Question

Propagation of error: Determine the uncertainty in the concentration if you dissolved 0.500 ± 0.001 g of NaCl in the average glass pipet volume determined above. Use the SD of the volume and propagation of error rules to perform this calculation. Report the concentration and uncertainty both in terms of Molarity and ppm for Na+

Average is 24.9 mL and SD is 0.030

I get 0.34 +/- 0.002 for molarity but I don't know how to solve for ppm, Please help! Thanks.

Answer 1

Amount of NaCl=0.500 ± 0.001 g

average volume of pipet=24.9ml

SD=0.030

So volume of pipet=24.90.030

Average concentration= Average g of NaCl/average volume of pipet=0.500g/24.9ml=0.02008 g/ml

So uncertainty= sqt of [(0.001/0.5)^2 + (0.030/24.9)^2] * average conc=Sqrt [0.000004+0.00000144] * 0.02008=0.00233*0.02008=0.000047

0.02008+/-0.000047 g/ml

Convert to ppm

[Average concentration =0.02008g/ml=20.08 mg/ml=20.80mg/10^-3L=20080 mg/L=20080 ppm

First multiply by 1000 as 1g=1000mg and then multiply by 1000 again as 1ml=10^-3L)

(1ppm=1mg/L)]

now average conc=20080ppm

so we had to multiply it by 10^6

uncertainty also has to be multiplied by same constant

[ error rule : R+R, R=c *X then R=c* X)

uncertainty=0.000047*10^6=47

So concentration=20080+/- 47 ppm

propagation of error rule for multiplication by constant says