2007 Solutions to Monthly Question

Can the colour of stars reveal anything about their surface temperature? Which of Orion's most visible stars is the coolest? See my picture below, which I captured on Christmas Eve with a simple digital camera by using a tripod and using an exposure of 16 seconds. (The orange streaks were caused by moving clouds, and yes, my guests thought I was wierd.)

A set of colour filters is used to arrive at an approximation of a star's surface temperature.

The V filter blocks out low wavelengths, so if it gives out a high reading then a lot of low -wavelength or high energy radiation is being emitted by the star. The opposite is true for a B filter. So for a hot star, V>B, and B-V will result in a negative value. The U-filter screens out even lower wavelengths than a B filter. But the argument is simialr in that a negative value for U- B reflects a hotter star. The actual relationship between Kelvin temperture and U-B or B-V is logarithmic.

The graph below plots the theoretical blackbody Kelvin temperature of a star against its colour index. Betelgeuse is clearly the coolest star in the Orion constellation, with a surface temperature below 5000 K. Our sun's surface temperature is close to 6000 K.

The question was: There are two green solutions on a table at a pool party. One contains green harmless green vegetable dye, and the other has 10 g of poisonous nickel sulfate, NiSO₄ dissolved in 500 ml of water(also green in colour). Using a single chemical in the pool's vicinity, how do you tell them apart?

Reach for pH+ in the shed of pool maintenance supplies. pH+ contains the alkaline solid sodium carbonate, Na₂CO₃. Raising the pH of the vegetable dye with a gram or two of the product pH+ will create a clear blue mixture. But adding carbonate to a nickel sulfate solution will precipitate NiCO₃ and turn the solution milky green.

If the precipitate is allowed to settle, will the solution be safe and free of the poisonous nickel compound? No matter how much carbonate is added, the filtrate will remain green due to NiCO₃'s partial solubility, so it is not entirely free of Ni⁺². NiCO₃ has a Ksp of 1.42×10^-7 or a solubility of 3.77 X 10^-4 moles/L = 0.0447 g/L.

But to put it in perspective, the LD50 for nickel carbonate in guinea pigs is 0.062g/kg of body weight. If the ratio applies to humans, 4.7 g would be lethal for 50% of humans. So although I would not drink the filtrate, it would seem to be far below the lethal level after it has been precipitated. The original solution, however, was potentially lethal indeed.

Reference:
Berkow, Robert(editor)The Merck Manual 16th edition. 1992

I was surprised to see potassium ferrocyanide listed as an ingredient on this container of salt. What is the purpose of K₄Fe(CN)₆, and why is it safe, in spite of its scary name?

Solution:

As indicated on the label, iodide is also added to prevent endemic goitre, a condition in which the thyroid gland in the neck can swell up grotesquely. But iodide can oxidize to iodine. To prevent this, salt producers include a reducing agent. Normally sugar does the trick, but potassium ferrocyanide can also give back electrons to iodine and reduce it back to the useful iodide form, according to the following:
Fe(CN)₆^-4-->Fe(CN)₆^-3 + 1 e^-

I₂ + 2 e-->2 I^-
In both ferrocyanide and ferricyanide(Fe(CN)₆^-3), the poisonous cyanide is tightly bound to the iron, and is therefore harmless. Only hot, strong acid, and light(when the ferrocyanide is dissolved) will release the dangerous HCN. In a worst case scenario, if a small amount of cyanide would somehow escape ( not much is added to the entire package) it would be comparable to the amount of cyanide found naturally in the cyanoglucosides of a few apple seeds. Besides my family and relatives have been using this type of salt for years, and no one has fallen ill from it.
Reference:
Berkow, Robert(editor)The Merck Manual 16th edition. 1992

Solution to April 2007 Question of the Month

The question was:

A newly discovered planet is 13.5 times more massive than the earth but half as dense. Approximately, how much longer would it take to orbit this new planet, and why is your answer an approximation?

Solution:

Since density is mass/volume, the only way that the planet is 13.5 times more massive and yet half as dense is if it has 27 X the volume. If the planet is 27X more voluminous, and since it is probably spherical like the earth, it will have a radius that is three times(cube root of 27 = 3) larger.(the rest of terms cancel in the volume of sphere formula.) The circumference will also be three times larger, and at equal speeds, it will take approximately three times longer to orbit. The reason it is an approximation is that in reality you have to factor in the height above the surface. Let it equal to h, and let R = radius of earth. Cp= circumference of orbit around new planet;
Ce= circumference of orbit around Earth;
the ratio of the circumherences then becomes
Cp/Ce = 2p(3R +h)/[2p(R +h)]
If h is a lot smaller than R, then the answer will be approximately 3.

Solution to May 2007 Question of the Month

The question was:

If equal and separate masses of alcohol and water are initially at the same temperature and they are heated for a short while, the alcohol will experience a higher change in temperature. What inverse relationship accounts for this behaviour? Why do we specify for a "short while"?

Solution:

Since water has a higher boiling point, it will eventually experience a higher change in temperature, but initially, prior to boiling, alcohol heats up faster, even though it absorbs the same amount of heat as water. This is a result of alcohol's lower specific heat. Since Q = mcDT, and since Q and m are equal for alcohol and water then,
Q/m = cDT, so
c_waterDT_water =c_alc.DT_alc,
hence the inverse relationship between temperature change and specific heat.
The bonds between the water molecules are like the links between the wagons of a train. Just like it is difficult to get a big train to reach a high speed, it takes a lot of energy to warm up water. Once a train is moving, it is difficult to stop it. Similarly, because of its high specific heat capacity, water is also "stubborn" when cooling.

Solution to June 2007 Question of the Month

The question was:

Richard Feynman, the Nobel prize-winning American physicist (1965), said that this is the most important and far-reaching hypothesis ever formulated about nature. What was he referring to?

Solution:

"All matter consists of atoms." Although it was first put forth as an idea thousands of years ago by Democritus, the notion was far from being universally accepted, as recently as the late 1800's. Finally the idea became a theory thanks to an experiment by Perrin, who obtained a value for Avogadro's number that was based on Einstein's mathematical treatment of Brownian motion. Since the value he obtained agreed with other methods that were not dependant on the kinetic molecular theory(which postulates that all consists of atoms), it validated the hypothesis. See Brownian Motion. For a more general history, see History of the Atom.

Ironically, in recent years,after Feynamn's death, physicists have come to admit that the majority of the universe does not consist of ordinary matter. In no way does this discovery belittle atomic theory. Without it we would have little insight into the inner working our planet. And yet astronomers cannot explain why stars from the edge of galaxies move just as fast as those close to its center. Nor can physicists account for a host of other phenomena discussed in the Standard Model.

Solution to July 2007 Question of the Month

The question was:

If it was possible to isolate 6 moles of hafnium ions and 8 moles of lutetium ions, together these cations would be 48 moles of electrons short of neutrality. What is the charge of lutetium ion?

Solution:

Let h = charge of hafnium ion and L = charge of lutetium ions. Since for each unit of charge, a mole of these positive ions will be 1 mole of electrons short of neutrality, then
6h + 8L = 48.
h = (48 - 8L)/6 = 8 - (4/3)L.
since the charge is positive and not fractional, then L = must be a multiple of 3 and less than 6 (since 6 would yield zero). L = 3, and h = 8 -(4/3)(3)= 4.

Solution to August 2007 Question of the Month

The question was:

In response to an article I wrote for Canadian Chemical News about my experiences and misadventures with pool chemistry, I received an email from a scientist who realized that commercial Ca(ClO)₂---one of the types of so-called "chlorine for swimming pools"--- contains calcium carbonate. Is his hypothesis correct: how does one check for the presence of carbonate?

Solution:

Very carefully. The standard test is to add HCl, which generates carbon dioxide:
2 HCl + CaCO₃--> CaCl₂ + H₂O + CO₂
But HOCl from aqueous calcium hypochlorite also reacts with HCl to create chlorine gas:
HOCl + HCl--> Cl₂ + H₂O, so the test has to be carried out in a fumehood.
I connected a flask containing HCl and calcium hypochlorite to a second flask containing limewater. After the rapid release of chlorine gas, the mixture continued to fizz, but gently, releasing a colourless gas.(watch video). At the other end, the limewater turned cloudy. CO₂ had been released by the reaction of excess HCl with the carbonate impurity in
Ca(ClO)₂.
The carbonate had been formed by the reaction of hypochlorite with carbon dioxide:
Ca(OCl)₂ + CO₂ --> CaCO₃ + Cl₂.
Also see Chemistry of Pool Water
Extra: Knowing When It's August

Solution to September 2007 Question of the Month

The question was:

A piece of aluminum foil is placed in a solution of copper (II) chloride, CuCl₂. Almost instantly a reaction begins as the Cu⁺² oxidizes the aluminum.
Someone who has run out of CuCl₂ attempts the same reaction using copper sulfate, but it fails. Why is there no reaction even though copper sulfate also contains Cu⁺²?

Solution:

Aluminum foil and most aluminum products are normally not reactive because they get covered by a thin oxide layer that fits nicely on top of the aluminum crystal. As a result oxygen or other oxidizing agents such as Cu⁺² cannot steal any more electrons from the aluminum. This is why the copper sulfate fails to react. But copper chloride contains chloride which penetrates the oxide layer and allows the aluminum underneath to react with the copper ion.

Solution to October 2007 Question of the Month

The question was:

In the shell model of the nucleus, there are certain magic numbers of nucleons (protons or neutrons): 2, 8, 20, 28, 50, 82, 126 that are more tightly bound than the next higher integer. A magic number of nucleons is important because it increases the likelihood that isotopes will be stable. If the number of neutrons and protons are both magic numbers (not necessarily the same one) we say the nucleus is doubly magic, and it is even more likely to be stable. Isotopes with doubly magic numbers include :

⁴He

¹⁶O

⁴⁰Ca, ⁴⁸Ca

⁵⁶Ni, ⁴⁸Ni

¹³²Sn

²⁰⁸Pb

None of the above isotopes are radioactive except for ¹³²Sn, which, in spite of its double magic number of 50 protons and 82 neutrons, has a half life of less than a day. So a few years ago I contacted a scientist to ask him why ¹³²Sn is radioactive.

Solution:

Here is the answer from Alex Brown of the National Superconducting Cyclotron Laboratory http://www.nscl.msu.edu
Sn-132 is doubly-magic, but being doubly-magic does not guarantee stability. There are other features that can make a nucleus unstable. In this case Sn-132 is too far from the "valley of stability" - it has too many neutrons. The neutrons in Sn-132 beta decay and turn into protons eventally leading to the most stable mass 132 nucleus Xe-132.
The "magic number" of 50 protons for Sn does show up by the fact that Sn has more stable isotopes than any other element - they are Sn-112, Sn-114, Sn-115, Sn-116, Sn-117, Sn-118, Sn-119, Sn-120, Sn-122 and Sn-124. There are other nuclei that we predict to be doubly-magic that are unstable, such as Sn-100 and Ni-78.
At our National Superconducting Cyclotron Laboratory are are trying to produce these nuclei and study their properties.

Solution to November 2007 Question of the Month

The question was: A small amount of acetaminophen, Tylenol's active ingredient, is toxic to cats but not to dogs or humans. Why?

Solution:

After they have served their purpose, drugs in the body are sometimes broken down into other molecules, and then they are excreted. In acetaminophen's case, animals excrete a combination of unmetabolized acetaminophen and break down products.

In certain cells, acetaminophen is metabolized to its highly reactive metabolite N-acetyl-p-benzoquinoneimine(NAPQI).
This molecule can kill cells but it is usually picked up by other molecules and gotten rid of before it does too much damage, provided that there isn't too much NAPQI produced.

When the body gets rid of the acetaminophen, even before the reactive metabolites are made, it does so by using the enzyme glucuronyl transferase which conjugates acetaminophen to glucuronic acid for excretion. The problem with cats is that they have very little glucuronyl transferase. So instead of leaving their body, acetaminophen sticks around, gets converted into an excessive and lethal amount of reactive NAPQI. The lethal dose for a cat is 50 to 100 mg/kg. In humans it is 360 mg/kg. So even an infant of the weight of a cat can tolerate approximately 3.6 to 7 times more tylenol.
References: http://www.addl.purdue.edu/newsletters/1998/spring/acet.shtml
doi.wiley.com/10.1002/jps.2600630906
http://www.ansci.cornell.edu/plants/toxcat/toxcat.html

Solution to December 2007 Question of the Month

The question was: What molecule breaks down into acid and oxygen when it loses electrons, but turns into base and hydrogen when it accepts electrons? How is this relevant to basic life processes?

Solution:

Click on electrolysis.

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Comments:
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Born on: April 06, 1996

Solutions to 2007 Monthly Questions