Mathematics Question

Learning Goal: I’m working on a mathematics case study and need a sample draft to help me learn.

After your initial review of the operations and safety data sheets (SDS), you have determined the sampling you want to perform at Acme Automotive Parts (AAP). The table below lists hazards you want to sample and the sampling/analytical methods you decide to use. You can access the National Institute for Occupational Safety and Health (NIOSH) methods at and the Occupational Safety and Health Administration (OSHA) methods at .


Possible Method

Occupational Exposure Limits (OEL)

Manganese Fume (Welding)

NIOSH 7302

5 mg/m3 (OSHA Ceiling)

Copper Fume (Welding)

NIOSH 7302

0.1 mg/m3 (OSHA 8-hour TWA)

Lead Fume (Welding)

NIOSH 7302

0.05 mg/m3 (OSHA 8-hour TWA)

1,2,4 trimethylbenzene (Paint)

OSHA 1020

25 ppm (ACGIH 8-hour TWA TLV)

Toluene (Paint)

OSHA 111

50 ppm (ACGIH 8-hour TWA TLV)

Xylene (Paint)

OSHA 1002

100 ppm (OSHA 8-hour TWA)

Metal Working Fluids

NIOSH 5524

0.5 mg/m3 (NIOSH 10-hour TWA REL)

Noise (throughout plant)


90 dBA (OSHA 8-hour TWA)

Choose one hazard from the welding area, one hazard from the paint area, and the metal working fluids, and prepare one paragraph for each hazard (three paragraphs in total) answering each of the following questions:

  1. Which sampling media will you be using?
  2. What flow rate will you use?
  3. How will you calibrate the sampling train?
  4. Calculate the minimum sampling time you will require to be able to detect concentrations at the OELs listed in the table. Show your work in calculating the sampling times.
  5. Will you collect personal or area samples? Explain why.
  6. Are there any compounds listed in the method that might interfere with your sample?
  7. Are there any special storage or shipment requirements for your samples?

Prepare one paragraph that concludes how you would evaluate noise exposures in the facility. Discuss what type of sampling instrument you would use, how you would perform calibration, whether you would use personal or area samples, and which areas at the facility you would include in the evaluation.

For this assignment, you will use the formula provided in the Sampling Duration section in Chapter 6 of the textbook. You need to find the limit of detection in the sampling method and choose an occupational exposure limit to use the formula. See the PowerPoint presentation in the study guide for an example.

Your assignment must be a minimum of two pages in length, not including title or reference pages. Your assignment must use at least two references. One must be gathered from the CSU Online Library; the other may be your textbook. All references and in-text citations must be formatted according to APA standards.

For the welding and paint areas, you will need to consult the listed Method and locate the Limit of Detection. Be sure the units for the LOD are consistent with the Occupational Exposure Limit.

For the welding data, you will not need to convert to milligrams per cubic meter.

For the paint data, you will need to convert parts per million to milligrams per cubic meter.

The sequence of calculations is as follows:

Get all units of measure to be in milligrams (or micrograms) per cubic meter of air.

To be able to convert parts per million to milligrams/micrograms per cubic meter of air you need the molecular weight of the compound (you can Google this or locate it in the Method).

Use the following equation to convert ppm to mg/m3:

X mg/m3 = (# ppm this is the exposure limit from the table) times (molecular weight from Google or Method))/24.45

To get required sampling time to reach the Limit of Detection you use:

# mg/m3 (from above) = Limit of Detection (from Method) divided by (X liters or volume needed) x (1 cubic meter/1000 liters conversion factor)

Solve for X and multiply by the sampling rate to get number of minutes.

X liters = LOD divided by mg/m3

Make sure your units are consistent!!


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