Question

The balance says that you have weighed out 1.023 g of tris tostandardize a solution of HCl. Use the buoyancy correction in Section 2-3 and the density in Table 11-4 to determine how many grams you have really weighed out. The volume of HCl required to react with the tris was 28.37 mL. Does the buoyancy correction introduce a random or a systematic error into the calculated molarity of HCl? What is the magnitude of the error expressed as a percentage? Is the calculated molarity of HCl higher or lower than the true molarity?

Short answer

The true mass of the tris that is really weighed out is calculated as 1.0238g.

The error caused by buoyancy correction in molarity is ascertained to be a systematic error.

The error is expressed in percentage error as\(0.08\% \).

The molarity of HCl calculated is lower than the true molarity.

Step-by-step solution

Definition of molarity, random errors, and systematic errors.

Air has buoyancy due to which an object weighs less in the air than and it is not the same as it does in a vacuum. Buoyancy correction is made to obtain the accurate measurement of the object weighed which is the difference between the density of the object and the density of the weights that have been used to calibrate the balance.

Molarity is one of the parameters used to express the concentration of a solution. It is expressed as,

\({\rm{Molarity}} = \frac{{{\rm{ number of moles of solute }}}}{{{\rm{ volume of solution in L}}}}\)

Random errors are errors in experimental measurements due to unknown and unexpected alterations in the experiment caused by the surrounding conditions of the instrument.

Systematic errors are errors caused by inappropriate handling of instruments.

Percentage error is calculated as,

\(\% {\rm{ error }} = \frac{{{\rm{ theoretical value }} - {\rm{ experimental value }}}}{{{\rm{ theoretical value }}}} \times 100\)

 The mass of the cleaner and errors.

Mass of tris weighed is given as\(1.023\;{\rm{g}}\).

Using the buoyancy correction and density able given in the textbook, the true mass of tris that was weighed is calculated as,

\(\frac{{(1.023)\left( {1 - \frac{{0.0012}}{{8.0}}} \right)}}{{1 - \frac{{0.0012}}{{1.33}}}} = 1.0238\;{\rm{g}}\)

This error in buoyancy is termed is a Systematic error caused by errors in weighing balance.

The percentage error in molarity of HCl calculated using theoretical weight measurement of tris is given as

\(\begin{array}{c}{\rm{\;\% error}} = \frac{{1.0238 - 1.023}}{{1.023}} \times 100\\ = 0.08\% \end{array}\)

As the true mass of tris weighed is greater than that of the measured mass, so the molarity of HCl calculated is lower than that of the true molarity