Salt Forms and Free-Drug-Equivalent Solubility Inputs

Why Salt-Form Concentrations Need Careful Interpretation

A salt form can dissolve rapidly and produce a high measured concentration of drug-related material. That result is useful, but it does not automatically describe the equilibrium solubility of the parent drug. A report may give the mass of the whole salt, the mass of parent drug represented by that salt, or the molar concentration of salt formula units. Those quantities are not interchangeable.

The distinction matters when assigning a physicochemical input for a PBPK model. A concentration measured shortly after adding a soluble salt may reflect rapid dissolution before the parent drug precipitates. Treating that transient value as the parent drug’s equilibrium solubility can overstate the concentration that remains dissolved after equilibration. Earlier material on intrinsic solubility and pH-dependent total solubility establishes why pH and the relevant solid phase matter; here the emphasis is on interpreting salt-form measurements and their concentration basis.

Definition: A parent-drug equivalent is the amount of parent-drug moiety represented by a measured amount of a salt. Its molar concentration counts parent moieties, not salt formula units; its mass concentration is the mass of parent drug alone, excluding counterions and water of crystallization. “Free-drug equivalent” in this context does not mean unbound drug or neutral drug.

Converting Salt Mass to Parent-Drug Equivalents

A salt formula unit may contain one or more parent-drug moieties. Let \(M_s\) be the molecular weight of the salt formula unit, including its counterion or counterions and any specified waters of crystallization. Let \(M_p\) be the molecular weight of the parent drug, and let \(\nu\) be the number of parent-drug moieties per salt formula unit. If the reported concentration \(C_s\) is a mass concentration of that salt, then dividing by \(M_s\) gives moles of salt formula units per volume. Multiplying by \(\nu\) gives moles of parent-drug moieties per volume.

C_{p,\mathrm{eq,molar}} = \nu\frac{C_s}{M_s}

The parent-equivalent mass concentration follows by multiplying the parent-equivalent molar concentration by \(M_p\). The same relationship can be written as a mass conversion:

C_{p,\mathrm{eq,mass}} = C_s\frac{\nu M_p}{M_s}

These equations assume that the reported mass concentration is genuinely expressed as the specified salt form, that the salt stoichiometry and formula mass are known, and that the assay value refers to the material dissolved rather than merely the amount added. If an assay already reports concentration “as parent” or “parent equivalent,” applying this salt-to-parent conversion again would count the conversion twice.

Key distinction: Conversion changes the basis for expressing an amount. It does not establish whether that amount is at equilibrium, whether it represents neutral drug, or how much drug is unbound.

Worked Example: Converting a 1:1 Hydrochloride Concentration

Suppose a hypothetical assay reports 6.00 mg/mL of an anhydrous 1:1 hydrochloride salt. The parent drug has \(M_p=250.00\ \mathrm{g/mol}\), the salt has \(M_s=286.46\ \mathrm{g/mol}\), and there is one parent moiety per formula unit (\(\nu=1\)). Convert the reported concentration to molar and mass parent-drug equivalents.

First express the reported salt concentration in grams per litre: \(6.00\ \mathrm{mg/mL}=6.00\ \mathrm{g/L}\). The salt formula-unit concentration is

C_s = \frac{6.00\ \mathrm{g/L}}{286.46\ \mathrm{g/mol}} = 0.0209453\ \mathrm{mol/L}

Because each formula unit contains one parent moiety, the parent-equivalent concentration is \(0.0209453\ \mathrm{mol/L}\), or \(20.9453\ \mathrm{mmol/L}\). Its parent-equivalent mass concentration is

C_{p,\mathrm{eq,mass}} = 0.0209453\ \mathrm{mol/L}\times250.00\ \mathrm{g/mol} = 5.23633\ \mathrm{g/L} \approx 5.236\ \mathrm{mg/mL}

The salt assay therefore corresponds to about \(20.95\ \mathrm{mmol/L}\) of parent moieties, or \(5.236\ \mathrm{mg/mL}\) of parent drug by mass. Neither result, by itself, says that this concentration is the parent drug’s equilibrium solubility.

Stoichiometry and Hydrates

The counterion and any waters of crystallization contribute to the salt formula mass, but they do not contribute parent-drug moieties. Stoichiometry matters just as much as formula mass: for a salt containing two parent moieties per formula unit, each mole of salt represents two moles of parent. Omitting either factor gives an incorrect parent-equivalent concentration.

Worked Example: A Hydrated Salt With Two Parent Moieties

Consider a hypothetical hydrated salt whose formula unit contains two parent-drug moieties, one counterion unit, and one water molecule. Let \(M_p=180.00\ \mathrm{g/mol}\), counterion-unit mass \(116.07\ \mathrm{g/mol}\), and water mass \(18.015\ \mathrm{g/mol}\). Its formula mass is \(2(180.00)+116.07+18.015=494.085\ \mathrm{g/mol}\). If an assay reports \(1.50\ \mathrm{mg/mL}\) of this salt, find the parent-equivalent molar and mass concentrations.

Convert the assay concentration to \(1.50\ \mathrm{g/L}\), then calculate salt formula units:

C_s = \frac{1.50\ \mathrm{g/L}}{494.085\ \mathrm{g/mol}} = 0.00303591\ \mathrm{mol/L}

There are two parent moieties per formula unit, so

C_{p,\mathrm{eq,molar}} = 2(0.00303591\ \mathrm{mol/L}) = 0.00607183\ \mathrm{mol/L}

The parent-equivalent mass concentration is \(0.00607183\ \mathrm{mol/L}\times180.00\ \mathrm{g/mol}=1.09293\ \mathrm{g/L}\), or approximately \(1.093\ \mathrm{mg/mL}\). The hydrate water and counterion are included in \(M_s\), but not in the parent-equivalent mass. Using the anhydrous salt formula mass for this hydrate would overestimate the moles represented by a given weighed mass.

Equilibrium Solubility Is Not the Same as Salt Dissolution

Solubility is an equilibrium property only when the conditions and solid phase are specified. A useful equilibrium-solubility result identifies the medium, temperature, pH or pH-control conditions, and the solid phase present at equilibrium. It also requires enough time for the relevant dissolution and precipitation processes to approach equilibrium, with a measurement procedure that distinguishes dissolved material from undissolved solid.

When a salt dissolves, its ions may separate in solution; the dissolved parent moiety need not remain as an intact salt molecule. If the solution becomes supersaturated with respect to a less soluble parent-drug solid, that solid can precipitate. A measurement taken before precipitation may therefore give a high, time-dependent concentration. If the system is later equilibrated with the parent solid at a controlled pH, the total dissolved parent concentration can be lower. The concentration at equilibrium depends on the specified conditions and solid phase, not just on the initial salt mass or its dissolution rate.

Worked Example: Interpreting an Early Salt-Dissolution Result

In a hypothetical experiment, \(10.0\ \mathrm{mg/mL}\) of an anhydrous 1:1 hydrochloride salt dissolves rapidly. The parent has \(M_p=300.00\ \mathrm{g/mol}\), and the salt has \(M_s=336.46\ \mathrm{g/mol}\). At 10 minutes, the dissolved concentration is reported on a salt-mass basis. After equilibration at controlled pH with parent-drug solid present, a separate measurement gives \(0.900\ \mathrm{mg/mL}\) of dissolved parent, reported as parent mass. What do the results show?

The early salt concentration is \(10.0\ \mathrm{g/L}\). Its parent-equivalent molar concentration is

C_{p,\mathrm{eq,molar}} = \frac{10.0\ \mathrm{g/L}}{336.46\ \mathrm{g/mol}} = 0.0297212\ \mathrm{mol/L}

The corresponding parent-equivalent mass concentration is \(0.0297212\ \mathrm{mol/L}\times300.00\ \mathrm{g/mol}=8.91636\ \mathrm{g/L}\), or \(8.916\ \mathrm{mg/mL}\). This is the amount of parent moiety represented by the early dissolved salt; it is not an equilibrium value merely because it has been converted to parent units.

The later measurement is already expressed as parent mass, so it should not be converted from salt mass. It is \(0.900\ \mathrm{g/L}/300.00\ \mathrm{g/mol}=0.00300\ \mathrm{mol/L}\) of parent moieties. Under the stated equilibrium conditions, this is the result relevant to the parent-solid equilibrium measurement. The contrast with the early result is consistent with a high initial dissolved concentration followed by precipitation or other equilibration; the numbers alone do not establish the detailed mechanism.

Practical Checks Before Using a Solubility Input

A PBPK input should preserve both the chemical identity and the measurement meaning of the source value. Before using a reported number, check whether its units are salt mass, parent-equivalent mass, or molar concentration; whether the molar basis is formula units or parent moieties; and whether hydrates or solvates are included in the stated formula mass. Also determine whether the assay measured material actually dissolved, and whether the result was collected at equilibrium or at a specified early time.

Several observations should prompt caution: visible precipitate, a concentration that falls with time, pH drift during dissolution, a value that depends strongly on filtration or sampling time, or a report that omits the solid phase and concentration basis. These are not proof that a result is unusable, but they limit what can be inferred from it. In particular, an early dissolution concentration may be useful for describing a dissolution experiment while remaining unsuitable as an equilibrium-solubility input.

Reported result	Appropriate interpretation	Do not infer automatically
Mass concentration of a specified salt	Convert with salt formula mass and parent stoichiometry to parent equivalents.	That the value is parent equilibrium solubility.
Concentration explicitly reported as parent equivalent	Use the stated parent basis, checking the assay definition.	That it should be converted from salt mass a second time.
Early concentration after salt addition	A time-specific dissolution or apparent-concentration result.	That it persists after equilibration.
Equilibrium concentration with conditions and solid phase stated	An equilibrium result for those stated conditions and that solid phase.	That the same value applies at a different pH, temperature, or solid phase.

The main alternative to a salt-mass conversion is to use an assay that already quantifies dissolved parent drug on a parent-equivalent basis. That avoids converting the salt mass, but it does not remove the need to establish whether the measurement is an equilibrium result. Conversely, a salt-mass assay can be converted rigorously when the formula and stoichiometry are known, but conversion alone cannot repair missing equilibrium information. These approaches answer different questions: one establishes the amount of parent moiety represented; the other establishes what was dissolved under the measurement conditions.

Derivation and Common Pitfalls

The conversion follows directly from counting formula units. A volume \(V\) containing salt mass \(m_s\) contains \(m_s/M_s\) moles of salt formula units. Each formula unit contains \(\nu\) parent moieties, so the amount of parent is \(\nu m_s/M_s\) moles. Dividing by \(V\) gives the molar concentration formula. Multiplication by \(M_p\) then gives parent mass per volume:

\frac{m_s}{V} \left(\frac{1\ \mathrm{mol\ salt}}{M_s\ \mathrm{g\ salt}}\right) \left(\frac{\nu\ \mathrm{mol\ parent}}{1\ \mathrm{mol\ salt}}\right) \left(\frac{M_p\ \mathrm{g\ parent}}{1\ \mathrm{mol\ parent}}\right) = \frac{m_s}{V}\frac{\nu M_p}{M_s}

The units cancel to mass of parent per volume, which also checks the basis of the result. This derivation assumes that the salt formula represents the weighed material and that the assay concentration is on a salt-mass basis. If the material is a hydrate but an anhydrous formula mass is used, the calculated formula-unit concentration is too high for a given measured mass. If \(\nu\) is omitted for a salt containing multiple parent moieties, the parent amount is too low by that stoichiometric factor.

A frequent error is to reason, “The salt dissolved to \(10\ \mathrm{mg/mL}\), so the parent drug’s solubility is \(10\ \mathrm{mg/mL}\).” This is wrong because the reported mass may include counterion and water, and because the measurement may be early rather than at equilibrium. The correction is to identify the reported mass basis, convert to parent equivalents if needed, and separately verify whether the measurement represents equilibrium under the conditions relevant to the input.

Key takeaway: Salt-to-parent conversion answers “how much parent moiety does this salt concentration represent?” Equilibrium-solubility interpretation answers “how much parent-related material remains dissolved at equilibrium under specified conditions?” A reliable input requires keeping those questions separate.

Check Your Understanding

For each item, identify the concentration basis and show how it should be interpreted.

A 1:1 salt has \(M_s=310.00\ \mathrm{g/mol}\) and \(M_p=250.00\ \mathrm{g/mol}\). An assay reports \(3.10\ \mathrm{g/L}\) salt. What are the parent-equivalent molar concentration and mass concentration? Solution: \(3.10/310.00=0.0100\ \mathrm{mol/L}\) salt; with \(\nu=1\), this is \(0.0100\ \mathrm{mol/L}\) parent. Parent mass is \(0.0100\times250.00=2.50\ \mathrm{g/L}\).
A salt formula unit contains two parent moieties. An assay reports \(0.00200\ \mathrm{mol/L}\) of salt formula units. What is the parent-equivalent molar concentration? Solution: \(2\times0.00200=0.00400\ \mathrm{mol/L}\) parent moieties.
An assay already reports \(1.20\ \mathrm{mg/mL}\) “as parent.” Should the value be multiplied by the parent-to-salt mass fraction? Solution: No. It is already on a parent-mass basis; applying that conversion again would be a double conversion. Verify the assay’s stated basis, but do not treat it as salt mass without evidence.
A soluble salt gives a high concentration at 5 minutes, followed by visible parent-drug precipitate and a lower stable dissolved concentration. Which result is automatically the parent equilibrium solubility? Solution: Neither is automatically suitable without checking the conditions and solid phase. The early result is time-specific and may be transient; the later result is more consistent with equilibration, but must still be interpreted with its pH, temperature, and solid phase specified.