Lectures_Part 3_Calculations in Analytical Chemistry.pptx

Class lecture on basic analytical chemistry

1. Part 3 Lecture Series: Calculations in Analytical Chemistry

2. Learning Outcomes Describe methods used to compute results of quantitative analysis. Describe various SI units used in Analytical Chemistry. Describe the mole, a measure of the amount of a chemical substance. Methods of expressing concentrations of solutions. Calculations on Chemical Stoichiometry.

3. Units of Measurements SI Units International System of Units (SI)-standard system of units adopted by scientists. System is based on the seven fun­damental base units Other useful units, such as volts, hertz, coulombs, and joules, are then derived from these base units.

4. Amount of chemical species in Analytical Chemistry often expressed from mass measurement. Such measurements, metric units of kilograms (kg), grams (g), milligrams (mg), or micrograms ( μg ) are used. Volumes of liquids are measured in units of liters (L), milliliters (mL), and sometimes microliters ( μL ). The liter, the SI unit of volume, is defined as exactly 10 -3 m 3 , The milliliter is defined as 10 -6 m 3 or 1 cm 3 . Mass and Weight Mass is a measure of the amount of matter of a substance. Weight is the force of attraction between a substance and gravity. Gravitational attraction varies with geographical location, the weight of an object depends on where you weigh it.

5. Prefixes of some units

6. The expression relating mass and weight:- where w is the weight of an object, m is its mass, and g is the acceleration due to gravity . A chemical analysis is always based on mass so the results will not depend on locality. In chemistry often mass and weight of an object are used interchangeably. Analytical data are however based on mass rather than weight . The act of determining the mass of an object is “weighing” in analytical chemistry. The mole The mole (abbreviated mol) is the SI unit for the amount of a chemical species Always associated with a chemical formula and represents Avogadro's number (6.022 X 10 23 ) of particles represented by that formula.  

7. The molar mass (M) of a substance is the mass in grams of 1 mol of that substance. Molar masses are calcu­lated by summing the atomic masses of all the atoms appearing in a chemical formula. Example the molar mass of glucose

8. Calculating amounts of substances in Moles or Millimoles Using examples to illustrate these calculations. Calculate the moles and millimoles of benzoic acid (M = 122. 1 g/mol) con­tained in 2.00 g of the pure acid. I mol of HBz has a mass of 122.1 g. Amount in mol of benzoic acid Amount in millimoles

9. Exercise Calculate the amount of Na + in grams (22.99 g/mol) contained in 25.0 g of Na 2 S0 4 (142.0 g/mol).

10. Calculate the amount of Na + in grams (22.99 g/mol) contained in 25.0 g of Na 2 S0 4 (142.0 g/mol). 1 mol of Na 2 S0 4 contains 2 mol of Na + . Moles of Na + Moles of Na 2 S0 4 Combining the two equations (moles of Na + )

11. Mass of sodium in 25.0 g of Na 2 S0 4 Number of grams of Na +

12. Solutions and their Concentrations Concentration of Solutions Concentration of chemical species in solutions are expressed in several ways. Molar concentrations The molar concentration ( C x ) of a solution of a chemical species X is the number of moles of that species contained in 1 L of the solution. The unit of molar concentration is molarity, M (mol L -1 ) Molarity also expresses the number of millimoles of a solute per milliliter of solution.

13. Illustration with examples Calculate the molar concentration of ethanol in an aqueous solution that contains 2.30 g of C 2 H 5 OH (46.07 g/mol) in 3.50 L of solution. Convert mass of ethanol to moles Divide the number of moles by the volume

14. Analytical Molarity Gives the total number of moles of a solute in 1 L of the solution (or the total number of millimoles in 1 mL). Specifies how the solution can be prepared. Equilibrium Molarity Expresses the molar concentration of a particular species in a solution at equilibrium. To state the species molarity, behavior of the solute when dissolved in a solvent must be known. Example Species molarity of H 2 SO 4 in a solution with an analytical concentration of 1.0 M Species concentration for H 2 SO 4 = 0.0M (H 2 SO 4 dissociates completely in solution). Equilibrium concentrations of other species would be:-

15. Example Calculate the analytical and equilibrium molar concentrations of the solute species in an aqueous solution that contains 285 mg of trichloroacetic acid, Cl 3 CCOOH (163.4 g/mol), in 10.0 mL (the acid is 73% ionized in water) Cl 3 CCOOH designated as HA Moles of HA The analytical concentration C HA

16. Equilibrium concentration 73% of the HA dissociates. giving H + and A - . The species molarity of HA is then 27% of C HA · The species molarity of A - is equal to 73 % of the analytical concentration of HA. Further

17. Example-Preparation of solution from a salt Describe the preparation of 2.00 L of 0.108 M BaCl 2 from BaCl 2 . 2H 2 0 (244.3 g/mol). 1 mol of the dihydrate yields 1 mol of BaC1 2 . To produce this solution we will need:-

18. Example Describe the preparation of 500 mL of 0.0740 M Cl - solution from solid BaCl 2 . 2H 2 0 (244.3 g/mol).

19. Percent Concentration Concentrations can also be expressed as a percent (parts per hundred). Percent composition can be expressed in several ways:- Weight percent is frequently used to express the concentration of commercial aqueous reagents.

20. Example:- Nitric acid is sold as a 70 % solution (reagent contains 70 g of HNO 3 per 100 g of solution). Volume/volume percent is commonly used to specify the concentration of a solution pre­pared by diluting a pure liquid compound with another liquid . Example:- A 5% aqueous solution of methanol usually describes a solution prepared by diluting 5.0 mL of pure methanol with enough water to give 100 mL. Weight/volume percent is often used to describe the composition of dilute aqueous solutions of solid reagents. Example:- 5% aqueous silver nitrate refers to a solution prepared by dissolving 5 g of silver nitrate in sufficient water to give 100 mL of solution. The type of percent composition being used must be stated always to avoid errors.

21. Parts per Million and Parts per Billion Parts per million (ppm) is used to express concentration of very dilute solutions. For even more dilute solutions parts per billion (ppb) is used to express concentration Parts per thousand (ppt) is also used to express concentration.

22. Example/Exercise Determine the molarity of K + in a solution that contains 63.3 ppm of K 3 Fe(CN) 6 (329.3 g/mol). Solution is dilute, its assumed density is 1g/mL

23. P-functions A way of expressing concentrations in terms of its p-function or p-value . The p-value is the negative logarithm (to the base 10) of the molar concentration of that species. For instance, for species X . P-values allow concentrations that vary over ten or more orders of magnitude to be expressed in terms of small positive numbers. Example. Calculate the p-value for each ion in a solution that is 2.00 X 10 -3 M in NaCl and 5.4 X 10 -4 M in HCI.

24. For pNa Example Calculate the concentration of Ag + in a solution that has a pAg of 6.372

25. Concentration Density and specific gravity solutions . Terms often used in analytical chemistry. Density of a substance is its mass per unit volume. Specific gravity is the ratio of its mass to the mass of an equal volume of water at 4 °C. Density has units of kg/L or g/mL in the metric system.

26. Specific gravity is dimensionless and not tied to any particular system of units. Density of water is approximately 1.00 g/mL, density and specific gravity are used interchangeably in analytical chemistry.

27. Typical label by a manufacturer on a reagent bottle

28. Example: Calculation on specific gravity Calculate the molar concentration of HNO 3 (63.0 g/mol) in a solution that has a specific gravity of 1.42 and is 70.5% HNO 3 (w/w). Calculate the grams of acid per liter of concentrated solution

29. Example/Exercise . Describe the preparation of 100 mL of 6.0 M HCl from a concentrated solution that has a specific gravity of 1.18 and is 37% (w/w) HCl (36.5 g/mol) Calculation of molarity of concentrated reagent. Number of moles of acid we require for dilution.

30. Calculate the volume of reagent we need to dilute. Dilute 50 mL to 100 mL Solution is based on the following principle

31. Chemical Stoichiometry Section provides a brief overview of stoichiometry and its applications to chemical calculations. Stoichiometry : Quantitative relationship between reacting chemical species. Relationship among the number of moles of reactants and products in a balanced equation. Empirical Formula : simplest whole number ratio of atoms in a chemical compound. Molecular Formula : specifies the number of atoms in a molecule. Flow diagram for making stoichiometric calculations

32. Mass of a reactant or product is provided, convert to number of moles, using the molar mass. Stoichiometric ratio given by the chemical equation for the reaction Used to find the number of moles of reactant that combine with the original substance. The number of moles of product that form. Mass of the other reactant or the product is computed from its molar mass Structural formula Gives an idea of the bonding and orientation of bonds in a molecule. For Example, Ethanol and dimethyl ether share similar molecular formula (C 2 H 6 O) but different structural formula (C 2 H 5 OH and CH 3 OCH 3 )

33. Stoichiometric Calculations Balanced chemical equation gives the combining ratios, in units of moles of reacting substances and their products. Equation reads: 2 mol of aqueous NaI combine with 1 mol of aqueous Pb(NO 3 ) 2 to produce 1 mol of solid PbI 2 and 2 mol of aqueous NaNO 3 . Example/Exercise (a) Calculate the mass of AgNO 3 (169.9 g/mol) needed to convert 2.33 g of Na 2 CO 3 (106.0 g/mol) to Ag 2 CO 3 (b) Calculate the mass of Ag 2 CO 3 (275.7 g/mol) formed. Start by construction a balanced equation of the reaction

34. (a) From the balanced equation

35. Mass of AgNO 3 (b)

36. Example/Exercise Calculate the mass of Ag 2 CO 3 (275.7 g/mol) formed when 25.0 mL of 0.200 M AgNO 3 are mixed with 50.0 mL of 0.0800 M Na 2 CO 3 . Write a balanced equation for the reaction. Design the approach for the problem. Execute the calculations.

37. Solution Calculate the amount of reactants

38. Determine the limiting reagent A CO 3 2- ion reacts with two Ag + ions, 2 X 4.00 X 10 -3 = 8.00 X 10 -3 mol AgNO 3 is required to react with the Na 2 CO 3 . Ag 2 CO 3 produced will be limited by the amount of AgNO 3 (limiting reactant). Mass of Ag 2 CO 3 formed.

39. Exercise/Example Calculate the analytical molar Na 2 CO 3 concentration in the solution produced when 25.0 mL of 0.200 M AgNO 3 are mixed with 50.0 mL of 0.0800 M Na 2 CO 3 . Calculate the number of moles of Na 2 CO 3 reacting Unreacted moles of Na 2 CO 3 (at completion of reaction)

40. We calculate the molarity Na 2 CO 3 mol/L. Exercise Questions . 1. Describe the preparation of (a) 500 mL of 4.75% (w/v) aqueous ethanol (C 2 H 5 OH, 46.1 g/mol). (b) 500 g of 4.75% (w/w) aqueous ethanol. (c) 500 mL of 4.75% (v/v) aqueous ethanol. 2. Describe the preparation of (a) 500 mL of 0.0750 M AgNO 3 from the solid reagent. (b) 1.00 L of 0.285 M HCl, starting with a 6.00 M solution of the reagent.

41. 3. A 6.42% (w/w) Fe(NO 3 ) 3 (241.86 g/mol) solution has a density of 1.059 g/ mL. Calculate (a) The molar analytical concentration of Fe(NO 3 ) 3 in this solution. (b) The molar NO 3 - concentration in the solution. (c) The mass in grams of Fe(NO 3 ) 3 contained in each liter of this solution. 4. Convert the following p-functions to molar concentrations: (a) pH = 9.67. (b) pOH = 0.135. (c) pBr = 0.034. (d) pCa = 12.35

42. Exactly 0.2220 g of pure Na 2 CO 3 was dissolved in 100.0 mL of 0.0731 M HCI. (a) Calculate the mass in grams of CO 2 were evolved. (b) Calculate the molarity of the excess reactant (HCl or Na 2 CO 3 ).