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According to IUPAC, only physical quantities and variables must be italicised.

Section 8 Use of Italic and Roman Fonts for Symbols in Scientific Text of ICTNS Guidelines for Drafting IUPAC Technical Reports and Recommendations states that

a good general rule is that quantities, or variables, can be given a value, but labels cannot.

So why is it that [X] is not written as [X] when the concentration of species X is a physical quantity?

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  • $\begingroup$ Do you refer to [] as the chemical notation of cencentration? Or do you refer to one of the many other notations? $\endgroup$ – mhchem Nov 26 '19 at 8:12
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The overall rule” [1, p. 7] in

  1. The overall rule is that symbols representing physical quantities or variables are italic

a keyword here meaning that not every symbol of a physical quantity should be italicized. Chemical element symbols are always upright unless they are used to denote a locant in a name of a chemical substance [1, pp. 8–9]:

  1. Symbols for elements in the periodic system shall be roman. […]

  2. Symbols for physical quantities are single, or exceptionally two letters of the Latin or Greek alphabet, but they are frequently supplemented with subscripts, superscripts or information in parentheses to specify further the quantity. Further symbols used in this way are either italic or roman depending on what they represent. […]

[…]

  1. […] Letter symbols for elements are italic when they are locants in chemical-compound names indicating attach­ments to heteroatoms, e.g. О-, N-, A-, and P-. The italic symbol H denotes indicated or added hydrogen.

For example, amount concentration of nitrate can be displayed as $c_\ce{NO3-}$, $c(\ce{NO3-})$ or $[\ce{NO3-}]$, where “$c$” is italicized as a symbols for physical quantity, whereas “$\ce{NO3-}$” is upright as it is a specification with its own typography rules.

As for the general use of brackets in written text, according to Wikipedia

In English, typographers mostly prefer not to set brackets in italics, even when the enclosed text is italic.

Further, from Bringhurst' The elements of typographic style [2, p. 85]:

The sloped square brackets usually found on italic fonts are, if anything, even less useful than sloped parentheses. If, perish the thought, there were a book or film entitled The View from My [sic] Bed, sloped brackets might be useful as a way of indicating that the brackets and their contents are actually part of the title. Otherwise, vertical brackets should be used, no matter whether the text is roman or italic: “The View from My [sic] Bed” and "the view from my [sic] bed."

Similarly, from The Chicago Manual of Style (for earlier edition see this answer on English.SE):

6.5 Parentheses and brackets in relation to surrounding text. Parentheses and brackets should appear in the same font—roman or italic—as the surrounding text, not in that of the material they enclose. This system, though it may occasionally cause typefitting problems when a slanting italic letter touches a nonslanting roman parenthesis or bracket, has two main virtues: it is easy to use, and it has long been practiced.

Specifically for use in technical documentation and in mathematical notations, brackets could be treated as a notation for operator (like matrix delimiters) [4, p. 316], yet another reason to use roman typeface:

6.2.5.3 Special Bracket Notation for Specific Operators

[…]

  • Brackets only should be used to indicate chemical concentrations: $[\ce{S^2-}];$ $[\ce{Na+}];$ and isotopic prefixes: $[\ce{^{32}P}]\text{AMP}.$

The following comparison between the symbols fro amount concentration and specific optical rotatory power illustrates the problems arising from using italicized brackets, namely uneven spacing and clashing symbols:

$$ \begin{align} &[\ce{^{7}NO3-}] &\quad &\textit{[}\ce{^{7}NO3-}\textit{]} \\ &[α]_λ^θ &\quad &\textit{[}α\textit{]}_λ^θ \end{align} $$

References

  1. IUPAC “Green Book” Quantities, Units, and Symbols in Physical Chemistry, 3rd ed.; Cohen, R. E., Mills, I., Eds.; IUPAC Recommendations; RSC Pub: Cambridge, UK, 2007. ISBN 978-0-85404-433-7.
  2. Bringhurst, R. The Elements of Typographic Style, 3rd ed.; Hartley & Marks, Publishers: Point Roberts, WA, 2004. ISBN 978-0-88179-206-5.
  3. The Chicago Manual of Style, 17th ed.; University of Chicago Press: Chicago; London, 2017. ISBN 978-0-226-28705-8.
  4. The Manual of Scientific Style: A Guide for Authors, Editors, and Researchers, 1st ed.; Rabinowitz, H., Vogel, S., Eds.; Elsevier/Academic Press: Amsterdam; Burlington, MA, 2009. ISBN 978-0-12-373980-3.
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