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Sample Calculation for a mixture of crystalline silica:

Figure I:1-14 from TED 1.15 Chapter 1 Appendix I:1-5.

Two consecutive samples from the same employee taken from a combined exposure to crystalline silica dusts have the following results:

 
Sample Sampling period (Min.) Total volume (Liters) Respirable weight (mg) Respirable concentration (mg/m3) Laboratory results (%)
A 238 405 0.855 2.1 5.2 quartz

2.3 cristobalite

ND tridymite
B 192 326 0.619 1.9 4.8 quartz

1.7 cristobalite

ND tridymite
Total 430 731 1.474    

ND = Non Detected


Calculation of the TWA from the sampling and analytical data:

Step No. 1: Calculate the percentage of quartz, cristobalite, and tridymite in the respirable particulate collected


a. Quartz:
 
Percentage = [(weight of quartz in Sample A) + (weight of quartz in sample B)] x (100)
Total weight of respirable particulate collected
     

  = [0.052(0.855 mg) + 0.048(0.619 mg)] x (100)
(0.855 mg + 0.619 mg)

0.044 mg + 0.03 mg x (100)
1.474 mg
= 0.074 mg x (100)
1.474 mg
= 0.05(100) = 5%


b. Cristobalite:
Percentage = [(wt. of cristobalite in sample A) + (wt. of Cristobalite in sample B)] x (100)
Total weight of respirable particulate collected
     

  = [0.023(0.855 mg) + 0.017(0.619 mg)] x (100)
1.474 mg
     

  = [0.020 mg + 0.011 mg] x (100)
1.474 mg

0.031 mg x (100)
1.474 mg
= 0.021(100) =  2.1% =  2%



c. Tridymite: None Detected = 0%
Step No. 2 : Calculate the PEL for the mixture (use the formula in the OSHA Technical manual Appendix I-1.5)
 
 
PEL(mixture) = 10 mg/m3
[% quartz + 2(% cristobalite) + 2(%tridymite) + 2]
   
   

   
  = 10 mg/m3
[5.0 + 2(2.0) + 2(0) + 2]
   
   

   
  = 10
11
= 0.91 mg/m3


Step No. 3: Calculate the employee's exposure to respirable dust

 
Exposure = (sample weight A + Sample weight B)
Total volume of air sampled
   
 
  = (0.855 mg + 0.619 mg)
731 liters (1 m3/1000 liters)  
   
 
  = 2.0 mg/m(3)


Step No. 4: Adjust (where necessary) for sampling period less than 8-hours. Assume a zero exposure time for the sampling period remaining.

 
Adjusted Exposure = (2.0 mg/m3)(430 minutes) + 0(50 minutes)
480 minutes
   
   

   
  = 2.0 mg/m3(430 minutes)
480 minutes
= 1.8 mg/m3


Step No. 5: Calculate the Severity of the exposure:

 
Severity = Adjusted Exposure
PEL (mixture)
   
   

   
  = (1.8 mg/m3)
(0.91 mg/m3)
= 2.0


Subject to SAE considerations, if the result from Step 5 is greater than 1.0 then an overexposure to the mixture of crystalline silica exists.

End of this page.

Last Updated on March 4, 1997 by Mike C. Rose