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Why do major websites such as NASA and Wikipedia discuss the composition of the earth's atmosphere in terms of percentage by volume instead of percentage by amount of substance? Isn't the percentage composition by volume undefined since all gases in the atmosphere occupy 100% volume of it?

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    $\begingroup$ It's easier for me to understand there is 78% by volume of $\ce{N2}$ in the atmosphere rather than in molar fraction because every constituants have different molar mass. And also everybody (even those who never studied chemistry) is able to understand what is a volume fraction in an easy way. And I would add but not sure and no possible for me to do the calculation right now but the volume fraction of gases will be much less affected by a variation of temperature rather than the molar fractions. (but not sure) just idea. $\endgroup$ – ParaH2 Jun 7 '18 at 16:52
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    $\begingroup$ Percentage composition by volume will assume ideal gas behavior. Then for 78% by volume of $\ce{N2}$ 78 out of 100 molecules of gas will be $\ce{N2}$. $\endgroup$ – MaxW Jun 7 '18 at 17:11
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Let's be clear on what percent by volume means. If I say component $X$ is 25% by volume of a mixture of $X$ and $Y$, with a total volume of 1 L, it does not mean there is some 250 mL portion of the mixture that is solely occupied by $X$. That wouldn't be a mixture. It doesn't even mean that if I mentally subdivide that 1 L mixture into tiny identical cubes, one for each atom or molecule, then 1/4 of those cubes are occupied by atoms or molecules of $X$.

Instead, all it means is that I can prepare 1 L of the mixture by mixing some volume $V_X$ of $X$ and 3 times that volume ($V_Y = 3 V_X$) of Y. There's not even any guarantee that $V_X = \pu{250 mL}$, since sometimes volumes are non-additive, that is, $V_X + V_Y \neq \pu{1 L}$.

Now as it happens, for ideal gases, which the atmosphere is close to being, you can mentally subdivide the volume into tiny little equal-sized cubes, one for each atom or molecule in the mixture, and on average there would be one atom/molecule of $X$ in each fourth cube if $X$ is 25% by volume of the mixture. (I emphasize "on average" because of course since the gas atoms or molecules are continuously moving around randomly, they will bunch up and spread out momentarily all the time, so at any given instant there may be zero or many more than one $X$ atom/molecule per tiny cube.) Real mixtures in the liquid state often have at least some nonideality, e.g. even in a dilute solution of $\ce{NaCl}$ in water, you will find "structure" in the solution, with the $\ce{Na+}$ cations and $\ce{Cl-}$ anions surrounded by a fairly fixed arrangement of $\ce{H2O}$ molecules, almost like a tiny piece of clathrate, so a mental arrangement of tiny boxes is an even less accurate atomic-scale description of the solution.

In short, the percent by volume description of a mixture is only a way to characterize the amount of material that goes into it, it is not intended as any kind of implication of what the mixture looks like at the atomic scale.

As for why NASA reports the composition of the atmosphere by percent by volume: probably because it's closest to the actual experiments done to measure it. You would typically measure the composition of a gas mixture by physically separating it (e.g. by lowering the temperature until each gas liquefied) and then measuring the volume of each component. You certainly could from those measurements easily calculate a percent by moles, but – why? You introduce a calculational step between the measurement and what you report, and scientists tend to prefer getting original data, right what comes from the instrument, if possible, as a way of avoiding even the smallest risk of some error introduced in calculation.

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Yes, the composition by volume is defined for mixtures.

According to ISO 80000 Quantities and units — Part 9: Physical chemistry and molecular physics, the volume fraction of substance $\mathrm{B}$ is defined as $$\varphi_\mathrm B=\frac{x_\mathrm BV_\mathrm{m,B}^*}{\sum\limits_i{{x_i}V_{\mathrm m,i}^*}}$$ where
$V_\mathrm{m,B}^*$ is the molar volume of the pure substances at the same temperature and pressure and
$x_i$ denotes the amount-of-substance fraction of substance $i$.

The IUPAC Quantities, Units and Symbols in Physical Chemistry (Green Book) uses the simple but similar definition $$\phi_\mathrm B=\frac{V_\mathrm B}{\sum\limits_i{V_i}}$$ where
$V_\mathrm B$ and $V_i$ are the volumes of appropriate components prior to mixing.

IUPAC also notes that other definitions are possible and that the term should not be used in accurate work without spelling out the definition.

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