[Joakim]

Hi,
This is my first post so please redirect me if this is the wrong place for this post.

I have been curious if a chemical reaction such as that used in (traditional) airbags (2 NaN3 → 2 Na + 3 N2) can be used to power a mechanism (of a single use consumer device), such as push a piston, with high pressure instead of high speed. I have no clue how to calculate the pressure it could sustain and push a piston with given an optimized proportions of chemicals.

Is there a way to calculate such a force or pressure given the chemical reaction?
Is an airbag type reaction only useful for creating large gas volumes quickly but not good for generating pressure? Perhaps another reaction is recommended? I'm hoping to avoid anything too dangerous, explosive or hot, such that it could be done in a plastic chamber
Am I asking the wrong questions in the first place?

Thanks in advance!

[Borek]

Do you know gas laws? Avogadro's principle?

[Joakim]

Thank you Borek for guiding me in the right direction!

I have tried to apply the ideal gas law to calculate the resulting pressure. This is under the assumption that the entire volume of a chamber can be filled with salt, followed by igniting and having the reaction take place converting everything to N2 and Na at a high pressure.

P=kT*N/V

k≈1.4*10^-23
T_reaction=300°C≈570°K
m/V=densty NaN3=1,9g/cm3=1.9*10³kg/m³
Molar mass NaN3=0.065kg/mol
m/N=0.065/(6*10²³)≈1.1*10^-25 kg/particle

P=kT*N/V=kT(m/V)/(m/N)=1.4*10^-23*570*(1.9*10³)/(1.1*10^-25)≈1.4⁸Pa≈1400 atm

If the calculation is accurate then the pressure is way more than sufficient to be useful, but I am concerned that this is not the right way to calculate and that the bottleneck is elsewhere, perhaps some equilibrium is reached in the reaction when a certain pressure is reached if the volume is not allowed to expand?

[Joakim]

oh I guess I missed that there are 3 particles of gas per 2 particles of salt, so the pressure would increase by 50% to 2100 atm

[Borek]

I have problems following what you did (which can mean you made some mistake that I am not recognizing). Better starting point would be PV=nRT and just going through the number of moles.

There are plenty of things that are wrong with this approach, but yes, details aside expected pressures are in the katm range assuming constant volume and reaction completion.

[Enthalpy]

[...] I'm hoping to avoid anything too dangerous [...]

NaN₃ is too dangerous. Very bad choice.

Any detonating substance produces a shock wave of huge pressure that is destructive to a chamber. What you need is a slow flame front. Air+propane mixture, air+gasoline mist with proper octane rating, with luck air+methane.

Even these flame fronts create over pressures several times bigger than the equilibrium computed by the ideal gas law. Difficult to predict, use experimental data.

Also, technology limits operating pressure of piston engines, notably at seal rings. Some engines do consume only a liquid as a propellant, like H₂O₂, N₂O₄, N₂H₄... In submarines, only a fraction of the produced gas is let out after expansion, the rest is compressed again, and a small amount of propellant is added. Igniting a liquid or solid propellant without much extra chamber volume is just excluded.

[Joakim]

Thank you both for the much needed input! I will not update the calculations as you confirm the results are already in the ballpark and the reaction used there seems ill advised anyway. I have since understood that NaN3 is not used anymore in airbags in favor of Nitroguanidine, Guanidine nitrate or the likes. Still, pressures in the katm range are way over the top in terms of usefulness.

I have in mind something powering an espresso maker or bicycle pump for example which would require pressures in the tens of atm, not thousands. So either 99% of chamber volume filled with air could reduce that I guess, but those risks of shock waves still sound very dangerous, although that safety concern must have  been solved somehow with those Hövding airbags worn around the neck. Maybe its just a different story when the volume is not constrained?

I hear what you are saying though and am inclined to follow your advice of a air propane mix or the like, thank you for that suggestion Enthalpy. Perhaps it is eaven feasible to replace a combustion reaction with one where the device is activated by opening the gate between two substances allowing them to mix and create a gas (oxidization? forgive my very limited chemistry background). Could it be favorable in terms of cost, safety and absence of generated heat? If you have any further suggestions I'm all ears. Thanks again, I love these forums where anyone can get expert advice