When I go through the OP's question and comments by my collogues, it's evident that OP is not simply satisfied with the comments even though andselisk's comment is the clearly answer to OP's major concern in laboratory safety. So I thought this answer may be good enough to satisfy OP's concern about the quote from University of Berkley website, which states:
Both nitric and perchloric acids are incompatible with organic acids (such as acetic acid) and should not be stored together.
According to California State University (Northridge) website, the following reduction potentials for the given half reactions have been listed:
$$\ce{CO2 (g) + 2H+ + 2e- <=> HCOOH} \qquad E^\circ =\pu{-0.114 V} \tag1$$
$$\ce{HClO + H+ + e- <=> 1/2Cl2 (g) + H2O} \qquad E^\circ =\pu{+1.630 V} \tag2$$
$$\ce{ClO4- + 2H+ + 2e- <=> ClO3- + H2O} \qquad E^\circ =\pu{+1.226 V} \tag3$$
$$\ce{NO3- + 2H+ + e- <=> 1/2N2O4 (g) + H2O} \qquad E^\circ =\pu{+0.798 V} \tag4$$
According to equations $(1)$ and $(3)$ (formic acid and perchloric acid mixture):
$$\ce{ClO4- + HCOOH -> CO2 (g) + ClO3- + H2O} \qquad E^\circ_\mathrm{cell} =\pu{+1.340 V} \tag5$$
Thus, according to the redox equation $(5)$, a mixture of formic acid and perchloric acid would react spontaneously to produce gaseous product $(\ce{CO2})$ slowly to increase pressure in (obviously) closed containers, which is a safety hazard.
Similarly, according to equations $(1)$ and $(4)$ (formic acid and nitric acid mixture):
$$\ce{2NO3- + 2H+ + HCOOH -> N2O4(g) + CO2(g) + 2H2O} \qquad E^\circ_\mathrm{cell} =\pu{+0.921 V} \tag6$$
Therefore, according to the redox equation $(6)$, a mixture of formic acid and nitric acid would also react spontaneously to produce two gaseous products $(\ce{CO2} \text{ & } \ce{N2O4})$ slowly to increase pressure in (obviously) closed containers, which is even a higher safety hazard considering toxic nature of $\ce{N2O4}$.
Further, according to equations $(1)$ and $(2)$, formic acid and hypochlorous acid mixture in acidic conditions also a hazardous mixture. I mentioned this here because we commonly use bleach solution $(\ce{NaClO})$ to oxidized organic compounds in undergraduate teaching labs.
Late edit:
The carbonic acid mentioned in my answer is formic acid. I could not find the reduction potential for acetic acid. However, I assumed it should be in close proximity to formic acid according to Wikipedia, which has listed the half reaction of acetic acid in biological systems as follows:
$$\ce{CH3COOH + 2H+ + 2e- <=> CH3CHO + H2O} \qquad E^\circ = \pu{-0.58 V} \tag7$$
Yet, Mithoron's comment, "Acetic is nowhere near as easily oxidizable. It's the formyl group in formic that makes it reactive.," made me think about it a little further. For example, let's look at acetic acid in nitric acid situation. The redox reaction (from equations $(4)$ and $(7)$) is:
$$\ce{2NO3- + 2H+ + CH3CHO <=> CH3COOH + N2O4(g) + H2O} \qquad E^\circ_\mathrm{cell} = \pu{1.378 V} \tag8$$
This means a mixture of acetaldehyde and nitric acid is spontaneously making a gaseous mixture, not acetic acid and nitric acid!
Note: According to some educators, ChatGPT has some issues on accuracy (Ref.1).
References:
- Brandon J. Yik and Amber J. Dood, "ChatGPT Convincingly Explains Organic Chemistry Reaction Mechanisms Slightly Inaccurately with High Levels of Explanation Sophistication," J. Chem. Educ. 2024, 101(5), 1836–1846 (https://doi.org/10.1021/acs.jchemed.4c00235).
