Your text presents an example of propagation of error through a dilution operati

Question

Your text presents an example of propagation of error through a dilution operation (p.19). Assume that the relative uncertainty of the commercial solution is the same as in the example and that the dilution still yields a final concentration of 1000. ppb.

Recalculate the uncertainty in ppb if the relative uncertainty of the syringe is 0.00681 and the uncertainty of the volumetric flask is 0.0597 mL. The total volume of the flask is still 250.0mL. Report the +/- value in ppb and to 1 decimal place. Don't type in the "=/-" or units, just the number.

Explanation / Answer

Uncertainty in volume = 0.0597 mL.

Volume of the flask = 250.0 mL.

Relative uncertainty in volume, u(v) = 0.0597 mL/250.0 mL = 0.0002388

Relative uncertainty in syringe, u(s) = 0.00681

Let the relative uncertainty in ppb be u(c). Therefore, u(c) = u(v)2 + u(s)2 = (0.00681)2 + (0.0002388)2 = 0.006814

Uncertainty in ppb = (0.006814)*(1000 ppb) = 6.814 ppb 6.8 ppb

The uncertainty in ppb = 6.8 (ans).

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