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Evolution Friday : Fossil Horses

One of the oldest pieces of evidence supporting the theory of evolution is the fossil record. Fossils are the ancient bones (or other evidence) from life that are preserved in rock. The fossil record provides an astounding array of evidence that supports the theory of evolution. Through the study of fossils, an overwhelming body of evidence has accumulated depicting the progress of lifeforms on earth.
Because it is a bit much to tackle in one short essay, I’ll narrow my focus. I remember a neat exhibit I saw about eight years ago at a small museum in northern Nebraska. It is at the site of the Ashfall Fossil beds.
279.jpg
In the main lobby of this museum they have a display case showing foot bones from a variety of horse-like animals. Over the years there have been many many different kinds of horses. The modern horse (of genus equus) is the last from a diverse family ultimately descended from a common three-toed ancestors. Over time there has many different horse-like animals in wide variety of forms. All but one of the 27 genera that have existed are now extinct. That fact alone shows the creative but ruthless nature of evolution — that so many would come to exist, ultimately to dissappear and be replaced by another species.
One interesting thing about the ancestral species of horses is how their feet transformed from a three-toed structure into the modern horse’s hoof. These two forms are very different. It is hard to imagine how the one could gradually transform into the other. But evolution works on the principle of gradual change, with no intermediate form having a detrimental effect on the organism.
At first glance, this may seem to be a valid argument against evolution. Consider a more extreme, fictitious example: Why do you suppose that no animals have evolved jet engines? I believe it is because a jet engine is exceedingly complex. But not only that. Also because there is no conceivable benefit gained by most of a jet engine. A jet engine either works or else it doesn’t — and building 90% of a jet engine is an enormous burden on a struggling species. Thus you can’t invent a scenerio where gradual evolutionary pressure would result in a jet engine.
Contrast that with how animals do fly — by flapping wings. This process has some advantage even when the flight is limited. For example, the flying squirrel has relatively little adaptation (just a slightly modified rib cage and extra skin webbing their arms and legs) — and yet this enables the animal to move around a jungle better than a regular squirrel can. Given enough time and selective pressure, the flying squirrel might eventually evolve into an animal as adept at flying as a bat.
So how does the horse fit into this? The fossils from the Ashfall fossil beds show a variety of species of horses. The feet of those horses are structured from the same bones as both modern horses and the ancient three-toed ancestor. But they range in structure from very modern to very ancient in appearance. And the key point is — now that we can see them — it’s clear that all of them worked just fine.

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A hole in his heart

I just got word that my friend, Adam age 6 months, has come out of surgery for Atrioventricular (AV) Canal Defect. This surgery involved cutting open part of his heart.
These two images compare normal and AV canal defect hearts.
normal heart
av heart
In an AV heart, the piece of heart tissue called the Ventricular Septum that separates the left and right halves is missing. Surgery is used to rebuild this missing structure, and also to repair the tricuspid valves which are also misformed.
At first I thought that this defect was in some way related to the foramen ovale. The foramen ovale is a different kind of “hole in the heart”. It is present in the fetus, and serves to allow blood flowing through the heart to bypass the lungs. It is between the left and right atrium (not the ventrical is in Adam’s case). It’s needed because a fetus does not get its oxygen from the lungs — it gets it from the placenta via the umbilical cord. By bypassing the lungs, the fetus is able to redistribute the oxygenated blood more efficiently. At birth, the foramen ovale closes, causing blood flow to be sent to the lungs. If this fails to close, it can result in cyanotic heart disease, in which a newborn turns blue due to lack of oxygenated blood.
Here’s hoping to a speedy recovery for little Adam.

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Ephemeris Calculator

JPL has a ephemeris calculator that will determine where celestial bodies can be found in the sky. This is useful if you’re trying to find how far away a certain planet or asteroid is.
You could use this to keep track of 2004 MN4, an asteroid which will come close to the earth In 2029. It will pass inside the Moon’s orbit, although it won’t hit either the moon or earth. It should be visible with the naked eye — if you live in Africa, Europe or parts of Asia that is. MN4 is about 1000 feet across and would be locally but not globally devastating if it hit the earth.

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Ernst Mayr, an influential evolutionary biologist, dies

http://news.bbc.co.uk/2/hi/science/nature/4243805.stm
“…his definition of a biological species – an interbreeding population that cannot breed with other groups – is the most widely accepted one today.”

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Evolution Friday : DNA

The mitochondria is a small organelle found in all Eukaryotic organisms. Eukaryotes include all multicellular living things, such as trees, squid, sponges and people. They also include some single celled organisms like yeast, but not bacteria. One interesting feature of mitochondria is that they have their own genome made of DNA. It is possible to see the single, circular chromosome of the mitochondria under a microscope, and simple molecular techniques can be used to duplicate and analyze the mitochondrial DNA.



The National Institute of Health (NIH) has a division called the National Center for Biotechnology Information. They provide a lot of free services to facilitate research in the natural biological sciences. For one thing, they catalog DNA sequences from all living things as they are discovered. They also provide an analysis tooll called “BLAST” that lets you compare an input sequence to their entire database of sequences.



For today’s entry, I used the NCBI “nucleotide” search to download the entire mitochondrial sequence for the mouse. Here is the first seventy nucleotides of that sequence:

GTTAATGTAGCTTAATAACAAAGCAAAGCACTGAAAATGCTTAGATGGATAATTTTATCCCATAAACACA

To a human, that doesn’t mean much in its current form. However, it is possible to use the BLAST tool to find all other sequences that match the mouse mitochondrial sequence. I did a crude search so that I didn’t bog down NIH’s computers. Even a quick and dirty, crude search provides overwhelming support for this discussion.



The first hit I retrieved was the sequence for “Rattus norvegicus mitochondrial genome”. The rat is a closely related species to the mouse, so this isn’t surprising. Here is a comparison of sixty of the nucleotides between the mouse and the rat:

Score = 7868 bits (4092), Expect = 0.0
Identities = 7491/9142 (81%), Gaps = 297/9142 (3%)
Strand = Plus / Plus
Query: 4909  taagtacaataaccctacccctagccccccaactaattatc-tagaagtttaggatatac 4967
|||||||  |||||||||| ||  || |||||||||| | | ||||||||||||||||||
Sbjct: 4886  taagtaccctaaccctaccgctttcctcccaactaatca-catagaagtttaggatatac 4944



I find it amazing that two species are able to faithfully duplicate the DNA molecule year after year, from generation to generation, and only develop such small changes. This is due in part to the fact that most changes would be fatal to the organism; only in a few places are changes going to provide benefit or be inconsequential.



The next sequence to match the mouse mitochondrial genome is the mitochondrial genome from Acinonyx jubatus, which you might recognize by its common name: Cheetah. Here is a peak at part of that comparison:

Score = 3798 bits (1975), Expect = 0.0
Identities = 5322/6920 (76%), Gaps = 384/6920 (5%)
Strand = Plus / Plus
Query: 5019  taaggactgtaag-acttcatcct-acatctattgaatgcaaatcaattgctttaattaa 5076
||||||||| ||| || | || || ||||| ||||| ||||||||||   ||||||||||
Sbjct: 5895  taaggactgcaagaacct-at-ctcacatcaattgactgcaaatcaaacactttaattaa 5952

The Cheetah is more distantly related to the mouse than the rat is. The DNA supports this notion: The cheetah and the mouse share 76% identical bases, whereas the rat and the mouse shared 81%. That may not seem like very high numbers to some of you — until you start to think about the odds. If the Cheetah and the mouse had been invented simultaneously the chances that their genome would be this similar than the NCBI computer can calculate (after a probability gets below 1 in 10,000,…(with one hundred zeros)…0,000 it just gives up and calls it ZERO).



Moving down the list reveals more distantly related species. There is Parascalops breweri, the hairy-tailed mole and Saimiri sciureus, the South American squirrel monkey. How about the Common Marmoset (Callithrix jacchus). It is not surprising that all mammals have mitochondrial DNA sequences that are similar; this evidence is consistent with the theory of evolution. All mammals share a common ancestor. Over time as the decendants diverged into separate species, the mitochondrial DNA picked up random changes. You would expect more distantly related species to have even more changes than you see within the mammals.



And sure enough, this is the case. Drosophila melanogaster, the fruit fly has mitochondria.

Score =  683 bits (355), Expect = 0.0
Identities = 1057/1397 (75%), Gaps = 58/1397 (4%)
Strand = Plus / Plus
Query: 5345 tgattattctcaaccaatcacaaagatatcggaaccctata-tctactatttggagcctg 5403
|||||||| || || ||||| |||||||| |||||  |||| | || | |||||||| ||
Sbjct: 1080 tgattattttctacaaatcataaagatattggaactttatatttta-tttttggagcttg 1138

The matching sequence shown here is for one part of the mitochondrial DNA called the “cytochrome c oxidase I gene”. Just for fun, I searched the database again using that sequence as the input query. Here is another way to compare a large number of sequences (the most similar species are near the top of the list).:

1_18238  1      tgattattctcaaccaatcacaaagatatcggaaccctatatctactatttggagcctg 59
50302071 5345   ........................................................... 5403
34555991 5343   ......................................c...........c........ 5401
34221823 168561 ............................................g.....c........ 168619
3150275  5344   ......................................c...........c..g..... 5402
51980679 1            ................................c...........c........ 53
54654337 6238       .............c..t...........t.....t.................... 6292
44894095 5335   ....................t...........c........ct..........t..... 5393
38602501 5379       .............c........c.....c....................t..... 5433
4239858  16     .................c..t.....c........a.................       68
57014054 5363   .....g.....t.....c...........t..c...........t.............. 5421
22137340 3      ...................................                         37
414126   5798       .............c........c.....c.........t..........t..... 5852
34393057 16     .................c..............t..t..g..........g...t..... 74
14582815 5363   ..........................c........tt....c...t.......t..... 5421
30314638 16     .................c..............t..t..g..........g...t..... 74
12484073 16     ..........................c........tt....c...t.......t..... 74
23306916 5460   .....t..........................c........c...g.t.....t..... 5518
4239866  16     ..........................c........tt....c...t.......t..... 74
38602445 5390       ......................c..t..c.........t..........t..... 5444
38602543 5383   ..............a..c...........t.....t..............          5432
4894501  6719       .............c.......................                   6755
25005957 5474   .....c........t.................c.........t..g.......       5526
25005593 6989       ..........a.....t.....c........a.................       7037
16041651 5409   ..........................c.....c........                   5449
38603494 5527   .....t....................c.....c.....t......g.......       5579
21425525 5347       ..........a.....t...........c.........t..........       5395
14588633 5527   .....t....................c.....c.....t......g.......       5579
14588619 5527   .....t....................c.....c.....t......g.......       5579
4887659  6484   ...........t..............c.....t...........                6527
56713965 5349   ........t........c..............c.....t..c..t........t..... 5407
13676803 5394       ..........t.....t........t..c...........t........t..... 5448
56398532 5321       ..........t.....t...........t..t......t..........c..... 5375
15430509 5509   .....t...........c....................t...t..a.c..c........ 5567

NCBI also provides a “taxonomy” report view which is simply amazing. Of the first one hundred hits in its database for the mouse mitochondrial cytochrome oxidase C DNA sequence, it pulled out organisms from all kinds of coelomates. (Coelomates are animals that have a gut — so most multicellular animals but not, for example, sponges.)
What is simply amazing about this report is how it coincides exactly with animal taxonomy. Keep in mind that taxonomy was originaly developed with no knowledge of DNA! But here, with a simply 59 DNA base query to the database, the DNA itself reconstructs the relationship between the mouse and (in order as you go down the table) other kinds of mice, rats, cows, sheep, whales, hippos, primates, birds, amphibians, reptiles, fish and ending with a cricket.



I can understand how someone might question evolution prior to the discovery of DNA. But when presented with such phenomenal data as this…. it simply becomes rediculous. I suppose a creationist may argue that this is just the way God created life. I don’t want to argue with other people’s religious beliefs, but it seems to me that if God created life, then we have overwhelming evidence that evolution is the process God chose.


Taxonomy Report

Coelomata ………………………………….   100 hits   55 orgs [root; cellular organisms; Eukaryota; Fungi/Metazoa group; Metazoa; Eumetazoa; Bilateria]
. Deuterostomia ……………………………. 99 hits 54 orgs
. . Euteleostomi …………………………… 98 hits 53 orgs [Chordata; Craniata; Vertebrata; Gnathostomata; Teleostomi]
. . . Tetrapoda ……………………………. 83 hits 39 orgs [Sarcopterygii]
. . . . Amniota ……………………………. 81 hits 37 orgs
. . . . . Theria …………………………… 63 hits 26 orgs [Mammalia]
. . . . . . Eutheria ……………………….. 61 hits 24 orgs
. . . . . . . Murinae ………………………. 28 hits 5 orgs [Rodentia; Sciurognathi; Muridae]
. . . . . . . . Mus ………………………… 22 hits 3 orgs
. . . . . . . . . Mus musculus ………………. 22 hits 3 orgs
. . . . . . . . . . Mus musculus molossinus …… 1 hits 1 orgs
. . . . . . . . . . Mus musculus domesticus …… 1 hits 1 orgs
. . . . . . . . Rattus ……………………… 6 hits 2 orgs
. . . . . . . . . Rattus norvegicus ………….. 5 hits 1 orgs
. . . . . . . . . Rattus rattus ……………… 1 hits 1 orgs
. . . . . . . Cetartiodactyla ……………….. 24 hits 12 orgs
. . . . . . . . Pecora ……………………… 17 hits 5 orgs [Ruminantia]
. . . . . . . . . Bovidae …………………… 15 hits 4 orgs
. . . . . . . . . . Bovinae …………………. 13 hits 3 orgs
. . . . . . . . . . . Bos …………………… 12 hits 2 orgs
. . . . . . . . . . . . Bos grunniens ………… 1 hits 1 orgs
. . . . . . . . . . . . Bos taurus …………… 11 hits 1 orgs
. . . . . . . . . . . Bubalus bubalis ………… 1 hits 1 orgs [Bubalus]
. . . . . . . . . . Ovis aries ………………. 2 hits 1 orgs [Caprinae; Ovis]
. . . . . . . . . Cervus nippon yesoensis …….. 2 hits 1 orgs [Cervidae; Cervinae; Cervus; Cervus nippon]
. . . . . . . . Cetacea …………………….. 6 hits 6 orgs
. . . . . . . . . Odontoceti ………………… 2 hits 2 orgs
. . . . . . . . . . Berardius bairdii ………… 1 hits 1 orgs [Ziphiidae; Berardius]
. . . . . . . . . . Pontoporia blainvillei ……. 1 hits 1 orgs [Pontoporiidae; Pontoporia]
. . . . . . . . . Mysticeti …………………. 4 hits 4 orgs
. . . . . . . . . . Balaenoptera …………….. 2 hits 2 orgs [Balaenopteridae]
. . . . . . . . . . . Balaenoptera musculus …… 1 hits 1 orgs
. . . . . . . . . . . Balaenoptera acutorostrata . 1 hits 1 orgs
. . . . . . . . . . Eschrichtius robustus …….. 1 hits 1 orgs [Eschrichtiidae; Eschrichtius]
. . . . . . . . . . Balaena mysticetus ……….. 1 hits 1 orgs [Balaenidae; Balaena]
. . . . . . . . Hippopotamus amphibius ……….. 1 hits 1 orgs [Hippopotamidae; Hippopotamus]
. . . . . . . Primates ……………………… 4 hits 2 orgs
. . . . . . . . Ateles geoffroyi …………….. 1 hits 1 orgs [Platyrrhini; Cebidae; Atelinae; Ateles]
. . . . . . . . Tarsius bancanus …………….. 3 hits 1 orgs [Tarsii; Tarsiidae; Tarsius]
. . . . . . . Herpestes javanicus ……………. 1 hits 1 orgs [Carnivora; Fissipedia; Herpestidae; Herpestinae; Herpestes]
. . . . . . . Tamandua tetradactyla ………….. 1 hits 1 orgs [Edentata; Myrmecophagidae; Tamandua]
. . . . . . . Pipistrellus abramus …………… 1 hits 1 orgs [Chiroptera; Microchiroptera; Vespertilionidae; Pipistrellus]
. . . . . . . Chrysochloris asiatica …………. 1 hits 1 orgs [Insectivora; Chrysochloridae; Chrysochloris]
. . . . . . . Tupaia belangeri ………………. 1 hits 1 orgs [Scandentia; Tupaiidae; Tupaia]
. . . . . . Peramelidae …………………….. 2 hits 2 orgs [Metatheria; Peramelemorphia]
. . . . . . . Isoodon macrourus ……………… 1 hits 1 orgs [Isoodon]
. . . . . . . Macrotis lagotis ………………. 1 hits 1 orgs [Macrotis]
. . . . . Sauria …………………………… 18 hits 11 orgs [Sauropsida]
. . . . . . Neognathae ……………………… 17 hits 10 orgs [Archosauria; Aves]
. . . . . . . Passeriformes …………………. 10 hits 5 orgs
. . . . . . . . Vidua chalybeata …………….. 1 hits 1 orgs [Estrildidae; Viduinae; Vidua]
. . . . . . . . Cnemophilus macgregorii ………. 1 hits 1 orgs [Corvoidea; Corvidae; Corvinae; Cnemophilus]
. . . . . . . . Basileuterus ………………… 8 hits 3 orgs [Passeroidea; Fringillidae; Emberizinae]
. . . . . . . . . Basileuterus leucoblepharus …. 1 hits 1 orgs
. . . . . . . . . Basileuterus rivularis ……… 4 hits 1 orgs
. . . . . . . . . Basileuterus fulvicauda …….. 3 hits 1 orgs
. . . . . . . Buteo buteo …………………… 1 hits 1 orgs [Falconiformes; Accipitridae; Accipitrinae; Buteo]
. . . . . . . Aythya americana ………………. 1 hits 1 orgs [Anseriformes; Anatidae; Aythya]
. . . . . . . Bubo virginianus ………………. 1 hits 1 orgs [Strigiformes; Strigidae; Bubo]
. . . . . . . Opisthocomus hoazin ……………. 3 hits 1 orgs [Opisthocomiformes; Opisthocomidae; Opisthocomus]
. . . . . . . Arenaria interpres …………….. 1 hits 1 orgs [Charadriiformes; Scolopacidae; Arenaria]
. . . . . . Dinodon semicarinatus ……………. 1 hits 1 orgs [Lepidosauria; Squamata; Scleroglossa; Serpentes; Colubroidea; Colubridae; Colubrinae; Dinodon]
. . . . Batrachia ………………………….. 2 hits 2 orgs [Amphibia]
. . . . . Xenopus laevis ……………………. 1 hits 1 orgs [Anura; Mesobatrachia; Pipoidea; Pipidae; Xenopodinae; Xenopus; Xenopus]
. . . . . Plethodon cinereus ………………… 1 hits 1 orgs [Caudata; Salamandroidea; Plethodontidae; Plethodontinae; Plethodontini; Plethodon]
. . . Teleostei ……………………………. 15 hits 14 orgs [Actinopterygii; Actinopteri; Neopterygii]
. . . . Neoteleostei ……………………….. 14 hits 13 orgs [Elopocephala; Clupeocephala; Euteleostei; Neognathi]
. . . . . Holacanthopterygii ………………… 13 hits 12 orgs [Eurypterygii; Ctenosquamata; Acanthomorpha; Euacanthomorpha]
. . . . . . Percomorpha …………………….. 11 hits 10 orgs [Acanthopterygii; Euacanthopterygii]
. . . . . . . Takifugu rubripes ……………… 1 hits 1 orgs [Tetraodontiformes; Tetraodontoidei; Tetradontoidea; Tetraodontidae; Takifugu]
. . . . . . . Smegmamorpha ………………….. 3 hits 3 orgs
. . . . . . . . Hypoptychus dybowskii ………… 1 hits 1 orgs [Gasterosteiformes; Gasterosteoidei; Hypoptychidae; Hypoptychus]
. . . . . . . . Atherinomorpha ………………. 2 hits 2 orgs
. . . . . . . . . Gambusia affinis …………… 1 hits 1 orgs [Cyprinodontiformes; Cyprinodontoidei; Poeciliidae; Gambusia]
. . . . . . . . . Oryzias latipes ……………. 1 hits 1 orgs [Beloniformes; Adrianichthyoidei; Adrianichthyidae; Oryziinae; Oryzias]
. . . . . . . Perciformes …………………… 6 hits 5 orgs
. . . . . . . . Carangidae ………………….. 5 hits 4 orgs [Carangoidei]
. . . . . . . . . Trachurus …………………. 3 hits 2 orgs
. . . . . . . . . . Trachurus trachurus ………. 1 hits 1 orgs
. . . . . . . . . . Trachurus japonicus ………. 2 hits 1 orgs
. . . . . . . . . Caranx melampygus ………….. 1 hits 1 orgs [Caranx]
. . . . . . . . . Carangoides armatus ………… 1 hits 1 orgs [Carangoides]
. . . . . . . . Pterocaesio tile …………….. 1 hits 1 orgs [Percoidei; Lutjanidae; Caesioninae; Pterocaesio]
. . . . . . . Satyrichthys amiscus …………… 1 hits 1 orgs [Scorpaeniformes; Platycephaloidei; Peristediidae; Satyrichthys]
. . . . . . Paracanthopterygii ………………. 2 hits 2 orgs
. . . . . . . Bregmaceros nectabanus …………. 1 hits 1 orgs [Gadiformes; Bregmacerotidae; Bregmaceros]
. . . . . . . Melanocetus murrayi ……………. 1 hits 1 orgs [Lophiiformes; Ceratioidei; Ceratioidea; Melanocetidae; Melanocetus]
. . . . . Ijimaia dofleini ………………….. 1 hits 1 orgs [Stenopterygii; Ateleopodiformes; Ateleopodidae; Ijimaia]
. . . . Osteoglossum bicirrhosum …………….. 1 hits 1 orgs [Osteoglossomorpha; Osteoglossiformes; Osteoglossoidei; Osteoglossidae; Osteoglossum]
. . Meridiastra nigranota …………………… 1 hits 1 orgs [Echinodermata; Eleutherozoa; Asterozoa; Asteroidea; Valvatacea; Valvatida; Asterinidae; Meridiastra]
. Gryllotalpa orientalis ……………………. 1 hits 1 orgs [Protostomia; Panarthropoda; Arthropoda; Mandibulata; Pancrustacea; Hexapoda; Insecta; Dicondylia; Pterygota; Neoptera; Orthopteroidea; Orthoptera; Ensifera; Grylloidea; Gryllotalpidae; Gryllotalpinae; Gryllotalpa]

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Evolution Friday : Jim Miller

A friend of my parents wrote an amusing entry about the Bible and evolution. It was originally available here, from the Rapid City Journal.

Noah and evolution
Does a biblical story support evolution? John Tomasin of New Jersey recently pointed out that the story of Noah and his boat may support the theory of evolution.
Accordingly, all human beings alive today are direct descendants of eight survivors of the great flood. These include Europeans, Africans, Asians, Native Americans, Norwegians, Eskimos, Hebrews, Muslims, Buddhists, Pygmies, and you and me. If we look at the diversity, the results seem to point to an evolutionary process at work.
Can we then conclude that to deny that this diversity is due to evolution is to deny the Holy Scriptures?
JIM MILLER
Rapid City

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Delta G

Faithful viewer, One Day at a Time, asked how I knew that the the combustion of wax resulted in carbon dioxide and water vapor. Well, there are two things to this problem: stoichiometry and thermodynamics. Let’s tackle the thermodynamics first.
Every molecule has a certain amount of energy that it took to make it from its atomic parts. This energy is called the “Gibbs Free Energy” or just G for short. There are published tables that show the Gibbs Free Energy (G) for different molecules. For example, here is a short list of G values for various molecules:

Molecule G (kJ/mole)
CH4 (methane) -50.8
O2 (oxygen) 0
CO2 (carbon dioxide) -394.4
H2O (water) -237.2

Delta G is the term used to describe how much energy is released durnig a chemical reaction. Delta G is calculated from the sum of G for the reactants minus the sum of G for products.
So for this reaction:

CH4 + 2 O2 –> CO2 + 2 H2O

We can look up the G values for all four molecules involved. The left hand side has G of -50.8 kJ/mole. The right hand side has G of -868.8 kJ/mole. The difference (delta G) is -818.0 kJ/mole. A negative number like that indicates that the reaction produces a lot of energy. If you were to try running the reaction backwards (ie. to make wax out of water vapor and carbon dioxide), you would find that you had very little success. This is because you would have to add 818 kJ of energy per mole of reactants. Never mind what a kJ is or what a mole is. Suffice to say that that requires a lot of energy for not much stuff.
So in summary, by using thermodynamics and Gibbs Free Energy, we were able to discover that the chemical reaction of turning wax plus oxygen into water and carbon dioxide produces a lot of energy. This is useful, because if it doesn’t produce energy (e.g. has a postive delta G) then the reaction won’t happen.
It’s also import to make sure we don’t create or destroy matter. In other words, there must be the same number and kind of atoms on both sides of a chemical reaction. That is what they mean by stoichiometry. Thus “methane plus oxygen makes water and carbon dioxide” must be balanced. You’ll notice that in the above equation, I added a “2” in front of the water molecule product. That’s because for every molecule of methane that burns, two molecules of water are produced. Also, you’ll notice that I had to put a 2 in front of the oxygen as well. In that form, every molecule is accounted for. Of course, many more molecules are involved when burning an actual candle (on the order of 602,300,000,000,000,000,000,000 molecules), but the ratio ( one methane : two oxygen : one carbon dioxide : two water ) is conserved.
Now quiz yourself. Here are some chemical reactions that aren’t stochiometrically balanced. Try to figure out what terms to add to make the reaction balanced. (click and drag to select and see the hidden answer.)
1. H2 + O2 –> H2O  clickndrag—> Answer: 2 H2 + O2 –> 2 H2O —>tohere
2. CH3CH3 + O2 –> CO2 + H2O  clickndrag—> Answer: 2 CH3CH3 + 7 O2 –> 4 CO2 + 6 H2O  —>tohere

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Math

My favorite kind of math

I have a credit card that gives cash back on every purchase. I don’t remember the percentage off hand — so let’s call it X. I was wondering, if I always use my credit card to buy things, even the things i buy with the money I get back from them — what is the effective real cash back percentage?
For example, suppose that my credit card gives me 50% cash back on everything I purchase. I’m using an absurdly high number because it is easier to do the math — I know no such deal really exists!
Let’s start with ten dollars. I buy $10 with my credit card and get $5 back. If I spend that $5, I get $2.50 back. So far my $10 has bought $15 worth of merchandise, and I still have $2.50 left to spend! You can keep doing this forever, and if you do you’ll end up with exactly $20 worth of merchandise.
But how do we solve this problem for any cash back percentage? Well, to begin with, it is an infinite series, so we can never write the whole equation down. But we can start… Here I’ll use Y to represent the effective percentage rate, and also we’ll assume we have just one dollar.

Y = 1 + X + X2 + X3 + . . .

In other words, the effective buying power of one dollar is one dollar plus one times the cash back amount, plus that amount times the cash back amount again and so forth. Each new term is how much cash back you got on the previous purchase.
To help get to the next step I’ll rearrange the terms just slightly:
Y = X0 + X1 + X2 + X3 + . . .  EQ. 1

Recall that X0 is equal to 1. Anything to the zero power is one.
One more rearrangement:
Y = X0 + X ( X0 + X1 + X2 + . . . )

Notice that the term inside the parenthesis is equal to the right hand side of EQ. 1. Thus we can replace that infinite series with Y.
Y = X0 + X Y

And now it is easy to solve for Y:
Y = 1 + X Y

Y – X Y = 1

Y ( 1 – X ) = 1

Y = 1 / ( 1 – X )

Ta dah! We can verify with our one known : When X is 50%, Y is 2. Remember that 50% is actually 0.5 in the above equation (% means divide by 100). Sure enough Y is 2 when you work that out. Go ahead and plug your cash back bonus amount to see what it is really worth.

X =   
Y = ???  

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The old candle in the glass trick

So we were at a fancy dinner party the other night, and so naturally that was a perfect moment for kitchen chemistry. You may know the rule put down by my overbearing spouse — no chemistry in the kitchen. Which is what leaves me no other outlet but my friend’s kitchens or at fancy company dinner parties.
We took a burning candle and placed it on a saucer full of water. It was a mostly burnt out votive candle, so it floated nicely. I then put an inverted water glass over the candle. The flame went out, and water was drawn up into the glass.
This is a fun thing to do any time you are around candles and water glasses.
Here is what’s going on: Wax is a hydrocarbon — which means it is made of polymers composed of two hydrogen atoms and one carbon atom. Well, that isn’t entirely true — it is approximately true. For example, octane is a molecule that is a hydrocarbon with a formula C8H18. Dodecane has the formula C12H26. As the molecules get larger, they approach the 2:1 ratio. So to simplify our stoichiometry we’ll say that hydrocarbons are basically CH2. Molecular oxygen is O2. And this is how a hydrocarbon burns:

CH2 + 2 O2 –> CO2 + H2O

All off those molecules are gas (water is a gas at the temperature of combustion). So why does the water level go up? Two reasons: 1) The water vapor will condense and 2) The carbon dioxide may dissolve in the water. Thus the net reaction is consuming more gas than it produces, reducing the pressure inside the glass. Water is pulled up into the glass by the greater pressure exerted from the outside atmospheric pressure.

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Evolution Friday : Drug Resistant Pathogens

Today’s evolution piece is going to be short, due to the fact that I put it off until so late in the day. The topic is “drug resistance” — and it is a tragic and very real example of evolution in action. Through the course of a few years, or even less in laboratory conditions, strains of bacteria develop resistance to antibiotic drugs used to treat them. The process whereby fortuitous mutations confer special abilities which improve survival is called “natural selection”. Natural selection is a fundamental principle that explains how evolution occurs. This is a very real danger for modern medicine; one of my favorite celebs, Jim Henson, died from a drug resistant strain of streptococcus.
Drug resistance isn’t the only thing that pathogens evolve to cope with. Our immune system presents another sort of obstacle to their prosperity. Every year (in Asia it seems, for some reason) a new strain of the flu evolves. The new strain is sufficiently different than last year’s that the antibodies you’ve developed are no longer effective. (The flu is actually a virus, but it is able to evolve nonetheless since its genetic principles are the same as real living things.)
So there you have it. If evolution didn’t work, we wouldn’t all be coughing and sneezing (or worse) every January.