010

The Buddha and Colission Theory - How to Solve the Equation

In the past three years I've gotten a lot of traffic to my “Move Over Buddha” post. Some of the traffic, undoubtedly, trying to figure out the answer to the very question I was faced with:

Calculate the fraction of atoms in a sample of argon gas at 400 K that have an energy of 10.0 kJ or greater.

I know this only because I discovered that someone had left me a comment, asking for clarification.

It may help you if I explain a bit about where this comes from, and then rewrite the equation for you. Keep in mind that I haven't dealt with this kind of thing for about three years so, I'm a bit rusty. If you notice anything seriously wrong, leave a comment and let me know.

Collision Theory

With few exceptions, reaction rates increase with increasing temperature. A rule of thumb in chemistry is that an increase in temperature by 10 degrees C doubles the reaction rate. The rate constant's dependence on temperature is explained by collision theory. Collision theory assumes that, for a reaction to occur, reactant molecules must collide with an energy greater than some minimum value and with the proper orientation. This minimum energy of collision required for two reactant molecules to react is called the activation energy, or Ea.

Raising the temperature increases the fraction of molecules having high kinetic energies. These are the ones most likely to react when they collide. The higher the temperature, the larger the fraction of molecules that can provide the activation energy needed for reaction.

The fraction of reactant collisions having energy greater than the activation energy can change rapidly with even small temperature changes. It can be shown that f is related to the activation energy, Ea, by the equation



Let's define the parts of the equation:

f = frequency of molecules having a high enough kinetic energy to react (i.e. greater than the activation energy)

Ea = the energy of activation for the kind of molecule in question (i.e. argon molecules)

R = the universal gas constant (8.31 J/mol.K )

T = the absolute temperature (Kelvin)

e = the inverse natural logarithm (inverse ln).

Now, let's rewrite the equation slightly, just to help me clarify the math.


Let's add the values and units from the original problem.


The top uses kilojoules, while the bottom uses joules. Let's the top part by 1000/ k in order to bring the units on the top and bottom of the equation into agreement.  We'll also rewrite the temperature (400K) to make the math more clear.


Multiplying the top part of the equation, and the bottom part of the equation, the temperature unit (K) cancels, and the equation is somewhat simplified.



We can now invert the denominator to simplify the equation further, and make sure we deal with the units properly.


Multiplying across, the energy units (J - Joules) cancel and the equation if further simplified.


Dividing we end up with this:

Now, we take the inverse natural log of 3.0 mol and find the solution: 20.1 mol of argon.


I hope that explanation helped. If you see anything wrong with my math, or anything else. Let me know.

Tuesday, August 12, 2008

Please Help my Friend

I know I've not posted for a long time, but I thought it would be worth coming out of accidental hiatus to post this.

It turns out that Dan Smith, a long time friend of mine, is fighting cancer for the second time. He went in a year ago with thyroid cancer, which they thought they had treated successfully, but it's come back in a form no one expected.

You can find Dan's story here:

http://cad-comic.com/news.php?i=1668#1670
http://cad-comic.com/news.php?i=1673#1673
http://cad-comic.com/news.php?i=1673#1674
http://cad-comic.com/news.php?i=1684#1684

and here:

http://yw7.brushthralls.com/

This has hit me harder than I would have thought it might. It may be because I'm just coming out of losing my father to an aggressive brain cancer. I don't know.

Dan and I lost track of each other some years ago. There was a sort of unspoken falling out, as it were. (The details aren't important.) I've tried to make contact with him on a few occasions through email, but he's never returned them. In spite of that, I want to encourage everyone to go read Dan's story and, if you can, donate through PayPal at the http://yw7.brushthralls.com/ page, to help his family offset the medical costs.

Thank you.

Thursday, March 27, 2008

Aikido is Cool

First off, let me apologize for not posting in a very long time. Life has been busy and I've had other projects that needed my attention.

One thing that has been happening, though, is I'm trying to get back into shape. I've managed to do a light workout every morning for a month, and I think I've lost four pounds.

Part of what's driven this is that I miss doing martial arts. Years ago I studied Seidokan Aikido. I loved it! I never got my black belt or anything, but I did study very seriously for a couple of years, and even did some student teaching.

Anyway, I've been missing it and I've been trying to get myself back into shape so I can start doing it again.

On a whim, I hit YouTube and did a search for "aikido." I found some pretty cool stuff. I just did the search again today and . . . oh . . . my . . . word. This guy, Anthony Yates, 6th Dan in Yoshinkan Aikido, is amazing.

Friday, January 25, 2008

Root Canals and VH1

The morning of the first dental treatment went well. I woke up early, nervous as a fly at a frog convention. I took a shower, got dressed, found my wallet and keys, and headed out the door.

Arriving at the dentist's office I was greeted with a smile by the receptionist, a nice brunette in her late 40's. “Hello, Mr. Newman! How are you this morning?”

“I'm okay,” I lied.

“Good!,” the receptionist beamed. “Just take a seat and they'll be ready for you in a minute.”

“Don't you want me to pay you, first?” I questioned.

“No, usually we do that after. Sometimes more things get done, and sometimes less, depending on what happens.” she replied, confidently.

“Are you sure you don't want me to pay you now? I might not be in the mood to pay you after.” I asked, only half joking.

She paused and turned her chair towards me, looking off into space, her smile full of chagrin. “You may have a point.” She said, her eyebrows raised. “I've never thought about it that way.”

Seeing I'd turned her brain upside down, I felt my work was done and sat down to wait. There was a young mother and her 3 year old son waiting ahead of me but, much to their consternation, they called me in first.

“John?,” the blond, twenty-something dental assistant called. “Do you want to come back now?”

I got up from my chair and started going back to the treatment chairs. “Is that a trick question?”

Seated in the off-white chair, I was offered a remote control for the small, LCD television strategically mounted to the ceiling above. “Would you like to watch a little TV? Take you mind off being here a little bit?”

“Sure.” I said. “Thanks.”

It was about 8:10 in the morning and the only thing on most of the broadcast channels was news. I didn't need more stress, so I avoided all that. There was a golf game going on on ESPN. That was at least relaxing but, I don't like watching golf on TV. At least, not for very long.

After surfing through the channels a few times, I found three possible programs I could handle: an old episode of Pokemon on cartoon network, Xena – Warrior Princess, and VH1. I flipped between Pokemon and Xena a few times, getting quickly bored with each (was Xena this cheesy when I was younger?), and settled on a Lenny Kravitz video on VH1. Not bad. I sat in the chair, closed my eyes and listened to the music for a while.

Then a Britanny Spears Video came on an I went back to Pokemon until it was over.

The dentist, Dr. HS, came over, along with a cute assistant, a brunette, this time. I turned off the TV so I could give him my full attention. That, and I don't want to associate music with pain.

We exchanged pleasantries, I assured him it wasn't the work I was worried about so much as the needles, and so he got started strait away torturing me with the needles.

I've really got to be careful about what I say, in the future.

“Just little pinch,” he said, as he poked me on the outside part of my gums. It was just a pinch, too. Good for you, Doc.

“Just one more pinch,” he said, and then he poked me on the inside of my toothline. Dentists have a strange notion of what 'pinches' are like. Sure. Maybe a pinch from Godzilla's claws. I have to give it to Dr. HS, though. It didn't hurt for as long as I was used to for such things.

The dentist went away for awhile, to give the anesthetic time to kick in, so I turn the TV back on. After a couple of music videos, and some more channel surfing, he came back and got started on the root canal. To be honest, it went pretty fast. I was nervous watching all the weird tools he was using and listening to the drill, but it was over quicker than any I've had before.

After giving me false hope for less painful procedures to come, he brought back the needles to numb me for the rest of the work, a couple of extractions. As I sat there in the chair, smashing the ends of the arm rests under my grip and involuntarily groaning because of the continued torture, it occurred to me that I was actually going to pay this guy to hurt me. How sick is that?

The extractions went well, except for the last one. I could feel every poke, prod, pull, and twist with terrible exactness. Dr. HS got his needles out to “numb me up more” he said. I think it was just to get me to stop complaining about the other pain.

“Here! I'll give you something really painful to complain about!” I imagined him saying.

He didn't say anything of the sort, of course. But he still poked me with nasty sharp needles.

The anesthetic wouldn't take though. He'd try and get it out, I'd cringe and shout, and he'd give me more shots. It took six shots of, two or three absolutely excruciating ones directly into the nerves of the tooth (which about took me out of the chair and onto the ceiling), to get me numb enough to do the work. Dr HS estimated it was about three gallons worth.

When he came back once more to pull the last one I was seriously thinking of telling him just to yank the darn thing, regardless of how I was feeling, just to avoid the needles. Thankfully, three gallons had been enough.

It occurred to me that it was a good thing I never served in an actual war when I was in the USMC. If the torturers there had been trained as well as my dentist, I'd have rolled over like a bag of wet fish.

After it was done he took a couple more x-rays, just to make sure he'd gotten everything. I was fortunate in that he'd done his job right the first time and didn't have to get back into the chair. (No more torture, please! I'll talk, really I will!)

I headed back to the reception desk to pay my bill and pick up the prescriptions. “Great interrogation session Doc!” I said to myself. “Lot's of pain. I don't think I'll give you a tip, though.”

After paying the receptionist I realized how they got people to pay them for all the torture. The receptionist was the keeper of the prescription slips. Thank goodness my prayers have been answered. Dr HS gave me a prescription for Percocet, my old pain killing friend, and an antibiotic.

The dental assistant gave me directions on how and when to replace the gauze in my mouth. “You can remove it when you eat and drink of course,” she said.

I shook my head, wondering what gave her the idea I'd want to eat anything for the rest of the week, let alone that day.

After it was over, and my credit card balance was a little higher, I drove directly to the pharmacy to fill the prescriptions. The pharmacist asked, “Are you going to the dentist, or are you coming back?”

“Just got done,” I mumbled through the bloody gauze in my mouth.

“Oh, okay. I won't make you talk to me anymore, then.” he said, smiling sheepishly. I was grateful.

The rest of the day was a blur of pain, Percocet, and pirates. The dentist had told me to sit up to help keep the swelling down so I sat in my wife's blue recliner and watched the Pirates of the Caribbean movies. All three of them. Back to back. Mostly I just swallowed the pills, felt sleepy and drugged, and wondered how I could have a headache even while on Percocet.

Oh yeah. The girls kept fighting after they got home from school. That's when I got the headache. It's hard to tell what mood I'm in when I'm drugged out of my mind, I guess.

Several hours later, I finally removed the last of gauze. Most of the bleeding had stopped, and I just couldn't take it filling my mouth, anymore. After a few more hours of TV, water, and an upset stomach from the pills, I went to bed.

Thankfully, I felt a lot better in the morning. Not so much pain. I just felt like I'd been put through a clothes wringer and come out the other end.

Oh, yeah. I kind of did.