Calculating Thrust and Work for a Vinegar and Baking Soda Rocket

[alchemistf9]

I am a high school teacher attempting to give my students a project for designing a rocket powered by the chemical reaction between acetic acid and baking soda to produce CO2 gas.

I have done some simple calculations based on stoichiometric amounts of vinegar and acetic to produce a stoichiometric amount of CO2. I then have taken the moles of gas produced and solved for the pressure produced using the ideal gas law equation.

The calculations are attached in the Excel file.

Now I come to the troubling part. The students will be using a 2-L soda bottle as their rocket.

As the physics part of the project I would like to the students to calculate many things:

Fthrust and work done by the gas.

What are the simplest equations to use to calculate Fthrust and Work ?

I've attempted to make several equations which give me some very non-sensible results.

 

[mfb]

Do you plan to use some reaction mass, like water? A direct CO2 exhaust is quite inefficient. There are several threads about rockets in the forums (at least one of them is in the "Similar Threads" list below).

 

[PhysicoRaj]

I think the products, sodium acetate and water, or simply sodium acetate solution can act as the reaction mass right?

 

[mfb]

I'm not sure if that is a good idea...

 

[alchemistf9]

The reaction mass is the whole thing yes.

 

[alchemistf9]

I just need a simple equation for the force of Thrust

 

[mfb]

$F=\frac{dm}{dt}v \approx \rho A v^2$ where A is the area of the nozzle, rho is the density and v is the velocity there. Neglecting compression and inefficiencies, $\rho v^2 = 2 \Delta p$ with the pressure difference inside/outside. For gas as reaction mass (bad), compression is relevant, of course, so it might need a better analysis.