Category Archives: PERIODIC TABLE SMOOTHIE

Let’s add oxygen, fluorine and neon gases

Oxygen from Theodore Gray's amazing book, The Elements
Oxygen from Theodore Gray’s amazing book, The Elements

This post concludes the Periodic Table Smoothie experiment.

Recall that we’ve just finished adding one mole of nitrogen gas and created a bizarre boron polymer at the bottom of our vessel. The temperature was 350 °C and the pressure in our vessel was 891 kPa.

Today, we’re going to add 1.00 mole of oxygen gas, stand back and observe.

Nothing happens.

This is disappointing news.

Many of the substances in our vessel react (more accurately, explode) in the presence of oxygen but the ignition temperature for all of those explosions to take place is at least 500 °C. The temperature of our vessel is set at just 350 °C. At this temperature, nothing would actually happen.

There’s not enough activation energy to break bonds in the reactant particles in order to get the reaction started. We call this activation energy (EA) in chemistry. If we were to add a source of excessive heat (e.g. a matchstick), the vessel would explode.

Should we heat up the vessel to 500 °C and blow up the experiment right here?

If we did, the following reactions would happen:

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Enough of these reactions – particularly the first three – are sufficiently exothermic to trigger a chain reaction – at least up to the reaction of oxygen with beryllium carbide. The vessel would bang, explode, and shatter. The helium would float away, dangerous lithium amide would fly out sideways, and polyborazine powder, whatever that is, would land on the floor.

Let’s not ignite our experiment – not yet.

Conclusion after adding 1.00 mole of oxygen gas

Substance Amount in mol
He(g) 1.000
Be(s) 0.514
LiH(s) 0.000
Li2C2(s) 0.272
B2H6(g) 0.000
Be2C(s) 0.175
H2(g) 0.007
BeC2(s) 0.136
CH4(g) 0.009
N2(g) 0.552
NH3(g) 0.154
LiNH2(s) 0.277
polyborazine 12.194 grams

Pressure: 891 kPa (higher than before due to the addition of nitrogen gas)
Temperature: 350 °C (vessel is still being maintained at constant temperature)

Oxygen was relatively uneventful. Let’s add fluorine and see what happens.

Let’s add fluorine gas

elements110009
Elements by Theodore Gray

The following three reactions would all occur as 1.00 mole of fluorine gas is added:

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These two products are quite interesting:

  • HF, hydrogen fluoride, an aqueous solution of which was used by Breaking Bad’s Walter White to dissolve evidence (his victims)
  • NF3, nitrogen trifluoride, is used as an etching agent when making printed circuit boards (PCBs)

Let’s add neon gas

elements110010
Elements by Theodore Gray

When 1.00 mole of neon gas is added, the total pressure inside the vessel increases but no reaction occurs. The concentrations of all the other gases present are unaffected.

The End

That concludes our Periodic Table Smoothie experiment. The most interesting conclusion was the discovery of polyborazine, the bizarre solid that collected at the bottom of the vessel.

Also of interest was how easily we created ammonia, one of the simplest of biological compounds, just by mixing elements together. Could the compounds necessary for life be so easy to create that their existence is an inevitable consequence of the Big Bang? Is life inevitable? If the Big Bang were to happen all over again, would life occur? And would it look any different?

Possibly not.

Let’s add nitrogen gas

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‘Nitrogen’ page from Theodore Gray’s amazing book, ‘The Elements’

Initial conditions

Recall from last week that our Periodic Table Smoothie contains the following species:

Substance Amount present (moles)
He(g) 1.00000
Be(s) 0.51435
LiH(s) 0.27670
Li2C2(s) 0.27165
B2H6(g) 0.23300
Be2C(s) 0.17470
H2(g) 0.14267
BeC2(s) 0.13625
CH4(g) 0.00949

Pressure: 718 kPa
Temperature: 350 °C

Reactions of nitrogen in our 10-litre vessel

Our freshly-added 1.00 mol of nitrogen gas, N2(g), reacts with hydrogen gas to make ammonia in the following reversible (equilibrium) reaction. We will assume that the interior metal surface of the vessel is a suitable catalyst for this reaction (e.g. iron). 

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There are three other reactions below that might have occurred at higher temperature, but I’ve chosen not to raise the temperature of the vessel at this point. Rather, we’ll keep it at 350 °C to keep things manageable.*

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*I was tempted at this point to elevate the temperature of our vessel to 500 °C so that the second reaction could take place as well. This would produce copious amounts of smelly ammonia gas, which would allow for larger quantities of interesting organic compounds to be produced later on. To keep our simulation safe and (relatively) simple, I’ve decided to keep the vessel at 350 °C. Interesting compounds organic will still form – only in smaller amounts.

Equilibria

The ammonia reaction above (the first equation) is actually an equilibrium reaction. That means that the reactants are never completely used up, and the yield is not 100%.

Recall from Le Châtelier’s principle that removing product from an equilibrium reaction causes the position of equilibrium to shift to the right, forming more product. This is because:

“If an equilibrium system is subjected to a change, the system will adjust itself to partially oppose the effect of the change.” – Le Châtelier’s principle

There are three reactions that will remove ammonia from our vessel while it’s being produced, and I’ve put all three of these into the simulation. One of these is the reverse of the reaction above (producing hydrogen and nitrogen gases) and the other two are described below. Let’s take a look at those other two reactions.

With what will the ammonia react in our vessel?

Ammonia can undergo the following reactions with the other things in our vessel**

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**The ammonia does react with methane and beryllium as well, but only at temperatures of 1200 °C and 600 °C, respectively.

Two compounds will be formed: lithium amide and borazine.[1] Lithium amide reacts with nothing else in the vessel, so the reaction chain stops there. Borazine, on the other hand, is much more interesting.

We’ve made borazine!

Borazine is a colourless liquid at room at temperature. It boils at 53 °C and has a structure that resembles that of benzene.

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Borazine is isostructural with benzene
Because of the electronegativity difference of about 1.0 between the B and N atoms in the ring, borazine has a mesomer structure:

600px-borazin_mesomers

Like benzene, there is partial delocalisation of the lone pair of electrons on the nitrogen atoms.

Borazine polymerises into polyborazine!

Fascinatingly, borazine polymerises into polyborazine at temperatures above 70 °C, releasing an equal number of moles of hydrogen gas.[2] Polyborazine isn’t particularly well-understood or well-documented, but one recent paper suggested it might play a role in the creation of potential ceramics such as boron carbonitrides. Borazine can also be used as a precursor to grow boron nitride thin films on surfaces, such as the nanomesh structure which is formed on rhodium.[3]

Like several of the other compounds we’ve created in our Periodic Table Smoothie, polyborazine has also been proposed as a hydrogen storage medium for hydrogen cars, whereby polyborazine utilises a “single pot” process for digestion and reduction to recreate ammonia borane.

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Polyborazine’s chemical structure
The hydrogen released during the polymerisation process will then react further with a little bit of the remaining nitrogen to produce a little more NH3(g) – but not much. Recall from earlier that the ammonia reaction is an equilibrium one, and the yield of NH3(g) at pressures under 30 atmospheres is very low. Pressure in our vessel is still only around 7 atmospheres.

Simulation results

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Once polymerised, this would form about 12 grams of polyborazine:

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As far as I’m aware, no further reactions will take place in the vessel this week.

Conclusion after adding 1.00 mole of nitrogen gas

Substance Amount in mol
He(g) 1.000
Be(s) 0.514
LiH(s) 0.000
Li2C2(s) 0.272
B2H6(g) 0.000
Be2C(s) 0.175
H2(g) 0.007
BeC2(s) 0.136
CH4(g) 0.009
N2(g) 0.552
NH3(g) 0.154
LiNH2(s) 0.277
polyborazine 12.194 grams

Pressure: 891 kPa (higher than before due to the addition of nitrogen gas)
Temperature: 350 °C (vessel is still being maintained at constant temperature)

Next week, we’ll add a mole of oxygen gas to the vessel. Warning: it might explode.

References

  1. Stock, Alfred and Erich Pohland. “Borwasserstoffe, VIII. Zur Kenntnis Des B 2 H 6 Und Des B 5 H 11”. Berichte der deutschen chemischen Gesellschaft (A and B Series) 59.9 (1926): 2210-2215. Web.
  2. Mohammad, Faiz. Specialty Polymers. Tunbridge Wells: Anshan, 2007. Print.
  3. Toury, Berangere and Philippe Miele. “A New Polyborazine-Based Route To Boron Nitride Fibres”. Journal of Materials Chemistry 14.17 (2004): 2609. Web. 4 May 2016.

Let’s add carbon (graphite) powder

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‘Carbon’ page from Theodore Gray’s amazing book: The Elements

Today, we’re going to add 1.00 mole of carbon to our vessel. After adding boron last week, we left our vessel locked at 350 °C and with a pressure of 638 kPa. These reactions are taking place at 350 °C and constant volume (exactly 10 litres). Pressure inside the vessel will therefore change over time.

Allotropes of carbon

Carbon has various allotropes (structural arrangements of an element). Diamond is extremely strong and highly unreactive, while graphite is soft and brittle. The differences are all due to the type of bonding between carbon atoms. In diamond, carbon atoms are bonded by four strong covalent bonds with the surrounding atoms in a strong, hard three-dimensional ‘network lattice’. Graphite owes its softness and brittleness to the fact that its carbon atoms are bonded by only three strong covalent bonds in a two-dimensional ‘layer lattice’. Individual layers are very strong, but the layers can be separated by just the slightest disturbance. Touching graphite lightly onto paper will remove layers of carbon atoms and place them onto the page (such as in a pencil). Using a diamond the same way would likely tear the paper instead.

For this reason, I’m going to put graphite into the vessel instead of diamond. Diamond is so strong and inert that it’s unlikely to do any interesting chemistry in our experiment. Graphite, on the other hand, will.

The following seven chemical reactions will take place after adding carbon (graphite) powder

As soon as the carbon powder enters the vessel, it will begin to react with the following three species as follows:

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The ethyne produced in the third reaction will then react with any lithium and beryllium remaining in the vessel as follows:

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The hydrogen gas produced by the above two reactions will then react with lithium and carbon (if there’s any left) as follows:

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These reactions have the potential to all occur at the same time. Tracking them properly would require calculus and lots of kinetics data including the activation energy of each reaction and the rate constant for each equation. Quick searches on the National Chemical Kinetics Database yields no results for most of these equations, which means we won’t be able to use a computer model to calculate exact quantities of each product. Instead, I’m going to run a computer simulation using Excel that makes the following three assumptions:

  • all these reactions occur at the same rate;
  • all these reactions are first-order with respect to the limiting reagent;
  • all these reactions are zeroth-order with respect to reagents in excess.

The results will be a close approximation of reality – they’ll be as close to reality as we can get with the data that’s available.

Here are the results of the simulation

Here’s a graph of the simulation running for 24 steps. Exactly one mole of carbon powder is added at step 5.

Periodic Table Smoothie - Let's Add Carbon Carbon quickly reacts to form lithium carbide, beryllium carbide and two organic molecules: methane and ethyne
Carbon quickly reacts to form lithium carbide, beryllium carbide and two organic molecules: methane and ethyne

Summary of results

The results are incredible! We’ve made ethyne and methane, both of which have the potential to do some really interesting chemistry later on. I’m hoping that we can make some more complex organic molecules after nitrogen and oxygen are added – maybe even aminoethane – let’s see.

Hydrogen has also re-formed. I’m hoping that this gas lingers for long enough to react with our next element, nitrogen: we might end up making ammonia, NH3(g).

You may have noticed that I removed the “boron-lithium system” from the vessel. The 0.178 moles we created are now stored separately and will not be allowed to react any further. With such little literature about the reactivity of B3Li, it’s impossible to predict what compounds it’ll form later on. B3Li is so rare that doesn’t even have a Wikipedia page.

Pressure in the vessel increases to 718 kPa after carbon is added
Pressure in the vessel increases to 718 kPa after carbon is added
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Mass of sludge in the vessel changes after adding carbon

Here’s what’s present in the vessel after adding carbon

Substance Moles present after 500 ‘steps’
He(g) 1.00000
Be(s) 0.51435
LiH(s) 0.27670
Li2C2(s) 0.27165
B2H6(g) 0.23300
Be2C(s) 0.17470
H2(g) 0.14267
BeC2(s) 0.13625
CH4(g) 0.00949

We also have 0.178 moles of B3Li stored separately in another vessel.

Next week, we’ll add nitrogen and see what happens.

Let’s add boron powder

elements110005
‘Boron’ page from Theodore Gray’s book, The Elements

Boron is a metalloid: an intermediate between the metals and non-metals. It exists in many polymorphs (different crystal lattice structures), some of which exhibit more metallic character than others. Metallic boron is non-toxic, extremely hard and has a very high melting point: only 11 elements have a higher melting point than boron.

British scientist Sir Humphrey Davy described boron thus:

“[Boron is] of the darkest shades of olive. It is opake[sic], very friable, and its powder does not scratch glass. If heated in the atmosphere, it takes fire at a temperature below the boiling point of olive oil, and burns with a red light and with scintillations like charcoal” – Sir Humphrey Davy in 1809

Initial condition

Before we add the 1.00 mol of boron into our reaction vessel, we need to recall what’s already in there from our experiments so far:

  • H2(g): 0.70 mol
  • He(g): 1.00 mol
  • Li(s): 0.40 mol
  • LiH(s): 0.60 mol
  • Be(s): 1.00 mol

The temperature of our vessel is 99 °C and the pressure of the gaseous phase is 525.5 kPa.

Now, let’s add our 1.00 mol of boron powder.

Which reactions take place?

Boron reacts with hydrogen gas to produce a colourless gas called borane, BH3(g), according to the following equation[1]:

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Boron also reacts with lithium in very complex ways. If we heat the vessel up to 350 °C, we’d expect to see the formation of a boron-lithium system with chemical formula B3Li according to this equation[2]:

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Notice that now we’ve heated up our vessel to 350 °C to allow this reaction to happen, the lithium at the bottom of the vessel has melted.

Boron reacts with lithium hydride as well, but only at temperatures around 688 °C. With our vessel’s temperature set at 350 °C, we won’t observe this particular reaction in our experiment.[3]

Some allotropes of boron – in particular, the alpha allotrope that was discovered in 1958 – is capable of reacting with beryllium to form BeB12. Because we’re using beryllium powder, which has semi-random  symmetry, we won’t see any BeB12 forming in our vessel. Alpha-boron only exists at pressures higher than around 3500 kPa. At our moderate pressure of only 525.5 kPa, powdered (semi-random) boron will prevail and no BeB12 will form.[4]

For simplicity’s sake, let’s assume that the two reactions above take place with equal preference.

Boron powder reacts with hydrogen gas

Let’s do an ice table to find out how much borane we make.

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A quick n/ratio calculation shows us that the hydrogen gas is limiting in this reaction:

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We can expect all of the hydrogen gas to react with the boron powder.

units are mol 2 B 3 H2 2 BH3
I 0.50 0.70 0
C -0.466 -0.70 +0.466
E 0.0333 0 0.466

Borane is very unstable as BH3, and it would probably dimerise into B2H6(g). This is still a gas at 350 °C and is much more stable than BH3. For the rest of this experiment we’ll assume that our 0.466 mol of BH3 has dimerised completely into 0.233 mol of B2H6.

Boron powder reacts with lithium

With the molar ratios present in our vessel, at 350 °C, we’d expect to witness the formation of a boron-lithium system, with chemical formula B3Li.

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A quick n/ratio calculation shows that in this reaction, the boron powder is limiting.

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All of the remaining boron therefore reacts with lithium. To calculate exactly how much B3Li we’ve created, let’s do another ice table:

units are mol 3 B Li B3Li
I 0.533 0.40 0
C -0.533 -0.178 +0.178
E 0 0.222 0.178

What’s in our vessel after adding boron?

We have the following gas mixture in our vessel:

Helium gas, He(g): 1.00 mol

Helium is an inert noble gas that will probably remain in the vessel until the end of the experiment. It’s used in party balloons.

Borane gas, B2H6(g): 0.233 mol

We made this today. Borane is used in the synthesis of organic chemicals via a process called hydroboration. An example of hydroboration is shown below.

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At the bottom of the vessel, there’s a sludge, which contains the following liquids and solids:

Molten lithium, Li(l): 0.22 mol

Lithium is used in the production of ceramics, batteries, grease, pharmaceuticals and many other applications. We’ve got 0.22 moles of lithium, which is about 1.5 grams.

Beryllium powder, Be(s): 1.00 mol

Beryllium is used as an alloying agent in producing beryllium copper, which is used in springs, electrical contacts, spot-welding electrodes, and non-sparking tools.

Lithium hydride, LiH(s): 0.60 mol

Lithium hydride is used in shielding nuclear reactors and also has the potential to store hydrogen gas in vehicles. Lithium hydride is highly reactive with water.

Boron-lithium system, B3Li(s): 0.178 mol

We made this today… but what is it? Not much is known about this compound – in fact, it doesn’t even have a name other than “boron-lithium system, B3Li”. It’ll probably decompose eventually in our experiment – maybe when we alter the pressure or temperature of the vessel at some later stage. We’ll need to keep an eye on this one.

The original H2(g) and B(s) have been reacted completely in our experiment.

What’s the pressure in our vessel now?

At the end of our reaction, the temperature of our vessel is still set at 350 °C and the pressure of the gaseous phase inside the vessel can be calculated to be a moderate 638 kPa as follows:

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*It should also be noted that some evidence exists for a reaction between LiH and BH3, forming Li(BH4). The reaction seems to take place stepwise with increasing temperature. A quick read of this paper suggests that in our vessel, which is at 350 °C, any Li(BH4) formed would actually break back down into boron powder and hydrogen gas, which would in turn react with each other and with lithium metal to form BH3 and LiH again. The net result would be a negligible net gain of LiH and a negligible net loss of boron powder. We will continue calculating this Periodic Table Smoothie under the assumption that if any Li(BH4) forms, it breaks down before we add the next element, and the overall effect on our system is negligible.

**Li(BH4) is an interesting compound: it’s been touted as a potential means of storing hydrogen gas in vehicles – it’s safer and releases hydrogen more readily than LiH, which was mentioned above.[5]

Next week, we’ll add element number 6, carbon, and see what happens.

References

  1. “Borane”. Wikipedia. N.p., 2016. Web. 14 Apr. 2016.
  2. Okamoto, H. “The B-Li (Boron-Lithium) System”. Bulletin of Alloy Phase Diagrams 10.3 (1989): 230-232.
  3. Matkovich, V. I. Boron And Refractory Borides. Berlin: Springer-Verlag, 1977. Print.
  4. Gaulé, G. K. Boron, Volume 2: Preparation, Properties And Applications. New York: Plenum Press, 1965. Print.
  5. Saldan, Ivan. “A Prospect For Libh4 As On-Board Hydrogen Storage”. Open Chemistry 9.5 (2011): n. pag. Web.

Let’s add beryllium powder

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‘Beryllium’ page from Theodore Gray’s book, The Elements

Initial condition

  • H2(g): 0.70 mol
  • He(g): 1.00 mol
  • Li(s): 0.40 mol (still solid: it melts at 180.5 degrees)
  • LiH(s): 0.60 mol
  • Pressure = 525.5 kPa
  • Temperature = 99°C

No reactions!

Beryllium doesn’t react with any of the things in the vessel: H2(g), He(g), Li(s) or LiH(s). My one mole of beryllium powder (which would cost me over $70) would just sit at the bottom of the vessel doing nothing.

With not much else to write about in the Periodic Table Smoothie this week, it might be a good idea to calculate how much this Periodic Table Smoothie would have cost in real life.

Element Cost per kg[1]  Molar mass  Cost per mole
H2  $              4.00 2  $       0.008
He  $            52.00 4  $       0.21
Li  $          270.00 6.941  $       1.87
Be  $      7,840.00 9.01  $    70.64
B (next week)  $    11,140.00 10.811  $  120.43
TOTAL cost of 1.00 mol of each of the first five elements  $        193.16

Conclusion

The addition of beryllium was highly uneventful. The vessel still contains the following:

  • H2(g): 0.70 mol
  • He(g): 1.00 mol
  • Li(s): 0.40 mol (still solid: it melts at 180.5 degrees)
  • LiH(s): 0.60 mol
  • Pressure = 525.5 kPa
  • Temperature = 99°C

We’ll add boron next week and see what happens.

Let’s add lithium powder

Lithium: a page from Theodore Gray's book The Elements
Lithium: a page from Theodore Gray’s book The Elements

Initial condition

  • Hydrogen gas, H2(g): 1.00 mol
  • Helium gas, He(g): 1.00 mol

Last week, our vessel contained a mixture of hydrogen and helium gases. No chemical reactions have occurred so far, but that is about to change. Today, we’ll add 1.00 mole of lithium powder to the mixture and observe our first chemical reaction.

What does lithium look like?

Lithium is a soft, silvery metal with the consistency of Parmesan cheese. Lumps of lithium can be cut with a knife and it’s so light that it floats on oil. It would float on water as well if it weren’t for the violent reaction that would take place. Lithium is very well-known by science students for its ability to react with water, producing hydrogen gas and an alkaline solution of lithium hydroxide.

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There’s no water in our vessel so the above reaction won’t actually take place. We’ve only got hydrogen gas and helium gas inside. Let’s see if our powdered lithium reacts with either of those gases.

Will the lithium powder react in our vessel?

Yes! Lithium reacts with hydrogen gas very slowly. One paper by NASA cited a reaction occurring at 29°C but the yield and rate were both very low. Because I want to initiate as many reactions as possible in this experiment, I’m going to heat my vessel to 99°C by immersing it in a bath of hot water. According to the NASA paper, this temperature would give my reaction a 60% yield after two hours.

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Lithium hydride is beginning to collect in the bottom of my 10-litre vessel. It’s a grey-to-colourless solid with a high melting point.

How much of each substance do we now have in the vessel?

First, we need to know which reagent is limiting. We can calculate this by using the following rule:

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Let’s substitute the values into the expression for all the reactants in this reaction: Li(s) and H2(g).

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If the yield was 100% (i.e. a complete reaction), I’d expect to make 1.00 mole of lithium hydride. However, we’re only going to get 0.60 moles because according to the NASA paper, the yield of this reaction is only 60% at my chosen temperature.

Let’s do an ‘ice’ table to find out how much of each reactant reacts, and hence how much of each substance we have left in our reactor vessel.

units are mol 2Li H2 2LiH
I (initial) 1.00 1.00 0
C (change) -0.60 -0.30 +0.60
E (equilibrium) 0.40 0.70 0.60

By the end of our reaction, we’d have:

  • H2(g): 0.70 mol
  • He(g): 1.00 mol
  • Li(s): 0.40 mol (still solid: it melts at 180.5 degrees)
  • LiH(s): 0.60 mol

What does 0.60 mol LiH look like?

Let’s use the density formula to try find out how many spoonfuls of LiH we’ve created.

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We’ve made 6.11 millilitres of lithium hydride powder! That’s a heaped teaspoon of LiH.

What’s the resulting pressure in the vessel?

Our elevated temperature of 99°C will have caused a considerable pressure increase inside the vessel.

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That’s 5.2 atmospheres (atm) of pressure, which is quite high. A typical car tyre is about 2 atm for comparison.

What if the vessel exploded?

BANG. The contents of the vessel, after they’ve rained down on an unsuspecting crowd, would react explosively with the water and other compounds in our bodies to produce caustic lithium hydroxide and toxic lithium salts. I recommend stepping away from the vessel and behind a thick safety screen at this point. Even though our imaginary vessel is quite strong, we better put on a lab coat and safety glasses as well—just in case.

Conclusion after adding lithium powder

  • H2(g): 0.70 mol
  • He(g): 1.00 mol
  • Li(s): 0.40 mol (still solid: it melts at 180.5 degrees)
  • LiH(s): 0.60 mol
  • Pressure = 525.5 kPa
  • Temperature = 99°C

Next week, we’ll add 1.00 mole of beryllium to the vessel and see what happens.

Reference: Smith, R. L.; Miser, J. W. (1963). Compilation of the properties of lithium hydride. NASA

Let’s add helium gas

elements1100021
‘Helium’ page from Theodore Gray’s amazing book, The Elements

Last week, we put 1.00 mole of hydrogen gas into a cylinder. The resulting pressure was 243 kPa and the temperature was maintained steady at 20°C. This week, we’ll add 1.00 mol of helium gas, He(g), to the vessel and see what happens.

Will the helium react with the hydrogen?

No. Helium is completely inert. Hydrogen and helium will co-exist without undergoing any chemical reactions.

What will the resulting pressure be?

This is a very simple calculation. With 2.00 moles of gas in the vessel, the pressure would be double what it was before. This is known as Dalton’s law of partial pressures: the total pressure in a vessel is equal to the sum of all the pressure of the individual gases in the vessel.

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Let’s convert that into pounds per square inch (psi) for easy comparison with everyday objects.

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That’s about the same as a hard bicycle tyre.

How fast are the molecules moving?

Remember from last week that when our vessel contained only hydrogen gas, the molecules were moving around randomly with an average speed of 1760 metres per second.

Kinetic molecular theory states that the kinetic energy of a gas is directly proportional to the temperature of that gas. The formula for kinetic energy is shown below:

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At constant temperature, heavier particles move more slowly than lighter ones. Even though they have the same kinetic energy, helium atoms at 20 °C move slower than hydrogen molecules at 20 °C because they have almost exactly double the mass. How much slower does the helium move? Let’s find out.

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The molecules are moving at 1245 metres per second, or 4482 km/h. This is slower than the hydrogen gas by a factor of exactly root 2.

The molecules in our vessel could orbit the Earth in just 6 hours if they were to move in a single direction at this speed. Because the motion of particles in our gas mixture is random – they jiggle about rather than move in a single direction – they stay securely in the vessel.

Conclusion after adding helium

No chemistry’s happening in the vessel – not yet. Molecules of hydrogen and helium are simply co-existing in our vessel, bouncing off each other at different speeds and not interacting in any other way.

  • Hydrogen gas, H2(g): 1.00 mol
  • Helium gas, He(g): 1.00 mol

For some chemistry to happen, we’ll need to add the next element, lithium. We’ll do that next week.

Let’s add hydrogen gas

Hydrogen: a page from Theodore Gray's book, The Elements
Hydrogen: a page from Theodore Gray’s book, The Elements

I’m going to add 1.00 mol of hydrogen gas, H2(g), to our 10-litre vessel. We’ll assume that the entire experiment is carried out at normal room temperature – let’s say it’s 20°C.

How much does a mole of hydrogen cost?

Hydrogen gas is a relatively cheap element, and my one mole of H2(g) would cost less than one cent at wholesale prices. That said, the shipping, handling and service fee would be a couple of orders of magnitude greater than the cost of the gas itself, and I’d probably need to give the store about a dollar for the privilege of taking one cent’s worth of hydrogen gas.

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What does a mole of hydrogen look like?

We’ll assume the temperature is 20°C and the atmospheric pressure is 102.3 kPa, which is what the Weather app on my phone is reading right now. After the hydrogen gas has been released from its high-pressure storage cylinder, my one mole of H2(g) would have a volume of 23.8 litres at these conditions. That’s about enough hydrogen gas to fill up a party balloon.

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Hydrogen is a colourless, odourless gas that’s lighter than air. It’d float upwards very quickly if I opened the valve in the store. I’m now going to squeeze all that gas into my 10-litre vessel.

What’s the resulting pressure of the vessel?

If I squeeze that 23.8 litres of hydrogen gas into my 10-litre vessel, the resulting pressure in the vessel must be greater than atmospheric pressure (1 atm) because I’ve compressed the gas. We can calculate the final pressure precisely by using the ideal gas law: PV=nRT.

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That’s significantly higher pressure than atmospheric pressure, which varies from 100 kPa to 102 kPa under normal weather conditions.

Interestingly, the pressure in the vessel, 243 kPa, is equal to 35.2 pounds per square inch (psi), which is the same as the recommended pressure for a car tyre.

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Other than making random movements inside the vessel, the hydrogen molecules won’t really do anything else.

How fast are the molecules moving about?

We can calculate the average speed of the molecules by using the following equation:

*Note that R is the gas constant, 8.31, and M is the molar mass in kg/mol

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The molecules are travelling at about 1760 metres per second (on average).

How much distance will the gas molecules travel before they collide with one another?

For this question, we need to calculate something called mean free path. The mean free path is the average distance we can expect each molecule to travel before it collides with another molecule. Mean free path is quite long in a vacuum, and very short at high pressure conditions. One of the formulae used to calculate mean free path, λ, is shown below.

**Note that in this formula, pressure (P) must be measured in pascals (Pa)- not kilopascals (kPa). We therefore need to multiply our kilopascal pressure by 1000 to convert it from kPa to Pa.

*** Note also that d is the diameter of the molecules being studied in metres. Wikipedia tells us that hydrogen molecules have a diameter of 120 picometres. I’ve used this value in the equation below.

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The molecules in our vessel collide with each other roughly every 260 nanometres. That’s tiny: it’s just a few percent of the width of a cell nucleus!

How often do the molecules collide?

Let’s go right back to Year 10 Physics for this one. The time between collisions will be equal to the average distance travelled between collisions divided by the average speed of the molecules:

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The molecules collide with each other roughly every 0.1478 nanoseconds.

How many times do the molecules bump into each other each second?

By taking the reciprocal of the average collision time, we can find out how many times the molecules collide with each other every second, on average:

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Each molecule in our ten-litre vessel makes 6.765 billion collisions per second with neighbouring molecules.

Apart from lots of uneventful particle collisions – a total of 4.07 decillion uneventful collisions per second to be precise – not much else is happening in our ten-litre vessel at this stage.

Conclusion

  • Hydrogen gas, H2(g): 1.00 mol

Next week, we’ll add some helium to the vessel and see what happens.

Periodic Table Smoothie

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Image from Randall Monroe’s excellent book, What If?: Serious scientific answers to absurd hypothetical questions

Yesterday, I was wondering what would happen if we mixed the entire periodic table of elements together in a blender. Unsurprisingly, it would explode, scattering radioactive dust and debris for miles around in a red-hot fireball formed from the simultaneous fission of the entire seventh row. The periodic table would only need to be the size of a matchbox in order for this explosion to happen.

Calculating exactly what would happen would be incredibly difficult. There are so many simultaneous reactions – including nuclear reactions – taking place that it’s almost impossible to predict the outcome in any more detail than “KABOOM”.

Making a real Periodic Table Smoothie  would be prohibitively expensive. You’d need 118 particle accelerators (costing $1 billion each) all pointing at the same target just to get single atoms of each element to collide at the same time. This is even more difficult than it sounds: those elements near the bottom of the periodic table (numbers 105 and above) are so unstable that they’d break down before they even reach the target. There are massive financial and physical challenges to mixing an entire periodic table up in a blender.

Instead of adding all the elements at the same time, I’ll be adding one element each week to an imaginary 10-litre vessel and documenting – as a theoretical exercise – what happens. Ultimately, we all know it’s going to explode at some point. But when will it do that? How many elements are we able to add before it finally explodes? Will we create anything interesting along the way?

This very idea was floated on Reddit’s AskScience forum in 2013 but nobody actually figured out (seriously) what would happen.

Join me next week to start the experiment.

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