you will need a particular acid:base ratio to make the reaction proceed as required

something like this https://www.omnicalculator.com/chemistry/henderson-hasselbal...

What do you mean by base conversion?
Changing numeral bases, such as converting from base 2 (binary) to base 10 (decimal). - https://en.wikipedia.org/wiki/Change_of_base
a base is a substance which dissociates in aqueous solution to form Hydroxide ions OH−. - https://en.wikipedia.org/wiki/Base_(chemistry)
System of Units (SI).
Amount nX is an elementary quantity, converting the elementary unit [x] into the SI base unit mole [mol] using the Avogadro constant NA. - https://www.bioblast.at/index.php/Amount_of_substance
The SI unit of concentration (of amount of substance) is the mole per cubic meter (mol/m3). - https://www.nist.gov/pml/owm/si-units-amount-substance
Stoffmenge f (genitive Stoffmenge, plural Stoffmengen). - (chemistry) mole (amount of substance). - https://www.dict.cc/?s=Stoffmenge
converted amount of substance base

in British English
NOUN
a measure of the number of entities (atoms, molecules, ions, electrons, etc) present in a substance, expressed in moles - https://www.collinsdictionary.com/dictionary/english/amount-...

I think they're saying you need to like adjust the quantities based on whatever the (new) base may be. Think of it like a recipe. On the package it says how to make it for 4 people, but if you make it for 2 people, you need to half all the ingredients. So your new base in this case would be 2 people. But in this case the "base", is also a dependent variable, which is why it says umgerechnet. So there is some calculation, the answer of which determines the "base". And then the quantity (Menge) that this phrase is talking about will presumably be some function (multiple or whatever (or calculation in this case better word)) of that (new) base.

I wouldn't want to use the etymology of base twice, so unless you can use a different word for the German "Base" here like "baseline amount" or something I would probably go for something like:
according to / as per (entsprechend) the base-adjusted quantity
OR a little more wordy:
as per the new quantity calculated given the new baseline / base
OR perhaps most elegantly:
according to the new quantity / amount / volume adjusted for the base / baseline

German term (edited): auf die Base umgerechneten Menge

Zunächst einige Erklärungen:

Die unedelsten Metalle (oft ebenfalls Basenbildner genannt) bilden die stärksten Basen, d. h. diese unterliegen bei der Auflösung in Wasser vollständiger elektrolytischer Dissoziation in die Metallkationen und Hydroxid-Ionen.
Zu den starken Basen gehören Kalilauge, Natronlauge, Barium-, Calcium- und Strontiumhydroxid, zu den mittelstarken Silberoxid (bildet mit Wasser ein – allerdings nicht rein herstellbares – Hydroxid, AgOH), zu den schwachen dagegen Ammoniumhydroxid, Magnesiumhydroxid usw.
:
Einwertige Basen können mit einwertigen Säuren nur neutrale, mehrwertige Basen dagegen auch basische Salze bilden, wenn die Neutralisation unvollständig ist. Neutralisations-, Protolyse- und Pufferungsvorgänge spielen sich ständig im lebenden Organismus ab, siehe Säure-Basen-Gleichgewicht…
:
Einwertige Basen können mit einwertigen Säuren nur neutrale, mehrwertige Basen dagegen auch basische Salze bilden, wenn die Neutralisation unvollständig ist.
:
Übersetzungen:
E bases
F bases
I basi
S bases
https://roempp.thieme.de/lexicon/RD-02-00317?searchterm=base...

Bei der Neutralisation reagiert eine Base mit einer Säure zu einem Salz und Wasser. Die Bestandteile in der Säure (Oxonium-Ionen) und der Base (Hydroxid-Ionen), die ihre sauren bzw. alkalischen Eigenschaften ausmachen, reagieren miteinander zu Wasser.
https://de.wikipedia.org/wiki/Salzbildungsreaktion

Die Stöchiometrie (von gr. στοιχεῖον stoicheion „Grundstoff“ und μέτρον metron „Maß“) ist ein grundlegendes mathematisches Hilfsmittel in der Chemie. Mit ihrer Hilfe werden aus der qualitativen Kenntnis der Reaktanten und Produkte einer Reaktion die tatsächlichen Mengenverhältnisse (Reaktionsgleichung) und Stoffmengen berechnet. In der chemischen Umgangssprache bezeichnet Stöchiometrie nicht die (meist triviale) Berechnung, sondern deren Ergebnis.
https://de.wikipedia.org/wiki/Stöchiometrie

Stoichiometry is not only used to balance chemical equations but also used in conversions, i.e., converting from grams to moles using molar mass as the conversion factor, or from grams to milliliters using density. For example, to find the amount of NaCl (sodium chloride) in 2.00 g, one would do the following:
[formule] = 0.0342 mol
In the above example, when written out in fraction form, the units of grams form a multiplicative identity, which is equivalent to one (g/g = 1), with the resulting amount in moles (the unit that was needed), as shown in the following equation
:
The following steps would be used:
1. Write and balance the equation
2. Mass to moles: Convert grams of Cu to moles of Cu
3. Mole ratio: Convert moles of Cu to moles of Ag produced
4. Mole to mass: Convert moles of Ag to grams of Ag produced
https://en.wikipedia.org/wiki/Stoichiometry

chemical equation is the symbolic representation of a chemical reaction in the form of symbols and chemical formulas. The reactant entities are given on the left-hand side and the product entities on the right-hand side with a plus sign between the entities in both the reactants and the products, and an arrow that points towards the products to show the direction of the reaction.[1] The chemical formulas may be symbolic, structural (pictorial diagrams), or intermixed. The coefficients next to the symbols and formulas of entities are the absolute values of the stoichiometric numbers.
https://en.wikipedia.org/wiki/Chemical_equation

Now to the question (expressed in German und improved):
"Die Menge einer bestimmten Substanz wird im Verhältnis zu der in die Basis umgerechneten Menge angegeben".
=>
"The quantity of a given substance is expressed as a ratio of the quantity converted to the base".

The quantity unit is secondary for this question, it is usually given in mol or gram.

(Or free base equivalent)

I assume they did some sort of titration to figure out the amount of the compound.

For example, they titrated it with NaOH. They recorded how much NaOH was needed to reach the endpoint and then used this to calculate the amount of the compound of interest.

[0070] For administration of pharmaceutically acceptable salts of the above compounds, the weights indicated above refer to the weight of the acid equivalent or the base equivalent of the therapeutic compound derived from the salt.
https://data.epo.org/publication-server/document?iDocId=3129...