1. LABORATORY MATHEMATICS MADE FUN Banzon, Johanna Joy V. Caig, Kristine Allyson

2. Molarity the concentration of a solution expressed as the number of moles of solute per litre of solution. Formula : the concentration of a solution expressed as the number of moles of solute per litre of solution. Formula :

3. EXAMPLE 1 What is the molarity of a solution made by dissolving 2.5 g of NaCl in enough water to make 125 ml of solution? MW OF NaCl = 58.44g Molarity of solution = 2.5g 58.44gx 0.125 = 0.3422 g of NaCl

4. EXAMPLE 2 How would you prepare 400.0 ml of 1.20 M solution of sodium chloride? Gram of solute = 1.20x58.44x0.4 = 28.1 g of NaCl

5. Molality Can be defined as"Total moles of a solute present in one kilogram of a solvent." The terms need, thus, to calculate molality are Moles of solute and the mass of solvent in kilograms. The solution is a homogenous mixture that is composed two components. One component is called as solute and another is known as solvent.

6. EXAMPLE 1 Question 1: An aqueous solution contains 5 grams of urea in 1000 grams of water at 25 degree Celsius. Calculate its molality. Solution: Moles of Urea = Mass in Grams 5 grams Molar Mass 60.06 grams/mole = 0.0832 moles Mass of water in kilograms = 1000 grams 1000 = 1 kilo gram Molality = Moles of Urea Mass of water in kilograms = 0.0832 moles 1 kg = 0.0832 moles/kg

7. EXAMPLE 2 Calculate the molality of a solution containing 6.3 grams of Oxalic acid crystals dissolved in 0.5 kilograms of solvent. Molecular weight of Oxalic acid = 126 grams/mole. Solution: Molality = moles of solute / kilograms of solvent Moles of Oxalic acid = Grams of oxalic Acid Molar Mass of oxalic acid = 6.3 grams of oxalic acid 126 grams/mole = 0.05 mole of Oxalic acid Molality = 0.05 moles of oxalic acid 0.5 kilograms of solvent = 0.1 m Molality of the given oxalic acid solution is 0.1 m.

8. Normality Normality could be defined as the number of gram equivalents of a solute present per litre (dm3) of the solution at any given temperature and It is expressed as N. A solution is generally described as a homogenous mixture in which some quality of solute (for example NaCl) is dissolved or stabilized, by a solvent (for example: H2O) Normality = Mass of the solute EW X Volume of the solution in litre

9. EXAMPLE 1 9.8 g H2SO4 is dissolved in water and 200 mL solution is prepared. Find normality of solution.MW of H2SO4=98; Valence H2SO4 = 2 Solution: Normality = 9.8 g 98x2 = 0.05 N

10. EXAMPLE 2 To make 600 ml of 3N H2SO4 how much substance must be weighted ? MW of H2SO4= 98; Valence = 2 Solution : Gram of solute = 3x98x2 = 588 g of H2SO4

11. Percent of Solution % Weight per Weight (w/w)= gram of solute gram of solution % Weight per Volume (w/v)= gram of solute ml of solution % Volume per Volume (v/v)= ml of solute ml of solution % Volume per Weight (v/w)= ml of solute gram of solution

12. Other Laboratory Mathematics Milliequivalent - Concentrations of electrolytes are often expressed as milliequivalents per liter, which is an expression of the chemical combining power of the electrolyte in a fluid. Formula : mEq/L= mg/dl x 10x valence molecular weight Example : If a solution contains 450 mg /dl SO4 -, How many mEq/dl of SO4 – does it contain. MW of SO4 = 96 ; Valence of SO4 = 2 Given :Solution : Mg/dl = 450mEq = 450x10x2 MW= 96 96 V= 2 = 94 mEq SO4 mEq=?

13. Millimoles- Molecular Weight = g/mole Millimole Millimole = 1/1000 of a mole = 1/1000 of a mole Formula : mmol/L= mg/dl x 10 molecular weight Example : Convert a 7 mg/dl monobasic sodium phosphate to millimoles per liter. MW = 138 Given :Solution : Mg/dl = 7 mmol/L = 7x10 MW= 138 138 = 1 mmol/L of monobasic sodium phosphate

14. Ratio Dilution - Adding more solvent to a solution to decrease the concentration is known as dilution. Starting with a known volume of a solution of known molarity, we should be able to prepare a more dilute solution of any desired concentration. Formula: C1V1C2V2

15. Dilution example : Make 5 mL of a 0.25 M solution from a 1 M solution. Formula: C1V1 = C2V2 Plug values in: (V1)(1 M) = (5 mL)(0.25 M) Rearrange: V1 = [(5 mL)(0.25 M)] / (1 M)V1 = 1.25 mL Answer: Place 1.25 mL of the 1 M solution into V1-V2 = 5 mL – 1.25 mL Final answer = 3.75 mL of diluent Dilution example : Make 5 mL of a 0.25 M solution from a 1 M solution. Formula: C1V1 = C2V2 Plug values in: (V1)(1 M) = (5 mL)(0.25 M) Rearrange: V1 = [(5 mL)(0.25 M)] / (1 M)V1 = 1.25 mL Answer: Place 1.25 mL of the 1 M solution into V1-V2 = 5 mL – 1.25 mL Final answer = 3.75 mL of diluent

16. Solution Properties Concentrations Colligative Properties Osmotic Pressure Redox Potential Conductivity / Resistivity pH and buffers

17. Concentrations Extent of saturations: Dilute- a solution containing a relatively small quantity of solute as compared with the amount of solvent. This term is the opposite of 'concentrated'. Concentrated - a solution containing a large quantity of solute as compared with the amount of solvent.

18. Saturated - is a chemical solution containing the maximum concentration of a solute dissolved in the solvent. Additional solute will not dissolve in a saturated solution. Supersaturated - a solution that contains more solute than it would if the dissolved solute were in equilibrium with the undissolved solute.

19. Colligative Properties Boiling point - are higher than that of the pure solvent. This effect is directly proportional to the molality of the solute. Osmotic pressure - is the pressure difference needed to stop the flow of solvent across a semipermeable membrane. The osmotic pressure of a solution is proportional to the molar concentration of the solute particles in solution.

20. Vapor Pressure- is always lower than the vapor pressure of the pure solvent. The vapor pressure lowering is directly proportional to the mole fraction of the solute. Freezing Point- are all lower than that of the pure solvent. The freezing point depression is directly proportional to the molality of the solute.

21. Redox Potential (Oxidation - reduction potential) Measures the capacity of a solution to either release or accept electrons from chemical reactions. Oxidation Is Loss, Reduction Is Gain. (of electrons) Conductivity - Is the measure of the amount of electrical current a material can carry. Electrical conductivity is denoted by the symbol σ and has SI units of siemens per meter (S/m).

22. Resistivity - Electrical resistivity is the measure of how much a material resists carrying an electrical current. Electrical resistivity is denoted by the symbol ρ and has SI units of ohm meter (Ωm).

23. pH and Buffers pH is a measure of the concentration of H+ [H3O+] ions in a solution. Only the concentration of H+ and OH- molecules determine the pH. When the concentration of H+ and OH- ions are equal, the solution is said to be neutral. If there are more H+ than OH- molecules the solution is acidic, and if there are more OH- than H+ molecules, the solution is basic. Buffers To be able to add a strong acid or base to a solution without causing a large change in the pH, we need to create a buffer solution. A buffer solution contains both a weak acid (HA) and its conjugate base (A-).

24. REFERENCES http://chemistry.about.com/od/chemistryglossary/a/dilutedef.htm http://www.chem.purdue.edu/jmol/gloss/supersatsoln.html http://chemistry.about.com/od/chemistryglossary/g/Saturated-Solution-Definition.htm http://chem.libretexts.org/Core/Physical_Chemistry/Physical_Properties_of_Matter/Solutions_and _Mixtures/Colligative_Properties http://chem.libretexts.org/Core/Physical_Chemistry/Physical_Properties_of_Matter/Solutions_and _Mixtures/Colligative_Properties http://www.molecularhydrogenfoundation.org/core-information/oxidation-reduction-potential- orp-explained/ http://www.molecularhydrogenfoundation.org/core-information/oxidation-reduction-potential- orp-explained/ http://chemistry.about.com/od/chemistryglossary/g/Electrical-Conductivity-Definition.htm http://chemistry.about.com/od/chemistryglossary/g/Electrical-Resistivity-Definition.htm http://chemcollective.org/activities/tutorials/buffers/buffers1 http://medical-dictionary.thefreedictionary.com/milliequivalent file:///C:/Users/jonasie/Downloads/handout_milliequiv.pdf http://chemed.chem.purdue.edu/genchem/topicreview/bp/ch3/solution.html file:///C:/Users/jonasie/Downloads/handout_milliequiv.pdf http://chemed.chem.purdue.edu/genchem/topicreview/bp/ch3/solution.html http://www.quansysbio.com/dilutions/ http://chemistry.tutorvista.com/inorganic-chemistry/molality.html www.chemistrytutorials.org/...problem-solutions/solutions...problem-solutions/solutio