# Dilutions and Propagation of Uncertainty

In-Class Worksheet

You didn’t forget about quantitative analysis, did you?

## Concentration units:

Complete the following (problem taken from Harris textbook)

1. 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:

1. 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)

1. 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.

1. How many grams of lead (II) nitrate are needed to make a 100.0 mL solution at 1000. ppm lead?

1. 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.

1. What is the concentration of vanillin in solution C in units of mg/L? (Show your work)

2. What is the concentration of vanillin in solution B in units of mg/L? (Show your work)

3. What is the concentration of vanillin in the original extract solution in units of mg/L? (Show your work)

4. What is the concentration of vanillin in the vanilla beans in units of mg/g? (Show your work)

## Propagation of Uncertainty:

1. What is the overall result with its propagated uncertainty for the following:

$(1.24 ±0.06) + (0.34 ± 0.02) + (8.19 ± 0.04)\nonumber$

1. What is the overall result with its propagated uncertainty for the following:

$\dfrac{(0.0023 ± 0.0002) \times (10.00 ± 0.05)}{0.103 ± 0.005}\nonumber$