While I cannot give insight into how to actually synthesize sulfuric acid to produce the one that you need I can tell you that different synthesis methods lead to different ratios of cis/trans isomers for sulfuric acid. Furthermore several articles have been written on using computer models to understand how it occurs.
Sulfuric acid has a tendency to form hydrates, the acids will produce small clusters containing a few water molecules. At 298 K and 50% relative humidity, a cluster with one sulfuric acid will contain about 1.5 waters (this estimate is based on equilibrium constants measured by Hanson and Eisele. [Hanson, D. R.; Eisele, F. L. J. Phys. Chem. A 2000, 104, 1715] Also the critical cluster has been measured and it contains from 7 to 13 sulfuric acids at a relative humidity of 2.3-15.3%.6 At 236 K and ca. 50% reltive humidity, the critical cluster should have 4 or 5 SAs. Thus, it is important to understand the acid-water and acid-acid interactions in clusters having several SAs to gain some insight of this nucleation process.
The manner in which sulfuric acid is prepared affects how these hydrates are formed. More importantly the ratio of the cis and trans structures of the hydrated sulfuric acid clusters depends on the how sulfuric acid is synthesized and not on the purity of the acid. There is some research on the various isomeric structures of the hydrated clusters of sulfuric acid, H2SO4(H2O)n (n = 1-5). It turns out that Due to the small energy difference between trans and cis conformations about two OH groups of sulfuric acid, there are three types of isomeric forms of the hydrated clusters of sulfuric acid which involve the proton nontransferred trans conformer, the proton transferred trans conformer, and the proton nontransferred cis conformer of sulfuric acid. In the case of transoid H2SO4, the proton transferred ion-pair structures become more stable than the proton nontransferred structures as the number of water molecules increases. The hydrated clusters of the cis conformation remain neutral hydrogen-bonded structures even if the number of water molecules increases. All stable clusters tend to form multi-cyclic structures. While both protons of sulfuric acid participate in cyclic hydrogen bonding in the neutral structures, the OH group of HSO4- in the ion-pair structures remains dangling because the counterion H3O+ prefers to make strong hydrogen bonds with water molecules and/or the HSO4- moiety. Take a look at the following 20 year old article Kurdi, L.; Kochanski, E. Chem. Phys. Lett. 1989, 158, 111
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