ppmv(stuff 1) = ppmw * spgr(stuff 1)/spgr(of the solution)

I like to look at formulas with the worst case to see if they make sense.  Suppose the stuff had infinite mass and tiny volume.  It could be 99% of the mass and .001% volume, the formula creates that.  And ther reverse no minimal mass huge volume.

It is not possible to directly convert a liquid mixture from/to ppmw and ppmv units. Firstly, to clear up any uncertainty, I assume you are talking about a mixture of two liquid, and not one liquid plus a solid or gas. The reason for my statement is that doing this type of "conversion" implies that the liquid volumes are simply additive. For many liquid-liquid systems, this would NOT be a good assumption. Mixing water and ethanol, for example, is not ideal, and the volume of the resulting mixture is not the sum of the two liquid volumes.

To put some numbers together for the sake of illustration, let's say we mix 100 liters of pure ethanol with 100 liters of pure water and ended up with 195 liters of ethanol-water mixture. What is the volume fraction of ethanol? Would it be 100/195? If you think "yes", then is the volume fraction of water also 100/195?
HTH,
Doug

Ok, I think I'm with you.  More background - our lab is providing ppmw S in gasoline (or diesel for that matter) and a process analyzer is giving it as ppmv.  We are trying to reconcile the two values

It sounds as if the process analyzer was designed for use in gas service. Reporting sufur in a liquid hydrocarbon stream as ppmw is the correct way of reporting in my view. If you vaporize all of a sample of the liquid, then you will have a vapor which can be analyzed and reported on a ppmv basis. In this case, you would be analyzing the vapor constituents of the stream, such as H2S, SO2, etc.

You should note that ppmv and ppm on a mole basis are one and the same.

Doug