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Pressure can be measured in $\pu{mmHg}$ which is equal to the pressure exerted by a “column of mercury” of a height expressed in $\pu{mm},$ at $\pu{0 °C}$ under Earth’s normal gravity.

Does the diameter of a tube that contains the mercury affect how high the mercury will rise? Why isn’t pressure measured in $\pu{mmHg^3}$ or some other unit of volume of mercury?

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    $\begingroup$ The diameter does not matter, which also answers your second question. That's just how pressure works. $\endgroup$
    – Ivan Neretin
    Commented Apr 13, 2020 at 20:09
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    $\begingroup$ Mercury barometersare typically scaled in millimeters, mm, which refers to the height of the column of mercury. The height of the column not only depends on the air pressure but also gravity. Here in US it is common for the barometric pressure to be reported in inches. Old timers like me also know "mm Hg" as the unit "torr." The pascal (symbol: Pa) is the SI derived unit of pressure which is now used by scientists. $\endgroup$
    – MaxW
    Commented Apr 13, 2020 at 20:10
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    $\begingroup$ @Zenix Please double-check authoritative sources before editing. AMA Manual of Style leans toward "mm Hg". However, SI brochure, IUPAC Green Book and ACS Style Guide suggest to avoid space and use "mmHg". Since Chemistry.SE tends to adhere to the international standards, we go with the latter. And neither "$\pu{mm^3Hg}$" nor "$\mathrm{0°C}$" was correct, which you didn't address in your edit. $\endgroup$
    – andselisk ♦
    Commented Apr 13, 2020 at 22:05
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    $\begingroup$ Consider diving in the water. For every ten meters, pressure increases by about one atmosphere (~100 kPa). Would it make any difference in pressure if one were to dive in a swimming pool or in a large lake? Ignoring the greater density due to dissolved salts, what about in the Pacific Ocean? $\endgroup$
    – DrMoishe Pippik
    Commented Apr 14, 2020 at 0:32
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    $\begingroup$ @Zenix I just pointed out what else could be improved, not your faults, and no, the rollback is merely an event in editing history and doesn't affect your reputation in any way:) $\endgroup$
    – andselisk ♦
    Commented Apr 14, 2020 at 10:55

2 Answers 2

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History and because of how pressure works

The original reason why mm of Hg are used is because of how chemists first started to measure and understand atmospheric pressure. The idea of the vacuum and atmospheric pressure is surprisingly new. Otto von Guericke demonstrated the power of atmospheric pressure by showing that two horses could not separate a brass sphere containing a partial vacuum only in the 17th century (remember a vacuum doesn't suck the atmosphere pushes).

This kicked off a vast amount of experimentation. Around the same time scientists like Torricelli and Pascal realised that they could measure atmospheric pressure by filling a closed tube with mercury and inverting it in a bath of mercury (you can do this with any fluid but mercury is about 13 times denser than water so the tube only needs to be a meter or so long; with water it needs to be ~10m long which is an inconvenient length in an indoor laboratory). The height of the mercury in the tube is a measure of the external pressure as a vacuum is formed above it in the closed tube. This simple instrument was used by a friend of Pascal to show that atmospheric pressure drops with height when he took a barometer up France's Puy de Dome mountain.

The diameter of the tube is irrelevant as pressure is weight/area (do the calculations and tube diameter cancels out).

We now call a tube like this a barometer. And the height the mercury rises to is a convenient measure of atmospheric pressure and can be read off using a simple ruler. We could use mm of water, but would need a much longer tube and an unusually inconveniently sized ruler. Hence why mercury is the fluid and a convenient way of measuring pressure is mm of Hg.

We tend to use modern SI units for pressure these days, not least because the wide use of mercury has been banned and calculations in consistent units are far easier.

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[OP] Does the diameter of a tube that contains the mercury affect how high the mercury will rise?

Surprisingly perhaps, it doesn't. This means that the shape of the vessel does not matter either, or whether it goes straight up or diagonally.

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Source: https://www.tec-science.com/mechanics/gases-and-liquids/pressure-in-liquids-hydrostatic-pressure/

Traditionally, this is a physics topic, even though pressure is an important variable in chemistry.

[OP] Why isn’t pressure measured in mmHg3 or some other unit of volume of mercury?

It is awkward to have a unit that looks like a length yet has the dimensions of force per area. There is an alternate name for the unit, Torr, that is less confusing. If you express the SI unit for pressure, pascal, in base units, you get $$1 \pu{Pa} = 1 \pu{kg m-1 s-2}$$ so the dimension of length in the denominator. However, after taking the time to think about the dimensions of acceleration, force, and pressure, it all makes perfect sense.

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