Question

Dental amalgam is a mixture of mercury, silver, tin, and copper. You need to veryify the Hg content of fillings by gravimetric analysis using HgS precipitation. In a preliminary experiment, you find that fillings contain 42.5 % Hg by weight. How large a sample of amalgam (in grams) would be needed to achieve 4 ppt accuracy? Your balance is a standard analytical balance readable to 0.0001 g.

Answer 1

Step 1: magnitude of the relative error

To achieve 4 ppt accuracy in a sample measured in grams, we must know that a ppt unit means that we have a wrong mass unit for every trillion (10¹²) of mass units. If we use the gram as the reference, we will use the relationship:

And 4 ppt will be:

Converting the percent result into ppt units:

Then, an accuracy of 4 ppt is a very strict condition for the analysis

Step 2: The relative error

The relative error of a mass measurement in a gravimetric analysis is given by the expression:

(1)

Where x is the result and m is the mass measured.

We know that

(2)

Because this is the expected accuracy in the result.

For the mass measurement, the balance is able to read a mass of 0.0001 g. Then, every result can be 0.0001 g more or less than the reported value. It is the absolute error:

(3)

Step 3: Calculations

Substituting (2) and (3) in equation (1):

Solving for m:

Remember that:

We have:

The mass of the sample must be 25*10⁶ g to achieve a tiny error of 4 ppt in a sample with 4.25*10¹¹ ppt of Hg