Should the pH of the sample be adjusted even for samples in acidic media?

The pH of the assay solution after the sample is added should be the same as that of the assay buffer that is supplied with the kit.
Low sample volumes (e.g. 0.1 mL) are not likely to affect the pH of the assay solution and therefore may not require pH adjustment.
Samples above 0.1 mL are more likely to affect the pH of the assay solution and therefore the pH of these samples should be adjusted as described in the data booklet, prior to addition to the assay.

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