A H₂/O₂ mixture at fixed temperature is stable below 0.01 atm, explosive between 0.01 and 0.1 atm, stable again between 0.1 and 3 atm, then explosive above 3 atm. What explains the non-monotonic behavior between the first and second limits?
AHigher pressure always increases reaction rate, so the first explosive region is just a pressure effect on Arrhenius kinetics
BAt the second limit, three-body gas-phase collisions become frequent enough to deactivate chain-carrying radicals, quenching the branching explosion
CAbove 0.1 atm, the reaction switches from branching to linear chain propagation, eliminating the exponential radical buildup
DHigher pressure reduces the diffusion rate of reactants, starving the reaction of fuel
Between the first and second explosion limits, the counterintuitive result is that increasing pressure can suppress an explosion. At the second limit, increased pressure makes three-body collisions (H· + O₂ + M → HO₂· + M) frequent enough to convert the reactive H· into the much less reactive HO₂·, effectively quenching chain branching. This is why the same mixture can be stable → explosive → stable as pressure rises — the dominant termination mechanism changes with pressure.
Question 2 Multiple Choice
What is the key mechanistic difference between a chain branching explosion and a thermal explosion?
AA chain branching explosion involves fuel being consumed faster; a thermal explosion involves heat being produced faster
BIn chain branching, the radical population grows exponentially because each branching step produces more radicals than it consumes; in a thermal explosion, heat builds up faster than it dissipates, accelerating the reaction rate through temperature
CChain branching explosions only occur in gas phase; thermal explosions only occur in condensed phase
DThermal explosions are controlled by initiation; chain branching explosions are controlled by propagation
Chain branching and thermal explosions are fundamentally different mechanisms. In chain branching, each branching step (e.g., H· + O₂ → OH· + O·) produces two radicals from one, so the chain carrier population grows exponentially — a purely kinetic runaway. In a thermal explosion, heat from the exothermic reaction accumulates faster than it can escape, raising temperature, which accelerates the rate (Arrhenius), which produces more heat — a thermal feedback loop. Both can occur in the same system (the third explosion limit in H₂/O₂ is thermal).
Question 3 True / False
In a linear chain reaction (no branching), the radical population remains approximately constant during propagation because each propagation step consumes one radical and produces exactly one new radical.
TTrue
FFalse
Answer: True
True. In a linear chain, propagation steps have the stoichiometry: radical + stable molecule → product + radical. The chain carrier count is preserved, so the reaction proceeds at a roughly steady rate determined by the balance of initiation and termination. This is distinct from chain branching, where one radical in can yield two or more radicals out, causing exponential growth in radical concentration.
Question 4 True / False
In a chain branching explosion, the radical concentration remains constant because each branching step simply replaces radicals rather than creating new ones.
TTrue
FFalse
Answer: False
False. This describes linear chain propagation, not chain branching. In chain branching, a single propagation step produces *more* radicals than it consumes — for example, H· + O₂ → OH· + O· converts one radical into two. If this branching rate exceeds termination, the radical population grows exponentially with each cycle, causing an accelerating (explosive) reaction rate. The distinction between linear propagation (constant radicals) and branching (growing radicals) is the mechanistic origin of explosive behavior.
Question 5 Short Answer
Why is initiation necessary to start a chain reaction even when the overall combustion is thermodynamically highly favorable (large negative ΔG)?
Think about your answer, then reveal below.
Model answer: Initiation is kinetically, not thermodynamically, necessary. The first step — bond homolysis to create radicals — has a very high activation energy, meaning it is extremely slow at room temperature despite being thermodynamically driven. Thermodynamic favorability tells you the final state is lower in energy, not how fast the reaction proceeds. Without initiation (heat, light, or a spark to provide activation energy), the kinetic barrier prevents the reaction from starting. Once the first radicals are created, the low-barrier propagation cycle takes over.
This question gets at the distinction between thermodynamic spontaneity and kinetic accessibility. The H₂ + ½O₂ → H₂O reaction is extremely exergonic, yet a mixture of H₂ and O₂ can sit stable in a container for years without a spark. The initial bond homolysis requires overcoming a large energy barrier — this is why a match is needed. The thermodynamic driving force explains *why* combustion releases so much energy; the activation energy of initiation explains *why* you need a spark to start it.