Formula for Hydrogen?

I admit it. I love TV game shows. Last Friday I watched one of my favourite shows while eating my (late) lunch. I was even moderately successful at answering some of the questions, until the Host asked The Chaser what the chemical formula for hydrogen was. This led to the following exchange:
Chaser: H
Host: Incorrect
Contestants: H one (we will assume they meant H₁)
Host: Incorrect. The correct answer is H two (we will assume he meant H₂)

So, who was right?

Let's take the Host's "correct" answer first.
The Earth's atmosphere contains small amounts of diatomic molecules of hydrogen gas. "Di" means two and "atomic" refers to atoms so hydrogen gas in the atmosphere is made up of molecules in which 2 atoms of hydrogen are bonded together. When we make hydrogen gas in the laboratory we are making these H₂ molecules. So it seems that the Host got it right ..... except ..... the question didn't ask for the formula of hydrogen gas found in the atmosphere!

So let's turn our attention to the Contestants' response.
Is H₁ a plausible chemical formula for hydrogen?
Not really. If there is only 1 atom of an element in the chemical formula, the "1" is trivial and not included in the formula, so H₁ is the same as H which was the Chaser's response!

So, was the Chaser right?
Is H a valid chemical formula for hydrogen?
Hydrogen is a strange atom. It has 1 proton in its nucleus, and 1 electron "orbiting" that nucleus. In fact, this 1 so-called "valence electron" is a feature common to all Group 1 metals (alkali metals), but other properties of hydrogen suggest it is more like a non-metal than a metal. This similarity to the Group 1 metals led to the prediction that it should be possible to create metallic hydrogen. This would be a solid in which the hydrogen atoms (protons in effect) would be held in a 3-dimensional array with delocalised electrons acting as the metallic bonds holding the array together. This metallic hydrogen would, in theory, be an excellent conductor, indeed it would be a "superconductor", which is why the race has been on to create it!

A chemical formula of a covalent molecule tells us how many atoms of each element are covalently bonded together, H₂ has 2 atoms of hydrogen with a covalent bond between them.
But the chemical formula for a 3-dimensional metallic array refers to the ratio of atoms of each element, if only 1 element is present in a metallic array, like that of sodium metal, then the chemical formula is just the symbol for the element, Na, in this case, or H if you are referring to metallic hydrogen.
So, H is a valid chemical formula for metallic hydrogen, if it exists.
But does metallic hydrogen exist?

In January 2017, researchers at Harvard University announced that they had produced metallic hydrogen in the laboratory using immense pressure. So metallic hydrogen, H, can exist.

Back to the game show.
The Host was right, H₂ is the chemical formula for gaseous hydrogen in the atmosphere.
The Chaser was right, H is the chemical formula for metallic hydrogen.
The Contestants were almost right: Chemists don't write H₁ they just write H.

There is a moral to this story.
Be careful when writing questions. The question should not be ambiguous unless you are prepared to accept multiple different answers that are correct.
Be even more careful when answering test and exam questions. If you need to make assumptions to answer the question you MUST state what those assumptions are when you write your answer.

Reference:

1. Ranga P. Dias, Isaac F. Silvera. Observation of the Wigner-Huntington Transition to Metallic Hydrogen. Science, 2017 DOI: 10.1126/science.aal1579

Tutorials Relevant to this Post

Periodic Table of the Elements
Elements and Compounds
Metals and Nonmetals
Molecular Formula

Naming Covalent Compounds
Empirical Formula and Molecular Formula
Trends in Group 1 Elements
Metallic Bonding

Suggested Study Questions

1. Use the Periodic Table of the Elements to find the chemical symbol for each of the following atoms:
• hydrogen
• helium
• carbon
• nitrogen
• oxygen
• chlorine
2. Write a molecular formula for each of the following diatomic gas molecules:
• hydrogen
• nitrogen
• oxygen
• chlorine
3. Give the number of atoms of each element present in the molecular formulae below:
• H₂O
• H₂O₂
• CO
• CO₂
• NH₃
• NO
• NO₂
• N₂O₂
4. Let M represent an atom of an element. Circle the elements below for which the molecular formula of the element at room temperature and pressure could be represented by M
• helium
• sodium
• oxygen
• iron
• gold
• neon
• chlorine
• nitrogen
• hydrogen
5. For the description of each molecule below, write the molecular formula
• one carbon atom and four hydrogen atoms
• one nitrogen atom and three chlorine atoms
• two nitrogen atoms and one oxygen atom
• one nitrogen atom and five oxygen atoms
• two chlorine atoms and two oxygen atoms
• one carbon atom, one hydrogen atom and three chlorine atoms
6. Given the name of each molecule below, write the molecular formula:
• hydrogen chloride
• carbon monoxide
• carbon dioxide
• sulfur dioxide
• sulfur trioxide
• sulfur dichloride
7. Consider the list of compounds with a possible molecular formulae below. Circle the incorrect formulae and justify your answer:
• water, 2HO
• carbon monoxide, C₁O₁
• hydrogen peroxide, H2O₂
• sulfur trioxide: SO₂
• ammonia, NH3
• hydrogen sulfide, H₂S
• carbon dioxide, C₂O
• sulfur dichloride, S₁Cl₂
8. From the list below, circle the elements that belong to Group 1 of the Periodic Table of the Elements:
• sodium
• helium
• oxygen
• lithium
• chlorine
• nitrogen
• carbon
• potassium
• calcium
9. Draw a table with the headings "metal" and "nonmetal". Place each of the following elements in the correct column:
• hydrogen
• helium
• calcium
• carbon
• nitrogen 
• potassium
• oxygen
• chlorine
• sodium
10. From the list below, circle the elements that would exist at room temperature and pressure as an array of "atoms" help together by delocalised electrons:
• hydrogen
• carbon
• sodium
• lithium
• nitrogen
• chlorine
• iron
• gold
• oxygen

Protonated Water Clusters

Water molecules are polar. This causes neighbouring water molecules to be attracted to each other, forming hydrogen-bonds that link them into chains or clusters. The evaporation of water requires relatively large amounts of energy in order to break the hydrogen-bond networks apart.

Protonated water clusters, which have protons bound to them, are important model systems for the study of proton hydration in aqueous solutions, the process that determines the acidity (pH) and electrical conductivity of water.

The smallest protonated water cluster is the hydronium cation consisting of a single water molecule with an associated proton.
The Zundel ion is another protonated water cluster and is formed when a single proton is shared by two water molecules.

Scientists have been using infrared spectroscopy to determine the bond strengths, geometrical structures and chemical properties of protonated water clusters. When molecules are irradiated with infrared light, they vibrate in ways that depend on the wavelength, the colour, of the light. The frequency of the resulting vibrations allows scientists to deduce the three-dimensional structure of the molecule and the strength of the bonds between its atoms.

Reference:

1. Marcel sBaer, Dominik Marx, Gerald Mathias. Theoretical Messenger Spectroscopy of Microsolvated Hydronium and Zundel Cations. Angewandte Chemie, 23 August 2010 DOI: 10.1002/anie.201001672
2. G. Mathias, D. Marx. Structures and spectral signatures of protonated water networks in bacteriorhodopsin. Proceedings of the National Academy of Sciences, 2007; 104 (17): 6980 DOI: 10.1073/pnas.0609229104

Study Questions

1. Draw the molecular structure of a water molecule.
2. Use the structure above to explain what is meant by water being a polar molecule.
3. Draw a diagram to show how a hydrogen-bond can be formed between two water molecules.
4. Write the molecular formula for the hydronium cation.
5. Give the structural formala for the hydronium ion.
6. Based on the description of the Zundel ion given above, write the molecular formula for the Zundel ion.
7. Give the structural formula for the Zundel ion.
8. Another protonated water cluster is the Eigen ion, H₉O₄⁺ . Give a possible structural formula for the Eigen ion.
   

Structure of Vodka

Vodka is a colourless, tasteless solution sold as an 80-proof beverage, which means it is a solution of 40% ethanol (ethyl alcohol) and 60% water. There are many different brands of Vodka at different prices, and people claim to be able to "taste" the difference. Scientists at the University of Cincinnati and the Moscow State University have been studying this phenomenon.

Dmitri Mendeleev, a Russian Chemist famous for his work on the Periodic Table, believed that a solution of 40% ethanol and 60% water would form peculiar clusters of molecules called hydrates.

Linus Pauling, a Nobel Prize winning Chemist, thought the hydrate clusters might consist of an ethanol molecule surrounded by a framework of hydrogen-bonded water molecules.

The scientists from the the Universities of Cincinnati and Moscow State analyzed the composition of 5 popular Vodka brands and found that they differed in their concentrations of ethanol hydrates. When people express a preference for one Vodka brand over another, it is not a question of "tasting" different, they appear to be perceiving the internal structure of the Vodka. Vodkas with a low concentration of ethanol hydrates might be perceived by drinkers as watery.

Reference:
Naiping Hu, Dan Wu, Kelly Cross, Sergey Burikov, Tatiana Dolenko, Svetlana Patsaeva, Dale W. Schaefer. Structurability: A Collective Measure of the Structural Differences in Vodkas. Journal of Agricultural and Food Chemistry, 2010; DOI: 10.1021/jf100609c

Study Questions:

• The concentration of beverages containing ethanol, such as spirits, are often labelled as "proof", eg, 100 proof, 80 proof. What other ways are there to express the concentration of solutions?

• Convert 80 proof to its equivalent for each of the different concentration measures you listed above.

• For the ethanol molecule, write

1. the structural formala
2. the condensed structural formula
3. molecular formula
4. empirical formula

• What is hydrogen bonding?
• Draw a diagram showing how water molecules can hydrogen bond to each other.
  

• Draw a diagram to represent an ethanol molecule surrounded by 5 hydrogen-bonded water molecules.
• At high alcohol concentration, clusters of ethanol molecules appear. What could hold these ethanol molecules together in a cage-like structure?