Answer to Question #125041 in Algebra for Nicole

Question

The purity of medicines is of concern for the industry, the regulator and the public. It is therefore import to regularly test the purity of medicinal compounds. A sample of paracetamol (acetaminophen) from a pharmaceutical manufacturer was analysed by dissolving 20.0mg of sample in 2ml of methyl alcohol and then bringing this solution to a total volume of 100ml with water. The sample was then analysed using a UV-Visible Spectrophotometer and the result compared with that of the same test performed on the same amount of a paracetamol standard known to be 100% pure. The test sample gave a reading of 0.0549 absorbance units while the standard gave a reading of 0.0558.

What is the quantity of paracetamol in the test sample and what is its percentage purity?

Answer 1

Solution.

From the condition of the question, we know that the standard sample (100% pure) gave a reading of 0.0558.

Let x - part of paracetamol in the test sample. And it gave a reading of 0.0549.

Part of paracetamol in the standard sample = 100% / 100 = 1.

From this conditions we will get a proportion:

$1/x=0.0558/0.0549$

Now by multiplying across we will get:

1 * 0.0549 = x * 0.0558

Now dividing two parts by 0.0558 we will get:

0.0549 / 0.0558 = x

$x≈0.98$

We know, that it was analysed 20.0 mg of sample. To find the quantity of paracetamol in the test sample we will multiply the part of paracetamol in the test sample by the quantity of sample:

x * 20 = 0.98 * 20 = 19.6 mg

To find percentage purity of the test sample we multiply part of paracetamol in the test sample by 100:

x * 100 = 0.98 * 100 = 98%

Answer: the quantity of paracetamol in the test sample is 19.6 mg, and its percentage purity is 98%.