# Dilutions and Volumetric Glassware

Learning Objectives

Following this activity, students should be able to:

• Determine volumes and concentrations in dilution calculations.
• Convert between different concentration units (e.g., ppm to M).
• Interpret a procedure for making a particular solution and assess the advantages of different dilution schemes.
• Choose the appropriate piece of glassware to ensure the desired level of precision of a particular solution.
• Compare the tolerance of various pieces of glassware.

## In the lab…

Ellen is doing an analysis of cadmium that requires a set of cadmium solutions ranging from 0.5 – 1.5 ppm. These solutions are called calibration standards and will be used to calibrate the atomic absorption spectrometer so unknown cadmium concentrations in water samples can be determined. She takes the following steps:

1. A 1000 ppm Cd solution was prepared by dissolving the necessary amount of Cd(NO3)2 in 100.00 mL of water. This is called the stock solution.
2. Solution A was prepared by diluting 5.00 mL of the 1000 ppm stock solution to a final volume of 50.00 mL.
3. Solution B was prepared by diluting solution A to a volume of 100.00 mL so the final solution contained 5.00 ppm Cd.
4. Solutions C – E were prepared from various amounts of Solution B using 50.00-mL flasks. Their concentrations are 0.5, 1.0 and 1.5 ppm Cd.

1. Sketch a cartoon or schematic illustrating the dilution procedure.

Solution

Cd Solution diluted

Volume used (mL)

Diluted Volume (mL)

Solution concentration (ppm Cd)

Solution concentration (M Cd)

A

Stock

5.00

50.00

B

Solution A

100.00

5.00

C

Solution B

50.00

0.500

D

Solution B

50.00

1.000

E

Solution B

50.00

1.500

1. How much Cd(NO3)2 should be used to prepare the stock solution? The molar mass of Cd(NO3)2 is 246.42 g/mol and Cd is 112.41 g/mol. Note: Concentration units pertain to just the solute that follow them, Cd not Cd(NO3)2.

1. Working together, determine the ppm Cd in Solution A.

1. Distribute missing entries in the third column among your group and determine the volume of each solution diluted to prepare solutions B – E. Share your results with your group members.

1. Determine how to convert from ppm Cd to M Cd and then complete the last column of the table.

1. What is the concentration of NO3- in Solution B in M? What is the concentration of NO3- in Solution B in ppm?

1. Which unit do you prefer for concentration? What do you think the benefits are of each?

There are several factors to keep in mind when preparing solutions:

• The accuracy and precision of glassware is essential to consider when preparing solutions.
• Graduated cylinders do not have the accuracy and precision of pipets.
• Glass transfer pipets are more precise than measuring (Mohr) pipets.
• The volume of glassware is only valid at the temperature printed on it. Using it at a different temperature is introducing some error into the measurement.
• A balance must be reached between maximizing accuracy and conserving materials. Keep in mind:
• Relative uncertainty is reduced with larger volume glassware.
• In general, fewer dilution steps are preferred because each step introduces some uncertainty.
• Serial dilutions are sometimes necessary for low concentrations.
• Waste disposal and analytical standards can be expensive.

## Sorting out Glassware

1. Label the types of glassware below.

1. Which pieces of glassware should be labeled “TC” (to contain) or “TD” (to deliver)?

1. What design feature do the most accurate pieces of glassware have in common? What role do you think this plays in allowing accurate volumes to be measured?

1. What type of glassware would be best for Ellen to use for the dilutions determined above?

1. Suppose Ellen only has 5.00-mL, 10.00-mL and 20.00-mL Class A transfer pipets available in her lab, but based on her calculations she needs a 15.00-mL pipet to make Solution E. Which action do you recommend for preparing Solution E?
1. Omit Solution E from her set of calibration standards.
2. Use a 20.00-mL pipet to make solution E, updating her lab notebook to reflect the change in concentration.
3. Use a 20.00-mL pipet to make solution E, but use a 5.00-mL pipet to remove the excess before diluting to volume in the flask.
4. Use a 10.00-mL pipet and a 5.00-mL pipet together.

## Tolerance

Tolerance is the permissible deviation from a specified value. All volumetric glassware has some tolerance for accuracy – that is, all glassware contains or delivers volumes that can be slightly different from the stated volume that is printed on the glassware. This (incomplete) table shows the tolerances for Class A volumetric flasks.

Capacity (mL)

Tolerance (mL)

% Relative Tolerance

10

±0.02

50

±0.05

0.10

100

±0.08

0.08

250

±0.12

500

±0.20

0.04

1000

±0.30

2000

±0.50

1. Would you expect the tolerance of a Class B flask to be greater or less than that of a Class A?

1. Consider a 100-mL volumetric flask. What is the maximum and minimum volume that could be contained in each of these flasks?

1. One way to represent the uncertainty in the volume contained in the flask is to use the % relative tolerance. Write a formula for calculating % relative tolerance for the volumetric flasks.

1. Assign the missing entries in the table to each group member. Share your results to complete the table.

1. As a group, compare the % relative tolerance for different size volumetric flasks. What happens to the % relative tolerances as the volume of the flask increases?

1. For optimum accuracy, do you recommend choosing a larger or smaller sized flask? On what do you base this decision?

1. As a group, brainstorm a list of experimental circumstances under which it would be advantageous to choose a smaller volumetric flask over a larger flask.

1. Based on your discussion, would you recommend Ellen make any changes to the flasks she uses to prepare her standards? Keep in mind cadmium is a toxic heavy metal that can be expensive to dispose of properly.