A pharmaceutical preparation of pH 6.2 is preserved with substance A (pKa 8.5). If the preservative effect is due to the undissociated molecule determine the per cent of active preservative present in the preparation.
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To determine the percent of active preservative present in the pharmaceutical preparation, we need to consider the pH of the solution and the pKa of the preservative substance.
The pKa of a substance refers to the pH at which half of the substance is in its acidic form and half is in its basic form. In this case, the pKa of substance A is given as 8.5.
We also know that the pH of the pharmaceutical preparation is 6.2. pH is a measure of acidity, with lower values indicating higher acidity. pH 6.2 is lower than the pKa of substance A (8.5), indicating that the pH is more acidic than the pKa.
When the pH is lower than the pKa, it means that the majority of the substance exists in its acidic form rather than its basic form. In other words, in this case, most of substance A is in its undissociated form, which is the active form responsible for its preservative effect.
To determine the percent of active preservative, we use the Henderson-Hasselbalch equation, which is given by:
pH = pKa + log([A-]/[HA])
Where [A-] is the concentration of the basic form and [HA] is the concentration of the acidic form.
In this case, since the pH (6.2) is lower than the pKa (8.5), the concentration of [A-] will be negligible compared to [HA]. Therefore, we can approximate that [A-] is close to zero, and the equation becomes:
pH = pKa + log([HA]/[A-]) ≈ pKa + log([HA]/0)
Since log(0) is undefined, this tells us that [A-] is negligible and [HA] is close to the total concentration of substance A in the preparation.
Therefore, the percent of active preservative can be estimated as the concentration of substance A in the preparation.
For an exact percentage, you would need to know the concentration of substance A in the preparation. If that information is not provided, it is not possible to calculate the exact percentage. However, based on the given information and the pH being lower than the pKa, we can conclude that the percent of active preservative is high, and most of substance A is present in its undissociated form.