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# 2.8: Problems


1. Indicate how many significant figures are in each of the following numbers.

a. 903

b. 0.903

c. 1.0903

d. 0.0903

e. 0.09030

f. 9.03 $$\times$$ 102
2. Round each of the following to three significant figures.

a. 0.89377

b. 0.89328

c. 0.89350

d. 0.8997

e. 0.08907
3. Round each to the stated number of significant figures.

a. the atomic weight of carbon to 4 significant figures

b. the atomic weight of oxygen to 3 significant figures

c. Avogadro’s number to 4 significant figures

d. Faraday’s constant to 3 significant figures
4. Report results for the following calculations to the correct number of significant figures.

a. 4.591 + 0.2309 + 67.1 =

b. 313 – 273.15 =

c. 712 $$\times$$ 8.6 =

d. 1.43/0.026 =

e. (8.314 $$\times$$ 298)/96 485 =

f. log(6.53$$\times$$10–5) =

g. $$10^{–7.14} =$$

h. (6.51 $$\times$$ 10–5) $$\times$$ (8.14 $$\times$$ 10–9)
5. A 12.1374 g sample of an ore containing Ni and Co is carried through Fresenius’ analytical scheme, as shown in Figure 1.1.1. At point A the combined mass of Ni and Co is 0.2306 g, while at point B the mass of Co is 0.0813 g. Report the weight percent Ni in the ore to the correct number of significant figures.

6. Figure 1.1.2 shows an analytical method for the analysis of Ni in ores based on the precipitation of Ni2+ using dimethylglyoxime. The formula for the precipitate is $$\ce{Ni(C4H7N2O2)2}$$. Calculate the precipitate’s formula weight to the correct number of significant figures.

7. An analyst wishes to add 256 mg of Cl to a reaction mixture. How many mL of 0.217 M BaCl2 is this?

8. The concentration of lead in an industrial waste stream is 0.28 ppm. What is its molar concentration?

9. Commercially available concentrated hydrochloric acid is 37.0% w/w HCl. Its density is 1.18 g/mL. Using this information calculate (a) the molarity of concentrated HCl, and (b) the mass and volume, in mL, of a solution that contains 0.315 moles of HCl.

10. The density of concentrated ammonia, which is 28.0% w/w NH3, is 0.899 g/mL. What volume of this reagent should you dilute to $$1.0 \times 10^{3} \text{ mL}$$ to make a solution that is 0.036 M in NH3?

11. A 250.0 mL aqueous solution contains 45.1 μg of a pesticide. Express the pesticide’s concentration in weight-to-volume percent, in parts per million, and in parts per billion.

12. A city’s water supply is fluoridated by adding NaF. The desired concentration of F is 1.6 ppm. How many mg of NaF should you add per gallon of treated water if the water supply already is 0.2 ppm in F?

13. What is the pH of a solution for which the concentration of H+ is $$6.92 \times 10^{-6} \text{ M}$$? What is the [H+] in a solution whose pH is 8.923?

14. When using a graduate cylinder, the absolute accuracy with which you can deliver a given volume is ±1% of the cylinder’s maximum volume. What are the absolute and the relative uncertainties if you deliver 15 mL of a reagent using a 25 mL graduated cylinder? Repeat for a 50 mL graduated cylinder.

15. Calculate the molarity of a potassium dichromate solution prepared by placing 9.67 grams of K2Cr2O7 in a 100-mL volumetric flask, dissolving, and diluting to the calibration mark.

16. For each of the following explain how you would prepare 1.0 L of a solution that is 0.10 M in K+. Repeat for concentrations of $$1.0 \times 10^{2} \text{ ppm } \ce{K+}$$ and 1.0% w/v K+.

a. KCl

b. K2SO4

c. K3Fe(CN)6

17. A series of dilute NaCl solutions are prepared starting with an initial stock solution of 0.100 M NaCl. Solution A is prepared by pipeting 10 mL of the stock solution into a 250-mL volumetric flask and diluting to volume. Solution B is prepared by pipeting 25 mL of solution A into a 100-mL volumetric flask and diluting to volume. Solution C is prepared by pipeting 20 mL of solution B into a 500-mL volumetric flask and diluting to volume. What is the molar concentration of NaCl in solutions A, B and C?

18. Calculate the molar concentration of NaCl, to the correct number of significant figures, if 1.917 g of NaCl is placed in a beaker and dissolved in 50 mL of water measured with a graduated cylinder. If this solution is quantitatively transferred to a 250-mL volumetric flask and diluted to volume, what is its concentration to the correct number of significant figures?

19. What is the molar concentration of $$\ce{NO3-}$$ in a solution prepared by mixing 50.0 mL of 0.050 M KNO3 with 40.0 mL of 0.075 M NaNO3? What is pNO3 for the mixture?

20. What is the molar concentration of Cl in a solution prepared by mixing 25.0 mL of 0.025 M NaCl with 35.0 mL of 0.050 M BaCl2? What is pCl for the mixture?

21. To determine the concentration of ethanol in cognac a 5.00 mL sample of the cognac is diluted to 0.500 L. Analysis of the diluted cognac gives an ethanol concentration of 0.0844 M. What is the molar concentration of ethanol in the undiluted cognac?

2.8: Problems is shared under a CC BY-NC-SA license and was authored, remixed, and/or curated by David Harvey.

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