As a successful purification scheme is carried out, the specific activity of a desired enzyme may decrease, though the samples are enriched in the desired enzyme. This is because specific activity is calculated per mg of protein, and often mg protein decreases as the scheme progresses.

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Both sentences are false. Specific activity should increase as purification progresses because it indicates the amount of enzyme activity per mg of protein, and purification aims to remove other proteins, increasing the proportion of the desired enzyme.

As a Successful Purification Scheme Is Carried Out, the Specific