Chemical calculations used in medicine (concentration, dilution)

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1 Chemical calculations used in medicine (concentration, dilution) Pavla Balínová

2 giga- G 10 9 mega- M 10 6 kilo- k 10 3 deci- d 10-1 centi- c 10-2 milli- m 10-3 micro- μ 10-6 nano- n 10-9 pico- p femto- f atto- a Prefixes for units

3 Basic terms MW = molecular weight (g/mol) = mass of 1 mole of substance in grams or relative molecular weight Mr Avogadro s number N = x particles in 1 mol Substance amount (n) in moles (mol) n = m/mw (m = mass (g)) Also used mmol, µmol, nmol, pmol,

4 Concentration amount of a substance in specified final volume Molar concentration or molarity (c) number of moles of a substance per liter of solution unit: mol/l = mol/dm 3 = M c = n (mol) / V (L) Molality (mol/kg) concentration of moles of substance per 1 kg of solvent

5 Molar concentration - examples 1) 17.4 g NaCl in 300 ml of solution, Mr (NaCl) = 58 c =? 2) 4.5 g glucose in 2.5 L of solution, Mr (glucose) = 180 c =? 3) Solution of glycine, c = 3 mm, V = 100 ml, Mr (glycine) = 75 m =? mg of glycine in the solution

Osmotic pressure Osmotic pressure π is a hydrostatic pressure produced by solution in a space divided by a semipermeable membrane due to a differential in the concentrations of solute.

6 Osmotic pressure Osmotic pressure π is a hydrostatic pressure produced by solution in a space divided by a semipermeable membrane due to a differential in the concentrations of solute. unit: pascal (Pa) Π = i x c x R x T Oncotic pressure = is a form of osmotic pressure exerted by proteins in blood plasma Osmosis = the movement of a solvent from an area of low concentration of solute to an area of high concentration! Free diffusion = the movement of solute from the site of higher concentration to the site of lower concentration!

Osmolarity Osmolarity (osmol/l) is a number of moles of a substance that contribute to osmotic pressure of solution The osmolar concentration of body fluids is

7 Osmolarity Osmolarity (osmol/l) is a number of moles of a substance that contribute to osmotic pressure of solution The osmolar concentration of body fluids is typically reported in mosmol/l. Osmolarity of blood plasma is mosmol/l π = i c R T The figure is found at

8 Osmolarity - examples Example 1: A 1 M NaCl solution contains 2 osmol of solute per liter of solution. NaCl Na + + Cl - 1 M does dissociate to 1 osmol/l 1 osmol/l 2 osmol/l in total Example 2: A 1 M CaCl 2 solution contains 3 osmol of solute per liter of solution. CaCl 2 Ca Cl - 1 M does dissociate to 1 osmol/l 2 osmol/l 3 osmol/l in total Example 3: The concentration of a 1 M glucose solution is 1 osmol/l. C 6 H 12 O 6 C 6 H 12 O 6 1 M does not dissociate 1 osmol/l

9 Osmolarity - examples 1. What is an osmolarity of 0.15 mol/l solution of: a) NaCl b) MgCl 2 c) Na 2 HPO 4 d) glucose 2. Saline is 150 mm solution of NaCl. Which solutions are isotonic with saline? [= 150 mm = 300 mosmol/l] a) 300 mm glucose b) 50 mm CaCl 2 c) 300 mm KCl d) 0.15 M NaH 2 PO 4 3. What is molarity (in mol/l) of 900 mosmol/l solution of MgCl 2?

weight per weight (w/w) 10% of KCl = 10 g of KCl + 90 g of H 2 O = 100 g of solution 2.

10 Percent concentration is expressed as part of solute per 100 parts of total solution (%) % = mass of solute x 100 mass of solution % concentration has 3 forms: 1. weight per weight (w/w) 10% of KCl = 10 g of KCl + 90 g of H 2 O = 100 g of solution 2. volume per volume (v/v) 5% HCl = 5 ml HCl in 100 ml of solution 3. weight per volume (w/v) the most common expression 0.9% NaCl = 0.9 g of NaCl in 100 ml of solution

11 Percent concentrations - examples 1) 600 g 5% NaCl,? mass of NaCl,? mass of H 2 O 2) 16 g of glucose is administrated to the patient intravenously as first aid during hypoglycemia. How many ml of 40% infusion solution of glucose will be administrated to patient? 3) How many ml of 95% ethanol (Spiritus absolutus) and how many ml of H 2 O do you need for preparation 250 ml 60% ethanol solution (Spiritus dilutus)? 4) Saline is 150 mm solution of NaCl. Calculate the percent concentration by mass of this solution. Mr(NaCl) = 58.5

12 Density ρ - is defined as the amount of mass per unit of volume ρ = m/v m = ρ x V and V = m / ρ - these equations are useful for calculations units: g/cm3 or g/ml - density of water = 1 g / cm 3 - density of 95% ethanol = 0.79 g/cm 3 - density of lead (Pb) = g/cm 3

13 Conversions of concentrations (% and c) with density 1) What is a percent concentration of 2 M HNO 3 solution? Density (HNO 3 ) = 1,076 g/ml, Mr(HNO 3 ) = 63,01? Conversion of molar concentration to % concentration? 2 M HNO 3 solution means that 2 mol of HNO 3 are dissolved in 1 L of solution Mass of HNO 3 m = n x Mr = 2 x = g of HNO 3 Mass of solution = ρ x V = x 1000 = 1076 g W = 126,02 x 100 = 11,71% ) What is the molarity of 38% HCl solution? Density (38% HCl) = g/ml and Mr(HCl) = 36.45? Conversion of percent by mass concentration to molar concentration? 38% HCl solution means that 38 g of HCl in 100 g of solution. One liter of solution has a mass m = V x ρ = 1000 x = g. 38 g HCl > 100 g of solution x g HCl > 1188,5 g of solution x = g HCl in 1 L of solution n = m / M = / = 12.4 mol of HCl c(hcl) = n / V = 12.4 / 1 = 12.4 mol/l

14 Conversions of concentrations (% and c) with density Conversion of molarity to percent concentration % = c (mol/l) x Mr 10 x ρ (g/cm 3 ) Conversion of percent concentration to molarity c = % x 10 x ρ (g/cm 3 ) Mr

15 Conversions of concentrations (% and c) with density - examples 1)? % (w/w) of HNO 3 ; ρ = 1.36 g/cm 3, if 1dm 3 of solution contains 0.8 kg of HNO 3 2) c (HNO 3 ) = 5.62 M; ρ = 1.18 g/cm 3, MW = 63 g/mol,? %

16 Dilution = concentration of a substance lowers, number of moles of the substance remains the same! 1) mix equation: m 1 x p 1 + m 2 x p 2 = p x ( m 1 + m 2 ) m = mass of mixed solution, p = % concentration 2) useful equation derived from the definition of dilution n 1 = n 2 V 1 x c 1 = V 2 x c 2

17 Dilution - examples 1) Mix 50 g 3% solution with 10 g 5% solution, final % concentration =? 2) Final solution: 190 g 10% sol.? m (g) of 38% HCl +? m (g) H 2 O 3) Dilute 300 g of 40% solution to 20 % solution.? g of solvent do you need? 4)? preparation of 250 ml of 0.1 M HCl from stock 1 M HCl 5) 200 ml of 0.2 M acid solution was diluted to the final volume of 0.8 litre. Molarity of final solution?

18 The dose of drug - problem 1) Nasal drops used to treat sinusitis include antibiotic drugs neomycine (1.32 g/l) and bacitracine (100 IU/mL). In the pharmacy these drops are prepared by dilution of solution Pamycon which contains 0.33% (w/v) of neomycine and 250 IU/mL of bacitracine. Calculate how many ml of Pamycon solution is necessary to prepare 10 ml nasal drops mentioned above. 2) AMOCLEN 250 syrup contains 250 mg of amoxicillin in 5 ml of syrup. The usual daily dose for children is 50 mg of amoxicillin per 1 kg of body weight. The total daily dose is divided into 3 individual doses to be administered every 8 hours. Calculate the volume of a single dose for a child weighing 12 kg.

Chemical calculations in medicine. Josef Fontana

Chemical calculations in medicine Josef Fontana Chemical calculations Expression of concentration molar concentration percent concentration conversion of units Osmotic pressure, osmolarity Dilution of