CALCULATIONS INVOLVING SOLUTIONS - …

1 44 One litre = 1 000 mL. Since mL = cm, then litre = 1000 decimetre (dm) = metre = 10 cm.( dm) = (10 cm). dm = 1000 cm = CALCULATIONS INVOLVING SOLUTIONSINTRODUCTION AND DEFINITIONSMany chemical reactions take place in aqueous (water) solution. Quantities of suchsolutions are measured as volumes, while the amounts of solute present in a given volumeof solution are the concentrations of the concentrations of SOLUTIONS are commonly stated in moles (of solute) per litre (ofsolution)(mol. L), or as Molarity (M), which means the same. In practical terms, however,-1amounts of solutes have to be measured as mass, for example in grams.

2 It is not possibleto measure the number of moles of a solid directly with a balance or any other of SOLUTIONS can also be expressed, therefore, in grams (of solute) per litre(of solution) (g. L).-1 Grams per litre is therefore a practical way to express concentration of solute in a per litre, or molarity, is more important in making CALCULATIONS and predictions aboutchemical of SOLUTIONS are defined in litres, (L), (which is sometimes expressed as dm, or3cubic decimetres). Millilitres (mL) are also used widely, but may have to be converted to1litres for some USEFUL FOR CALCULATIONS :It is important, therefore, to be able to convert grams to moles and moles to grams for of moles = or n = This can also be written:Actual mass (grams) = Number of moles x Molar mass, or m = n x MConcentration of a solution can be expressed as a formula:Concentration (in mol.)

3 L) = or C = -1 This can also be written:Number of moles of solute = Concentration (mol. L) x Volume of solution (litres)-1or n = C x VIt is suggested strongly that these formulae be remembered as word formulae, rather thanas algebraic formulae. With word formulae, the student is remembering the meanings of theparts of each formula. It is easy, with the algebraic formulae, to confuse n and m and one:A solution of sodium hydroxide has a concentration = mol. L (also written ). How many grams of sodium hydroxide are dissolved in L of solution?Calculate first the number of moles in the L of = = = Number of moles of solute = x = molSodium hydroxide: formula = NaOH, molar mass = ( + + ) g = gOne mole of NaOH = g, so mol of NaOH = g of solid sodium hydroxide dissolved in L solution makes a solution ofconcentration = two:What mass of lead nitrate should be dissolved in 250 mL of water to make a solutionof concentration nitrate: formula = Pb(NO), molar mass = g 250 mL = LConcentration = = = Number of moles of solute = x = molMass of lead nitrate required = ( x ) g = three.

4 What is the concentration of the solution if g of sodium carbonate is dissolvedin 200 mL of solution? 23 Sodium carbonate: formula = NaCO, molar mass = g 200 mL = L23 Number of moles of NaCO in g = = = = = MExample four:What volume of solution must be made if g of silver nitrate is to be dissolved tomake a solution of concentration = nitrate: formula = AgNO, molar mass = gNumber of moles of silver nitrate = = = molConcentration = = Volume = L = L = 600 mLCalculations of this kind should be practised until they can be done quickly and : many moles of calcium hydroxide are needed to make L of What mass of calcium hydroxide would be required?

5 2,What volume of potassium sulfate contains g of potassium sulfate? (Hint:first convert the number of grams to number of moles .)42 is the concentration of magnesium sulfate if g of crystals ( ) aredissolved in 500 mL of solution? is the mass of hydrogen chloride in of hydrochloric acid solution?(Hydrochloric acid is a solution of hydrogen chloride gas in water. "Concentratedhydrochloric acid" is approximately ). mass of iron(II) sulfate is present in mL of solution? CALCULATIONS INVOLVING PARTICULAR IONS IN A SOLUTIONC onsider a solution made by dissolving one mole of solid calcium chloride in one litre ofwater to make a solution that is in calcium one litre of solution contains mol of CaCl.

6 It can also be said to contain molof calcium ions and mol of chloride can be shown symbolically [CaCl] = [Ca] = [Cl] = +-(The square brackets, [ ], mean "concentration of ".)Further is the concentration of ammonium ions in ammonium sulfate solution?424 Formula for ammonium sulfate is (NH)SO. In a given volume of solution, there aretwice as many moles of ammonium ions as there are moles of ammonium sulfate or ofsulfate [NH] = 2[SO] = 2[(NH)SO]+2-4 Therefore [NH] = +2. What is the concentration of nitrate ion in aluminium nitrate solution? 33 Formula for aluminium nitrate is Al(NO).

7 3 Therefore [NO] = are the concentrations of iron(III) and of sulfate ions in iron(III) sulfate?243 Formula for iron(III) sulfate is Fe(SO)4 Therefore [Fe] = and [SO] = + a solution of silver sulfate in water, the concentration of silver ions is Whatis the concentration of sulfate ions in the solution?24 Formula for silver sulfate is AgSO44[Ag] = 2[SO] Therefore [SO] = +2-2-47 Exercises:1. What is the concentration of a) lead ions in a solution of lead nitrate?b) nitrate ions in a solution of zinc nitrate?c) ammonium ions in a solution of ammonium chloride?

8 3d) iron(III) ions in a solution of iron(III) nitrate where [NO] = ) iodide ions in a solution of magnesium iodide where [Mg] = + mass of solid would need to be dissolved in 250 mL of water to make a solutionin which a) [Cl] = , using potassium chloride?-4b) [SO] = , using sodium sulfate?2-42c) [Fe] = , using iron(II) sulfate-7-water ( )?2+4d) [NH] = , using ammonium hydrogenphosphate?+e) [Cl] = , using iron(III) chloride?-3. What is the molarity of chloride ions in each of the following SOLUTIONS ?a) g of sodium chloride are dissolved in 500 mL of ) g of calcium chloride is dissolved in mL of ) g of aluminium chloride dissolve in 600 mL of ) g of magnesium chloride and g of potassium chloride are dissolved togetherin 250 mL of ) g each of zinc chloride, potassium chloride, and iron(III) chloride are dissolvedtogether in 750 mL of make a solution that is in chloride, what volume of solution should be madea)if g of ammonium chloride is dissolved to make the solution?

9 B)if g of calcium chloride is dissolved to make the solution? CALCULATIONS INVOLVING CONCENTRATIONS OF SOLUTES INCHEMICAL REACTIONSThe basic procedure here is similar to that for other CALCULATIONS :1)Write a balanced )Write mole ratios under the equation, to show the ratio of moles of reactants to molesof products. 3) Write in the given data for concentrations and volumes, writing x for unknown ) Convert values of concentration and volume to moles . 5)Use ratios to calculate x. The ratio between the actual numbers of moles of the reactants(line 4 in example one on the next page) and the number of moles shown in the equation(line two in example one on the next page) are equal (line 5 in example one on the nextpage).

10 (Examples next page)48 Example one:What volume of hydrochloric acid will exactly neutralise mL of sodiumhydroxide solution?1)Write a balanced equation:2)Write mole ratios under the )Write in the given data for concentrationsand volumes, writing x for unknown )Convert values of concentration and volumeto ) Use ratios to calculate x: = The factor "/1000" converts the given volumes from millilitres to litres. Since it is acommon factor, it is cancelled from the next step. x = = 320 mLExample two:Silver nitrate solution of concentration is added to mL of sodium sulfidesolution, causing silver sulfide to precipitate.