Dilutions and Propagation of Uncertainty
- Page ID
- 280644
\( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)
\( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)
\( \newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\)
( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\)
\( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\)
\( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\)
\( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\)
\( \newcommand{\Span}{\mathrm{span}}\)
\( \newcommand{\id}{\mathrm{id}}\)
\( \newcommand{\Span}{\mathrm{span}}\)
\( \newcommand{\kernel}{\mathrm{null}\,}\)
\( \newcommand{\range}{\mathrm{range}\,}\)
\( \newcommand{\RealPart}{\mathrm{Re}}\)
\( \newcommand{\ImaginaryPart}{\mathrm{Im}}\)
\( \newcommand{\Argument}{\mathrm{Arg}}\)
\( \newcommand{\norm}[1]{\| #1 \|}\)
\( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\)
\( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\AA}{\unicode[.8,0]{x212B}}\)
\( \newcommand{\vectorA}[1]{\vec{#1}} % arrow\)
\( \newcommand{\vectorAt}[1]{\vec{\text{#1}}} % arrow\)
\( \newcommand{\vectorB}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)
\( \newcommand{\vectorC}[1]{\textbf{#1}} \)
\( \newcommand{\vectorD}[1]{\overrightarrow{#1}} \)
\( \newcommand{\vectorDt}[1]{\overrightarrow{\text{#1}}} \)
\( \newcommand{\vectE}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash{\mathbf {#1}}}} \)
\( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)
\( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)
In-Class Worksheet
You didn’t forget about quantitative analysis, did you?
Concentration units:
Complete the following (problem taken from Harris textbook)
- How many grams of nickel are contained in 10.0 g of a 10.2 wt % solution of nickel sulfate hexahydrate NiSO4.6H2O (formula mass, FM 262.85)
Define Mass % of “A” →
Define parts per million (ppm) aqueous and non-aqueous→
Define parts per billion (ppb) aqueous and non-aqueous→
Dilutions:
- Calculate the concentration of Copper in ppm if 0.1035 grams of copper metal is dissolved in a few mL’s of concentrated nitric acid then diluted to the mark with water in a 100.0 mL volumetric flask.
(assume ppm = 1µg/g = 1µg/mL)
- How many microliters of the standard above are needed to make 10.0 mL of an aqueous 1.0 ppm Cu solution? Assume as above.
- How many grams of lead (II) nitrate are needed to make a 100.0 mL solution at 1000. ppm lead?
- Vanillin, a chemical in vanilla beans that is used for vanilla flavoring, has an absorbance wavelength maximum of 352 nm. Rather than buying a bottle of vanilla extract, you have decided to make your own bottle by placing 2.134 g of vanilla beans in a 200.0 mL volumetric flask and diluting to volume with Vodka. Assuming 100% yield from the extraction (soaking at room temperature for 1 month), to determine the concentration of vanillin in the beans, you plotted the absorbance of vanillin standards vs. their concentration in units of mg/L in a 1.00 cm cuvette. A least-squares analysis of the standard curve gave a best-fit line of y = 0.0265x - 0.0002.
Upon extraction in the vanillin, you performed two dilutions: First, you took a 5.00 mL aliquot of the stock solution and diluted to 25.0 mL with Vodka to make solution B. Second, you took a 1.00 mL aliquot of solution B and diluted to 10.00 mL with Vodka to make solution C. The absorbance at 352 nm of solution C, when placed in a 1.00 cm cuvette, was determined to be 0.147.
- What is the concentration of vanillin in solution C in units of mg/L? (Show your work)
- What is the concentration of vanillin in solution B in units of mg/L? (Show your work)
- What is the concentration of vanillin in the original extract solution in units of mg/L? (Show your work)
- What is the concentration of vanillin in the vanilla beans in units of mg/g? (Show your work)
- What is the concentration of vanillin in solution C in units of mg/L? (Show your work)
Propagation of Uncertainty:
- What is the overall result with its propagated uncertainty for the following:
\[(1.24 ±0.06) + (0.34 ± 0.02) + (8.19 ± 0.04)\nonumber\]
- What is the overall result with its propagated uncertainty for the following:
\[\dfrac{(0.0023 ± 0.0002) \times (10.00 ± 0.05)}{0.103 ± 0.005}\nonumber\]
Contributors and Attributions
- Kyle Cissell, San Francisco State University (kacissel@sfsu.edu)
- Sourced from the Analytical Sciences Digital Library