# Do electronic balance weighings still need to be corrected for buoyancy error?

Buoyancy error is a weighing error due to the difference in the buoyant force exerted by a medium (commonly air) on the object and on the standard masses. The difference in buoyant force occurs when the object and the standard masses have standard masses (Skoog et al., 2014).

Knowing this, I am confused as to whether electronic macroanalytical balances need to be corrected for buoyancy error because of the following factors:

1. Electronic macroanalytical balances still get calibrated by weighing standard masses.
2. Closing the doors of the balance does not make the system inside of it evacuated. It still has air which can exert buoyant force on the object and on the standard masses.

Given the factors I mentioned, do electronic balance weighings stil need to be corrected for buoyancy error?

References:

• Fundamentals of Analytical Chemistry, Skoog, et al., 9e
• Well, if imagine trying to weigh a helium-filled balloon on an analytical balance by taping it to the weighing pan, I think the result will be negative. But I don't think the balloon has negative mass, so ... – Curt F. Oct 22 '17 at 16:39

A balance cannot determine the density of the weighted material and air automatically. For this reason a buoyancy error correction must be applied for high precision measurements.

Suppose you weigh $\pu{100.0000 g}$ water and have $\pu{100.0000 g}$ reference weights with a density of $\pu{8.0000 g cm^{-3}}$. Then the static buoyancy in air is equivalent to about $\pu{120 mg}$ and $\pu{15 mg}$ respectively, accounting for a difference of about $\pu{105 mg}$ in the reading of the balance.

Besides the static buoyancy there may also be dynamic buoyancy due to air flow caused by temperature differences between the weighted material and the surrounding air.

Dynamic buoyancy can be avoided be weighing in thermal equilibrium. Static buoyancy can be corrected by formulae involving the density of air, the density of the weighted material and the density of the reference weights.

• So would you have to accurately measure the pressure and temperature too. The temperature to determine the thermal expansion and so additional air displacement. Or just take the measurement in a vacuum... – zeristor Oct 22 '17 at 22:05
• Not to forget air humidity. Together with pressure and temperature you could calculate air density quite accurately. – aventurin Oct 22 '17 at 22:16

I think they must as the density of the material being weighed will change the correction. eg. The buoyancy of lead is much different from that of feathers.

• This is the correct answer. For analytical measurements, the buoyancy error should be accounted for. In general, what you're weighing will have a different density than the standard masses. Hence, calibration will fail to account for this effect (electronic balance or otherwise). SWHC also provide references (DOI: 10.1021/ed061p51, DOI: 10.1021/ac50021a062) which are very pertinent. I recommend to add a bit more detail to your answer to make it better received. – Linear Christmas Oct 22 '17 at 21:18

No, they don't have to be. I believe the electronic balance is calibrated for buoyancy under the current pressure of air when you 'tare' the scale.

If you have a scale that measures down to the mg you can test this yourself. Tare the scale with a syringe, and then create a vacuum with the syringe and lock it off. If you reweigh the syringe it will read as a negative mass, due to the loss of air in the syringe! I've done this myself to calculate the density of air.

• I recommend trying to weigh a helium or hydrogen filled balloon on any analytical scale you choose... – Curt F. Oct 22 '17 at 21:51