Propagation of Error in Preparing Solutions

Suppose  you have a bottle of 53.4% w/w NaOH (the density of which is 1.52 g/mL) from which you are to prepare a 1.000-L solution of 0.534 M NaOH.  Two obvious ways to prepare the solution are: (1) weigh out an appropriate amount of the stock solution of NaOH and dilute to volume; and (2) measure out an appropriate volume of the stock solution of NaOH and dilute to volume.  Which method will yield the most precisely known final molarity?  You may assume that the uncertainty in the stock solution’s concentration is ±0.4% w/w and that the uncertainty in the stock solution’s density is ±0.01 g/mL.  You also may assume that the formula weight for NaOH (39.9971 g/mol) is known exactly and that the digital pipet used to measure volume has an uncertainty of ±0.10 mL.

About the Author

ASDL Contributor

David Harvey

Professor of Chemistry & Biochemistry at DePauw University

David T. Harvey is a Professor Emeritus of Chemistry and Biochemistry at DePauw University in Greencastle, Indiana, where he has been a dedicated faculty member since 1986. Over his nearly four-decade career, Dr…
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