3.3 Gas Laws, Dalton Partial Pressures, Arc Dissociation & Sieverts Law

3.2 Stoichiometry, Gas Laws & Partial Pressures in Shielding Gases

Shielding gases in arc welding serve two primary purposes: physically displacing ambient air (nitrogen, oxygen, and moisture) to prevent weld contamination, and establishing an ionized plasma medium that controls electrical arc characteristics, droplet detachment mode, and weld pool thermocapillary fluid flow.

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1. Gas Stoichiometry & Equations of State in Welding Systems

Stoichiometric calculations in gas-shielded processes (GMAW, GTAW, FCAW-G, PAW) link mass, molar volume, and volumetric consumption rates. The chemical mole ($n$) represents $N_A = 6.022 \times 10^{23}$ particles: $n = \frac{m}{M}$ where $m$ is mass (g) and $M$ is molar mass (g/mol).

The Ideal Gas Law

At the temperatures and pressures typical of industrial gas delivery systems ($P < 25\text{ MPa}$, $T > 250\text{ K}$), shielding gases closely follow the ideal gas equation of state: $P V = n R T = \frac{m}{M} R T$ where:

• $P$ = absolute pressure ($\text{Pa}$ or $\text{N/m}^2$)
• $V$ = volume ($\text{m}^3$)
• $n$ = quantity of gas ($\text{mol}$)
• $R$ = universal gas constant $= 8.31446\ \text{J}/(\text{mol}\cdot\text{K}) = 0.082057\ \text{L}\cdot\text{atm}/(\text{mol}\cdot\text{K})$
• $T$ = absolute temperature in Kelvin ($\text{K} = {}^\circ\text{C} + 273.15$)

Gas Density and Buoyancy Dynamics

Rearranging the ideal gas law yields gas density $\rho$ as a direct function of molar mass, pressure, and temperature: $\rho = \frac{m}{V} = \frac{P M}{R T}$

Gas              Formula    Molar Mass (g/mol)   Density at 20°C, 1 atm (kg/m³)   Specific Gravity Relative to Air
Helium           He          4.003               0.166                            0.138 (strongly buoyant)
Nitrogen         N₂         28.013               1.165                            0.967 (neutral)
Air (ambient)    —          28.964               1.204                            1.000 (reference baseline)
Oxygen           O₂         31.999               1.331                            1.105 (slightly sinking)
Argon            Ar         39.948               1.661                            1.379 (sinking, blankets weld)
Carbon Dioxide   CO₂        44.010               1.842                            1.529 (heavily sinking)

Fluid Mechanics of Shielding Coverage: Argon vs. Helium

Because argon has a specific gravity of $1.38$ relative to air, it tends to sink and spread across the workpiece, establishing a stable, laminar protective blanket over the weld pool in flat and horizontal positions. Typical argon flow rates range from $20\text{ to }35\text{ CFH}$ ($9.4\text{ to }16.5\text{ L/min}$).

Conversely, helium has a specific gravity of only $0.14$, making it roughly seven times lighter than air. In an open shop environment, buoyant thermal plume forces cause helium to rise rapidly away from the torch nozzle. To maintain an equivalent protective barrier against atmospheric aspiration, helium requires volumetric flow rates two to three times higher than argon—typically $40\text{ to }60\text{ CFH}$ ($18.9\text{ to }28.3\text{ L/min}$).

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2. Dalton's Law of Partial Pressures in Gas Mixtures

Industrial shielding formulations are rarely pure gases; they are engineered binary and ternary mixtures designed to balance arc stability, penetration profile, travel speed, and spatter generation.

John Dalton established that the total pressure $P_{\text{total}}$ exerted by a mixture of non-reacting ideal gases equals the sum of the partial pressures $P_i$ exerted by each individual gas: $P_{\text{total}} = \sum_{i=1}^{k} P_i = P_1 + P_2 + P_3 + \dots + P_k$

For an ideal gas, the partial pressure $P_i$ is directly proportional to its mole fraction $x_i$, which is identical to its volumetric fraction in the mixture: $x_i = \frac{n_i}{n_{\text{total}}} = \frac{V_i}{V_{\text{total}}} \qquad \implies \qquad P_i = x_i P_{\text{total}}$

Shielding Blend        Composition (Vol %)        Partial Pressures at 1.0 atm (101.325 kPa)      Primary Welding Application
98% Ar / 2% O₂         x_Ar = 0.98, x_O2 = 0.02   P_Ar = 99.30 kPa, P_O2 = 2.03 kPa               GMAW spray transfer on stainless and C-steels
90% Ar / 10% CO₂       x_Ar = 0.90, x_CO2 = 0.10  P_Ar = 91.19 kPa, P_CO2 = 10.13 kPa             GMAW spray/pulse on structural steels
75% Ar / 25% CO₂ (C25) x_Ar = 0.75, x_CO2 = 0.25  P_Ar = 75.99 kPa, P_CO2 = 25.33 kPa             GMAW short-circuiting mode; deep penetration
50% Ar / 50% He        x_Ar = 0.50, x_He = 0.50   P_Ar = 50.66 kPa, P_He = 50.66 kPa              GTAW/GMAW thick aluminum and copper
98% Ar / 2% N₂         x_Ar = 0.98, x_N2 = 0.02   P_Ar = 99.30 kPa, P_N2 = 2.03 kPa               GTAW duplex stainless steel phase balance

The Chemical Role of Partial Pressure

In welding thermochemistry, the chemical activity and driving force for elemental oxidation or gas dissolution in the liquid weld pool depend on the partial pressure of the gas species at the pool surface, not its total supply pressure:

• In an $\text{Ar} - 2%\ \text{O}2$ blend at $1.0\text{ atm}$, $P{\text{O}_2} = 0.02\text{ atm}$. This low oxygen potential lowers the liquid droplet's surface tension without causing excessive loss of oxidizable alloying elements (such as $\text{Mn}$ and $\text{Si}$).
• In a $100%\ \text{CO}2$ shield, $P{\text{CO}_2} = 1.0\text{ atm}$. Extensive dissociation at arc temperatures produces high levels of active monatomic oxygen, requiring highly deoxidized filler wires (such as AWS A5.18 ER70S-6) to prevent carbon boil porosity.

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3. High-Temperature Arc Column Dissociation & Recombination Kinetics

An electric welding arc generates core temperatures ranging from $10,000\text{ to }20,000\text{ K}$, with periphery temperatures between $3,000\text{ and }7,000\text{ K}$. At these temperatures, polyatomic and diatomic molecules dissociate endothermically into neutral atoms, ions, and free electrons:

Dissociation Reaction             Standard Enthalpy ΔH° (kJ/mol)   Onset Temp (K)   Key Thermochemical Consequence in the Arc
CO₂ ⇌ CO + ½ O₂                  +283                              ~2,000           Releases reactive oxygen; dissociates fully above 4,000 K
O₂ ⇌ 2 O                         +498                              ~3,000           Lowers liquid droplet surface tension; stabilizes spray mode
H₂ ⇌ 2 H                         +436                              ~2,500           High thermal conductivity; risk of cold cracking (HICC)
N₂ ⇌ 2 N                         +945                              ~4,000           Extremely strong triple bond; dissolves interstitially in steel

The Thermodynamics of Enthalpy Transfer

Molecular dissociation and recombination serve as a potent heat transport mechanism within the arc:

1. Endothermic Dissociation in the Arc Column: When diatomic gases (such as $\text{H}_2$ or $\text{CO}_2$) enter the high-temperature core of the arc, they absorb massive quantities of thermal energy to break their molecular bonds ($436\ \text{kJ/mol}$ for $\text{H}_2$, $945\ \text{kJ/mol}$ for $\text{N}_2$). This dissociation cools the central plasma core, constricting the arc column and increasing current density.
2. Exothermic Recombination at the Workpiece: As the dissociated monatomic atoms ($H, O, N$) are driven downward by plasma jet flow (Maecker effect) toward the cooler weld puddle surface ($T \approx 1800\text{--}2500\text{ K}$), the thermodynamic equilibrium shifts back toward diatomic molecules. Recombination occurs directly at the weld pool surface, releasing the dissociation enthalpy: $2\text{H} \longrightarrow \text{H}_2 + 436\ \text{kJ/mol}$ This localized heat release broadens the weld puddle, increases joint penetration, and elevates travel speeds compared to pure argon shielding.

Reactive vs. Inert Gas Behavior: Metal Transfer Physics

Gas Formulation    Shielding Class   Metal Transfer Mode in GMAW              Bead Profile & Penetration Characteristics
Pure Argon (Ar)    Inert             Axial Spray (above critical current I_crit) Deep, narrow "finger-like" central root penetration
Ar + 1–5% O₂       Active/Oxidizing  Stable Axial Spray (lowers I_crit)       Broadened bead base, smooth toe blend, reduced undercut
Ar + 5–18% CO₂     Active/Oxidizing  Axial Spray / Pulsed Spray               Wide, uniform penetration profile, robust root tie-in
Pure CO₂           Active/Oxidizing  Globular or Short-Circuiting only        Broad, deep penetration; high spatter; no true axial spray
Ar + 25–75% He     Inert             Spray / Globular                         Broad, parabolic "bathtub" penetration; high heat input

When welding carbon or low-alloy steel under pure argon, cathode spots on the workpiece move erratically across oxide films, producing an unstable arc with wandering droplets and poor edge wetting. Adding $1\text{ to }5%\ \text{O}_2$ or $5\text{ to }10%\ \text{CO}2$ forms a thin, stable oxide film on the molten pool surface. This stabilizes cathode emission, reduces the molten metal's surface tension, and lowers the critical transition current ($I{\text{crit}}$) required for stable axial spray transfer by $20\text{ to }35\text{ A}$.

However, when the $\text{CO}_2$ content exceeds $\sim 18\text{ to }20%$, the electromagnetic pinch effect is disrupted by intense upward vapor pressure from $\text{CO}$ dissociation at the droplet tip. Axial spray transfer becomes unstable, forcing the system into globular transfer with coarse, irregular droplets and heavy spatter.

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4. Sieverts' Law & Diatomic Gas Dissolution Kinetics

When a diatomic gas species ($X_2$, such as $\text{H}_2$ or $\text{N}_2$) dissolves into a molten metal bath, it does not dissolve as a molecule; it dissociates into individual atoms dissolved in the liquid matrix ($[X]$): $\frac{1}{2} X_2(g) \rightleftharpoons [X]_{(\text{liquid metal})}$

Applying the law of mass action to this heterogeneous equilibrium: $K_X = \frac{a_X}{(P_{X_2})^{1/2}}$ Assuming Henry's law applies at low solute concentrations (where activity $a_X$ is proportional to weight percent $[\text{wt}%\ X]$): $[\text{wt}\%\ X] = K_X \cdot \sqrt{P_{X_2}}$ This mathematical relationship is Sieverts' Law. It dictates that the equilibrium concentration of a dissolved gas in liquid metal is directly proportional to the square root of its partial pressure, rather than to linear partial pressure.

Gas System   Equilibrium Constant at 1600°C (wt% · atm^-0.5)   Solubility at P = 1.0 atm (1600°C)   Primary Weld Defect Risk
Hydrogen (H) K_H ≈ 0.0027 (27 ppm)                             ~27 ppm (liquid iron)                Hydrogen-assisted cold cracking (HICC)
Nitrogen (N) K_N ≈ 0.0450 (450 ppm)                            ~450 ppm (liquid iron)               Strain aging embrittlement, gross porosity
Oxygen (O)   Non-Sieverts (forms stable oxides)                 ~0.23 wt% (un-deoxidized Fe)         Carbon boil CO porosity, oxide inclusions

The Solidification Rejection Mechanism

Dissolution of hydrogen and nitrogen into liquid iron is endothermic ($\Delta H_{\text{solution}} > 0$), meaning equilibrium solubility increases with rising temperature. At $1600^\circ\text{C}$, liquid iron dissolves up to $27\text{ ppm}$ of hydrogen and $450\text{ ppm}$ of nitrogen at $1\text{ atm}$.

During solidification and subsequent cooling, gas solubility drops precipitously across phase boundaries:

\begin{cases} \text{Liquid Fe at } 1538^\circ\text{C}: & \sim 25\ \text{ppm} \\[4pt] \delta\text{-ferrite (BCC) at } 1538^\circ\text{C}: & \sim 9\ \text{ppm} \\[4pt] \gamma\text{-austenite (FCC) at } 1400^\circ\text{C}: & \sim 5\ \text{ppm} \\[4pt] \alpha\text{-ferrite (BCC) at } 20^\circ\text{C}: & < 0.001\ \text{ppm} \end{cases}$$ As the solid-liquid interface advances during weld puddle solidification, partitioning rejects excess gas into the boundary liquid layer ($k_0 = C_s / C_l < 1$). If the local dissolved gas concentration exceeds the solubility limit and the combined partial pressures exceed the nucleation threshold ($P_{\text{gas}} > P_{\text{ambient}} + P_{\text{ferrostatic}} + 2\gamma/r$), gas bubbles nucleate and grow, forming **wormhole porosity** or trapping diffusible hydrogen that can trigger cold cracking. ---