Minimum resolution to acquire exact mass on a spectra from m/z peak
In mass spectrometry, resolution and mass accuracy are distinct yet related concepts.  Eliding the difference between the two often causes confusion.


  I'm having a little difficulty with finding what the minimum resolution required to obtain the exact mass of a 400 m/z peak on a mass spectrometry spectra is.


Resolution is a concept that always involves at least two chemical species that differ in $m/z$.  It doesn't make sense to talk about resolution if you are talking about a single ion.

Mass accuracy is a concept that more or less assumes there is a single chemical species at a single $m/z$.  It's very easy to define: how different is a measured $m/z$ from the correct $m/z$?

Now, due to the presence of multiple stable isotopes for most elements commonly seen in organic mass spectrometry, almost no compound will give rise to a single chemical species with a single $m/z$ value.  If your compound ionizes to give singly charged ions ($z=1$), these isotopologues will be separated by approximately 1 $m/z$.

A nice coincidence among commonly occurring elements in organic chemistry ($\ce{CHNOPS}$) is that the lightest stable isotope is by far the most abundant.  (This isn't true of $\ce{Cl}$, $\ce{Br}$, $\ce{Fe}$ though.)  For molecules as small as 400 Daltons, this means that the most abundant isotopologue will be (a) the lightest of all possible isotopologues, and (b) monoisotopic.

Thus, to get an accurate mass (really accurate $m/z$) measurement of an compound you'll need a resolution that is better than unit mass resolution.  

However, you won't necessarily need a much greater resolution than that.  A lot depends on your sample.  Can you assume that there is only one chemical compound present that gives an $m/z$ of 400 Da?  If so, then even "low resolution" mass spectrometers can give very accurate masses.  However, if your sample is complex or contains other compounds that give ions very close to and $m/z$ of 400, then you will need more resolving power to separate the contaminating ions from your peak of interest.  In that case, it's impossible to say how much resolving power you need without specifying what the contaminants are.

For example, say your compound is $\ce{C29H37N}$, for example, maybe it's N-(3,3,3-triphenylpropyl)octan-1-amine.  In electrospray mass spectrometry it ionizes as $\ce{(C29H37N + H)+}$ at an $m/z$ of 400.3010.  If that was the only compound in your sample, then even old TOF instruments with resolutions as low as 2000 would suffice to obtain an accurate mass.  However, if there was also some $\ce{C26H41NS}$ in your sample, say 1,6-dimethyl-4-pentadecylquinoline-2-thione, its $\ce{(C26H41NS + H)+}$ ion would have an $m/z$ of 400.3043.  That would mean you would need a resolution of at least 122,000 to tell those two peaks apart, generally available only on Orbitrap or FT-ICR instruments.  But if there was no such contaminant in your sample, you wouldn't need that degree of resolution.