Preface: This tutorial is written at the level of a university student who has had at least one course each in chemistry and physics. I hope readers with less formal training can nonetheless take away the essential character of the monograph: intuitive insight into key physical phenomena – such as the idea that hydrogen is a gaseous metal and the analogy between electricity and hydrogen as energy carriers – but intuition confirmed by mathematical and physicochemical argument. The first section presents the potential benefits of hydrogen fuel, and the eighth reiterates the challenges. Six intervening sections link the promise and challenges. – ARM

(Note: The sections below are essentially complete, but the remaining sections are in progress.)

1. Promise of Hydrogen

Hydrogen fuel, especially coupled with fuelcells, offers a solution to worldwide problems caused by the approaching scarcity of fossil fuels and ongoing atmospheric emissions of greenhouse gases. Hydrogen is sometimes termed the “forever fuel” and the “universal fuel” because, respectively, it is an energy carrier that is constantly recycled, and it can be produced from numerous primary energies. In several ways, hydrogen is analogous to electricity: (1) It is manufactured rather than recovered from geological deposits; (2) it is readily transmitted via pipelines that are analogous to electrical conductors; (3) when produced from clean primary energies, it is as clean in its applications as electricity, (4) in chemical processes, it often exists (up to being solvated) as a fundamental particle, the proton, and (5) electricity and hydrogen can always be interchanged, in a kind of yin-and-yang relationship, via electrolysis or fuelcells.

Below, I will provide the foundations of the above academic facts. However, practical widespread use of hydrogen is not yet a fait accompli, and I will also describe challenges that must be overcome before a hydrogen-based civilization can become reality.

2. Hydrogen in Nature

Hydrogen is the most abundant element in nature. About three-quarters of the ordinary matter of the universe is hydrogen. It and helium are the primary elements of the universe, and the heavier elements are derived from them though fusion processes in stars. On Earth, because hydrogen, like elemental metals, is a reductant - a substance having a tendency to donate electrons - it does not exist in elemental form but in chemical combination with oxidants. Hydrogen on Earth commonly exists in combination with oxygen, with the most abundant compound being water.

The unique position of hydrogen is shown by its position in the periodic table of the elements (see Fig. 1). As the table shows, most of the elements of nature are metals, and while most have the familiar metallic properties of hardness, reflectivity, electrical conductivity, and thermal conductivity, not all do. Mercury (Hg), a liquid, lacks hardness. Hydrogen, a gas, would seem to lack all metallic properties. Nonetheless, the most fundamental characteristic of a metal is its tendency to donate electrons in chemical reactions, and on this basis, hydrogen is classified as an alkali metal in the first column of the table. Moreover, solid hydrogen, at 14 K, has decidedly metallic properties, including electrical conductivity. Viewing hydrogen as a gaseous metal clarifies how fuelcells work (see "Fuelcell Tutorial" listed in the bibliography).

Periodic Table of the Elements Figure 1. The position of hydrogen in the periodic table shows that it behaves chemically like a metal.

In some published periodic tables, hydrogen is also placed in the halogen family as a nonmetal. While it can accept electrons (e.g., in LiH), this is not its typical role in chemical reactions.

3. Properties

Several important properties of hydrogen are listed in Table 1. In comparison to air (see also Table 1), hydrogen exhibits 14-fold lower density, 3.8-fold higher speed of sound, and seven-fold higher thermal conductivity. These exceptional properties of hydrogen have useful applications: Its low density and high sonic speed are exploited in the supersonic tube vehicle (STV) concept, and its high thermal conductivity has been exploited by using hydrogen gas as a coolant for nuclear reactors so as to avoid radioactive contamination of the coolant.

Under conditions normally encountered, hydrogen exists as a diatomic molecule, H2, and unless otherwise stated, when we say “hydrogen,” we mean the diatomic molecule. With a mass of only 2.0 amu, compared to 4.0 for helium and 32 amu for oxygen, it is the lightest of all gases. Because the two atoms are held together by a covalent bond, and because of mirror-image molecular symmetry, the molecule has no permanent dipole moment. Low molecular mass and lack of charge separation are the main determinants of the properties in Table 1.

Table 1: Propertiesa of Hydrogen and Comparison with Properties of Air
Property Hydrogen Air Hydrogen Value/Air Value
Molecular mass, amu 2.016    
Boiling point, K 20    
Melting point, K 14    
Density (ρ ), g/L 0.082 1.16 0.071
Viscosity (µ), µPa-s 9.0 18.6 0.48
Speed of Sound, m/s (km/h) 1,310 (4,720) 346 (1,246) 3.8
Thermal Conductivity, mW/m-K 187 26.2 7.1
a At pressure P = 100 kPa and temperature T = 298-300 K

The invaluable ideal gas law can be derived from the kinetic theory of gases, in which gas molecules are treated as point masses exhibiting elastic collisions with the walls of their container (i.e., no kinetic energy is lost to the walls). The ideal gas law is stated as

P V = n R T (1)

where P is pressure in kPa, V is volume in m3, n is number of moles in mol, T is temperature in K, and R is the universal gas constant, with R = 0.008 314 m3 kPa / (K mol). By definition, one kilopascal equals 0.01 bar. Please note that this result is independent of the identity of the gas and applies to mixtures as well as pure gases. For example, methane, air, or hydrogen, or any of their mixtures, will equally obey the law if the assumptions of the kinetic theory are satisfactorily approximated.

We can easily derive an alternative, simpler but gas-specific form of the law as follows. From equation (1)

P = (n/V) R T (2)

P = ρ R* T(3)

where ρ is gas density in kg/m3 and constant R* = 4.124 m3 kPa / (K kg). Note that R*, distinct from the universal gas constant R in equation (1), converts molar concentration (mol/m3) into conventional density (kg/m3). Therefore, R* = R/M, in which M is the molar mass of the molecule in kg/mol, and constant R* is not universal but varies with the gas.

To intuitively understand the ideal gas law, it is useful to express equation (3) with gas density on the left-hand side:

ρ = P / (R*T)(4)

A gas more closely obeys the ideal gas law to the extent that it approximates the assumptions of the kinetic theory, in particular, that individual gas molecules do not interact, and they thus behave as point masses. Intuitively, therefore, the ideal gas law will be better obeyed when the gas density is lower. From equation (4), density will be low when either pressure P is low or temperature T is high. Because hydrogen in any case has the lowest density of any gas, it most easily approximates the assumptions of the kinetic theory and more widely obeys the ideal gas law.

Temperature is a direct measure of the mean speed (or other molecular motion, namely, vibration and rotation) of the molecules comprising a gas. To aid our understanding of the properties in Table 1, we will rewrite equation (3) as

T = P / (ρ R*)(5)

Thus, at a given pressure, hydrogen has the highest temperature of any gas because it has the lowest density. For hydrogen to exert a given pressure on a container, its molecules must collide with the container walls at higher speed to compensate for their smaller molecular mass.

We can sketch an explanation (using broad brush strokes) of several of the properties in Table 1 from what we now know about the molecular properties of hydrogen. The low melting and boiling points follow from the hydrogen molecule’s absence of a permanent dipole moment and its low volume, with consequent low surface area, which reduces intermolecular Van de Waals forces. Density has already been dealt with implicitly in deriving equation (3). Consider viscosity as the drag (force) on two opposing plates, closely-spaced on a macroscopic scale, when a gas flows through the gap between the plates. Low viscosity relative to other gases is expected because of hydrogen’s small molecular volume, which reduces interaction of the surfaces of the molecules with the plates, as well as interaction of the molecules themselves. Note, however, that the viscosity is only about half that of air (see Table 1). High thermal conductivity is related, in part, to hydrogen’s high molecular mean speed, which we discussed in connection with equation (5).

Infinitesimal volume element G with volume ΔV Figure 2. Infinitesimal volume element G with volume ΔV

We will look more closely at the speed of sound s in a gas. Sound is a longitudinal mechanical wave and propagates through a gas via collisions between molecules. For wave propagation in a gas, in analogy to transverse wave propagation along a wire, the medium must exhibit both elasticity and inertia. Elasticity is provided by the fact that a gas can be compressed, and inertia is provided by the mass associated with gas density. Consider an infinitesimal rectangular prism of gas G, with volume ΔV and cross-sectional area ΔA, in the path of an advancing longitudinal pressure pulse. As the wave reaches G, the gas within increases in pressure by ΔP, but the pressure increase is resisted by the inertia of the mass of gas in G. It is the give-and-take of these two opposing forces – elasticity and inertia – that causes the sound wave to propagate at a finite and distinct value.

A formula for the speed of sound in a gas medium can be derived from Newton’s second law

ƒ = m a(6)

where ƒ is the compression force on the gas within G, m is the mass of the same gas, and a is acceleration that the mass experiences. Total force ƒ on the volume of gas in G is given by the formula ƒ = ΔP ΔA. The mass of gas m in G is m = ρ ΔV = ρ ΔA (s Δt), where ρ is gas density in g m-3, s is the wave propagation speed in m/s, or speed of sound, and Δd = s Δt is the length in meters of volume element G in the direction of wave propagation for time increment Δt (see Fig. 2). By definition of acceleration, a = – Δs / Δt, in which the sign is negative because the wave is decelerated by the inertia of the mass within G. Substituting these results for ƒ, m, and a in equation (6) gives

ΔP ΔA = – (ρ ΔA s Δt) (Δs / Δt)(7)

Simplifying and solving this for quantity ρ s gives

ρ s = – ΔP / Δs(8)

We will write equation (8) in terms of Δs / s because it allows three factors to be combined as a constant for ideal gases. Accordingly, multiplying both sides of the equation by s, and solving for s, gives the following equation for the speed of sound in an ideal gas

s = [ΔP / ρs / s)]1/2(9)

Although it is beyond the scope of this article to prove it, for a given ideal gas, quantity ΔP / (Δs / s) is directly proportional to P and we have

ΔP / (Δs / s) = s ΔPs(10)

s lim Δs → 0 ΔPs = s dp/ds = γ P(11)

where γ is a proportionality constant for ideal diatomic gases, such as hydrogen, and P is the gas pressure. Constant γ is termed the adiabatic index in the literature.

We can therefore write equation (9) as

s = [γ P / ρ]1/2(12)

which is our final form for an equation for the speed of sound in an ideal gas.

I have empirically determined for you the value of γ for four diatomic gases – hydrogen, nitrogen, oxygen, and air (nitrogen plus oxygen) – at 298-300 K and computed the mean value of the adiabatic index as γdiatomic = 1.41375 x 103 kg / (m s2 kPa).

We see that the final equation for the speed of sound, equation (12), contains the two factors always required for wave propagation: an elasticity factor, P, and an inertial factor, ρ. Because hydrogen has the lowest density of any gas, the equation shows that it has the highest speed of sound of any gas.

To test equation (12) against experiment, we will compute the speed of sound for hydrogen. Using pressure P = 100 kPa, ρ = 0.0824 kg/m3, shown in Table 1, and γdiatomic = 1.41375 x 103 kg / (m s2 kPa), equation (11) gives s = 1310 m/s, which agrees with the value in Table 1 to three significant figures. Please compute for yourself the speed of sound in oxygen at P = 100 kPa, given that ρ = 1.3080 kg/m3. (The empirical value is s = 330 m/s.)

Despite its reputation to the contrary, hydrogen is not very reactive under ambient conditions, at least with respect to oxygen or air. In principle, one could take hydrogen and oxygen in the stoichiometric ratio of two volumes (moles) of hydrogen and one volume (mole) of oxygen, place them in a sealed container, and the mixture would remain essentially unchanged for decades. Exposing the mixture, however, to a spark or a catalyst such as metallic platinum could result in an immediate conflagration. (Because of the possibility of a spark from static electricity, the reader should not attempt this experiment.)

The chemical equation describing the reaction, along with its associated free-energy values ΔG and ΔG, are given by

H2 + ˝ O2→ H2O (gas), ΔG = -229 kJ/mol, ΔG = 42 kJ/mol(13)

The Gibbs free energy ΔG for the reaction is the energy difference between initial and final thermodynamic states of the reaction and describes the maximum energy, in any form, that can be extracted from the reaction. The activation energy ΔG, a quasi-thermodynamic variable, is the energy of a loosely bound complex of hydrogen and oxygen atoms, termed the activated complex, that lies between the initial and final states and is unstable with respect to both reactants and products. The relationships among ΔG, ΔG‡, and the initial and final states of the reaction are shown schematically by the reaction profile in Figure 3.

Equation (13) and Fig. 3 explain why hydrogen and oxygen can result in a conflagration if exposed to heat or a catalyst, yet remain quiescent for a long period of time if undisturbed. The negative free-energy difference of ΔG = -229 kJ/mol shows that the reaction can release large amounts of energy in the form of heat, light, or electricity; however, being a thermodynamic state-variable, it does not determine the rate of the reaction.

Figure 3. The reaction profile describes the free-energy changes as the reaction progresses from initial state to final state. Figure 3. The reaction profile describes the free-energy changes as the reaction progresses from initial state to final state. Activation energy ΔG = 42 kJ/mol represents an energy barrier (see Fig. 3) to the progress of the reaction, and for reaction to occur, the reactants must scale the energy barrier. An even higher barrier exists for reaction of hydrogen with air. The activation energy, by determining the concentration of the fleeting, quasi-thermodynamic activated complex, does indeed determine the reaction rate. A catalyst accelerates the reaction by lowering the energy of the activated complex; heat accelerates the reaction by increasing the energy of the initial state. In either case, the result is lowering of the energy difference between initial state and activated complex. An activation energy of ΔG‡ = 42 kJ/mol, a consequence of the covalent bonds in hydrogen and oxygen, makes the reaction so slow in the absence of heat or a catalyst that the reactants may take decades to react to a detectible degree.

Hydrogen is physiologically inert. Some other fuels, such as methane, have a low degree of physiological activity but are not as inert as hydrogen. Nonetheless, hydrogen can result in suffocation by displacing air in the respiratory system (see section 7 below).

4. Production and Distribution

In terms of moles, hydrogen rivals all chemicals in annual quantity produced, but since it has an atomic mass of unity, the annual mass produced is not so large. Annual worldwide hydrogen production is estimated as 45 million tonne (metric ton). Most of this is used for the frontend of large-scale chemical processes such as anhydrous ammonia synthesis and gasoline refining, and little is sold as hydrogen per se to consumers, i.e., as “merchant hydrogen”.

Methods of production ….

Methods of distribution …..

5. Hydrogen as an Energy Carrier

6. Storage

7. Safety

8. Challenges of Hydrogen

9. Bibliography

1. Promise of Hydrogen 2. Hydrogen in Nature 3. Properties 4. Production and Distribution 5. Hydrogen as an Energy Carrier 6. Storage 7. Safety 8. Challenges of Hydrogen 9. Bibliography

Updated: 6 January 2010
Copyright © 2009
by Supersonic Tubevehicle LLC