Question bank — Combustion of hypergolics — N₂O₄ + UDMH - MMH; ignition delay

False. The whole point is self-ignition on contact — there is no igniter to fail, which is exactly why they suit restartable upper stages and thrusters.

False. A long delay lets unburnt propellant pool in the chamber; when it finally lights, all of it ignites at once and the pressure spike ("hard start") can rupture the engine.

False. Delay is kinetics (how fast it starts); flame temperature is thermodynamics (how much energy is released, see Adiabatic flame temperature). A fuel can start fast yet release only modest energy — they are independent axes.

True. Since $\tau \propto 1/k$ and $k$ grows with $T$, $\tau$ shrinks as $T$ rises. A cold engine ignites sluggishly — the danger scenario for hard starts.

True. The rate constant carries $e^{-E_a/RT}$, but delay is its reciprocal, so the sign flips: $\tau \propto 1/k\propto e^{+E_a/RT}$.

False. ${\text{N}}_2{\text{O}}_4$ is the oxidiser (electron acceptor / oxygen carrier). The hydrazine derivative is the fuel (electron donor). See Redox in combustion.

False. The stable product is ${\text{N}}_2$ (very strong triple bond). NOₓ appears only as a minor high-temperature trace; for stoichiometry take products as ${\text{CO}}_2,{\text{H}}_2\text{O},{\text{N}}_2$.

Partly false. It is a sum of three clocks — physical mixing, liquid-phase pre-ignition reactions, thermal runaway — but the rate-limiting chemical step is Arrhenius-controlled, which is why $\ln \tau$ vs $1/T$ still plots straight.

False. Their pre-ignition chemistry has a low $E_a$ (~17 kJ/mol in the worked example), which is precisely why they ignite even in cold space. Violence of release ≠ height of the barrier.

False. ${\tau }_{ign}$ also falls strongly as pressure rises — higher pressure packs molecules closer, raising collision (reaction) rates. Correlations often carry a $\tau \propto P^{-n}$ factor alongside the Arrhenius term.

Oxygen doesn't balance. Right side needs $2(2)+4=8$ O atoms, so you need $a=2$ molecules of ${\text{N}}_2{\text{O}}_4$ (which supply $4a=8$ O), not one. Correct: ${\text{C}}_2{\text{H}}_8{\text{N}}_2+2{\text{N}}_2{\text{O}}_4\to 2{\text{CO}}_2+4{\text{H}}_2\text{O}+3{\text{N}}_2$.

Wrong x-axis. The linear relation is $\ln \tau =\ln C+(E_a/R)(1/T)$, so you plot against $1/T$, not $T$. Only then is the slope $E_a/R$ (with $R$ the gas constant).

Coefficients give moles, not mass. From $4{\text{CH}}_6{\text{N}}_2+5{\text{N}}_2{\text{O}}_4$, multiply by molar masses: $\frac{5\times 92}{4\times 46}=2.5$ (oxidiser mass over fuel mass). Ratios of masses require molar mass, per Stoichiometry and limiting reagent.

Miscalculated. $M(\text{MMH})=12+6+28=46$ g/mol. It's NTO (${\text{N}}_2{\text{O}}_4$) that is $92$ — remember the mnemonic "NTO is Ninety-two", and MMH is exactly half.

Backwards. The N–N single bond is weak (~160 kJ/mol) and ${\text{N}}_2$'s triple bond is very strong (~945 kJ/mol). Trading weak for strong releases huge energy, so hydrazines are eager reducers (Bond enthalpy and reaction energetics).

Unrelated quantities. $I_{sp}$ (Specific impulse and rocket performance) depends on exhaust energy and molecular weight, not on how quickly ignition begins. Delay and $I_{sp}$ are set by different physics.

Because time-to-ignite scales as the reciprocal of the reaction rate: $\tau \propto 1/k$, and $k\propto e^{-E_a/RT}$, so $\tau \propto e^{+E_a/RT}$.

Extra fuel keeps combustion products cooler at the chamber walls (protecting the metal) and lower-molecular-weight exhaust can improve $I_{sp}$ — a trade of some peak energy for hardware survival and performance.

A low $E_a$ means the ignition reaction proceeds fast even at low temperature, so the pair still lights reliably in the cold vacuum of space where there is no warmth to help it along.

Because one stage — the pre-ignition chemistry — is rate-limiting and Arrhenius-controlled; it dominates the total time, so the sum inherits its exponential temperature dependence.

Subtraction cancels the unknown fitting constant $\ln C$, leaving one equation in one unknown: $\ln ({\tau }_1/{\tau }_2)=(E_a/R)(1/T_1-1/T_2)$.

Both propellants are liquids at room temperature, so tanks can sit filled for years, whereas cryogenic oxygen/hydrogen boils off and demands constant refrigeration.

The exponent $E_a/RT\to 0$, so $e^{+E_a/RT}\to 1$ and $\tau \to C$, its smallest floor value — ignition becomes essentially instantaneous, limited only by mixing.

The exponent $E_a/RT\to \infty$, so $\tau$ blows up — the delay grows dramatically, which is the classic recipe for a hard start when a cold engine is first fired.

It shortens: denser gas means more frequent collisions and faster reaction, so a low-pressure start (e.g. vacuum ignition of a thruster) is inherently more sluggish than a high-pressure one — an extra reason cold vacuum starts are watched carefully.

No. You would remove only the physical-mixing clock (part of what $C$ lumps together); the liquid-phase pre-ignition chemistry and thermal-runaway clocks still take finite Arrhenius-controlled time.

The oxidiser becomes the limiting reagent: some fuel goes unburnt, energy release drops, and the mixture runs fuel-rich — cooler flame but wasted propellant if taken too far.

No reaction, no delay to measure, no flame. "Hypergolic" only means on contact — separation is precisely why the propellants can be stored safely side by side until injected.

No. Stoichiometric burning gives near-peak flame temperature, which can overheat chamber walls; that is why real engines back off to a fuel-rich mixture despite the slight energy sacrifice.