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A very common analytical method for detection of more than 70 elements is ICP-OES (Wikipedia page). But apparently, it's not suited for some substances (cited from this paper, section 6.2, page 12):

The elements that are not usually determined by ICP/OES fall into three basic categories. The first category includes those elements that occur either as trace contaminants in the argon gas used in the ICP/OES ($C$ from $CO_2$), constituents of the sample solvent ($C$, $O$, $H$), or as contaminants from the environment or atmosphere ($N$ for example). The second category encompasses those elements that require high excitation energy, such as the halogens. These elements could be determined with poor LOD, however. The third category is the family of short-lived radioactive elements that are commonly determined by $\gamma$-ray spectrometry.

So, apparently, when I'm working with, say carbon-based fuels, and I want to determine $C$ contents, ICP-OES would not be the method of choice, at least not the standard variety. So, what else would be the typical choice? Or are there modifications to ICP-OES, such as using very pure $Ar$, or $He$, as the plasma gas and sealing the plasma chamber from the atmosphere?

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For N:

Total N = N from NO2 + N from NO3 + Total Kjeldahl N

The methods from here are:

Liquid Chromatography: NO2, NO3

Specific electrodes: NO3, Kjeldahl

Spectrophotometry: NO2

This for water including wastewater. I don't know the aplicability for other samples.

Also ICP-MS is worth researching.

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The analytical method preferred for CHNO (and also S, X, etc) determination is elemental analysis, usually by combustion.

For example, if a molecule has the generic formula $\ce{C_wH_xN_yO_z}$, combustion would produce:

$$\ce{C_wH_xN_yO_z + (w +\frac{x}{4}+\frac{y}{4}+\frac{z}{2})O2 -> wCO2 + \frac{x}{2}H2O +\frac{y}{2}N2}$$

Determining the masses of $\ce{CO2}$, $\ce{H2O}$, and $\ce{N2}$ given off by the combustion is the first step in determining how much carbon, hydrogen, and nitrogen was in the original sample. The remaining mass is oxygen.

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