How Do You Calculate the Changing Mass of a Sublimating Solid?

[tempneff]

Hi all, I am forced to step outside of my field to investigate a problem that might root in sublimation of solids. I am trying to calculate the mass (after a certain time) of a material that we know is sublimating at , say .000123 g/(cm^2 hr). Is it as simple as multiplying the rate by the initial surface area and time?

Subliming for 20 cm^2 solid for 1000 hrs: mass = .000123*20*1000 = 2.46 grams of material turned to gas?

Seems to me that since the surface area is changing I have to integrate. Am I making it too complicated?

Note: (Consider the solid in vacuum and isothermal and the sublimation rate is for this environment)

 

[Borek]

Your guesses are as good as mine.

Is the solid in the form of a single chunk, or some powder? What fraction of the original mass is lost? (these will not change the general picture, but they can justify some approximations).

Please note this question should land in the homework section (as it is indistinguishable from a HW problem). Moving.

 

[tempneff]

The material is in a single chuck (small cylinder). The fraction of the original mass is exactly what I hope to find out.

It would make a good homework problem, it is actually an investigation of an electrical problem. I am wondering if this sublimation eventually leads to reformation of conductive solids that short my circuit.

Can we model it as a simpler problem, maybe how long it takes for a chuck of dry ice to disappear at room temp and 1atm? It's the same principal right? I'm EE so I'm stretching outside my realm..

 

[Borek]

The material is in a single chuck (small cylinder). The fraction of the original mass is exactly what I hope to find out.

If the change in mass is low enough, change of the size of the cylinder is so small you can assume its surface is constant - that makes calculation quite easy.

Exact value depends on so many factors I am not sure it is possible to calculate without lot of other data (sublimation speed is a function of the vapor pressure, that in turns depends on the air flow around the element; exact modeling of such things is typically a nightmare). No idea what the number you listed comes from, can be it is a maximum rate (in which case it can be used to estimate maximum possible mass loss, and the real loss is almost guaranteed to be lower), can be it is some average (which will give a reasonable estimate for 'typical' condition, but can be seriously off if your setup is non-standard).

Note: the above is an educated guess based on my old experience with diffusional transport processes. They are in many ways similar, but not identical, so my intuition can be off.

 

[DeeNos]

Hello,

I would like to clarify that the sublimation rate of solids is a well-studied phenomenon and is affected by various factors such as temperature, pressure, and surface area. It is not as simple as multiplying the rate by the initial surface area and time.

In order to accurately calculate the mass of a material that is sublimating, you need to take into account the changing surface area over time. This can be done by using integrals, as you have mentioned. The equation you have provided is a good starting point, but it may not give you an accurate result.

Additionally, it is important to consider the conditions under which the sublimation rate was measured. As you have mentioned, the sublimation rate for a solid in vacuum and isothermal conditions may differ from that in other environments. It is important to take this into account when calculating the mass of the material.

In summary, the calculation of the mass of a material undergoing sublimation is not a simple process and requires careful consideration of various factors. It would be best to consult with experts in the field or conduct further research to ensure accurate results. I hope this helps.