# Calculation of Molar Masses. Molar Mass. Solutions. Solutions

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1 Molar Mass Molar mass = Mass in grams of one mole of any element, numerically equal to its atomic weight Molar mass of molecules can be determined from the chemical formula and molar masses of elements Each H 2 O molecule contains 2 H atoms and 1 O atom Each mole of H 2 O molecules contains 2 moles of H and 1 mole of O One mole of O atoms corresponds to g Two moles of H atoms corresponds to 2 x g Sum = molar mass = g H 2 O per mole Calculation of Molar Masses Calculate the molar mass of the following Magnesium nitrate, Mg(NO 3 ) 2 1 Mg = N = 2x = O = 6 x = Molar mass of Mg(NO 3 ) 2 = g Calcium carbonate, CaCO 3 1 Ca = C = O = 3 x Molar mass of CaCO 3 = g Iron(II) sulfate, FeSO 4 Molar mass of FeSO 4 = g Solutions Solutions Solution: a homogenous mixture in which the components are evenly distributed in each other Solute: the component of a solution that is dissolved in another substance Solvent: the medium in which a solute dissolved to form a solution Aqueous: any solution in which water is the solvent The properties and behavior of solutions often depend not only on the type of solute but also on the concentration of the solute. Concentration: the amount of solute dissolved in a given quantity of solvent or solution many different concentration units (%, ppm, g/l, etc) often expressed as Molarity 1

2 Solution Concentrations Molarity = moles of solute per liter of solution Designated by a capital M (mol/l) 6.0 M HCl 6.0 moles of HCl per liter of solution. 9.0 M HCl 9.0 moles of HCl per liter of solution. Solution Concentrations Molarity can be used as a conversion factor. The definition of molarity contains 3 quantities: Molarity = moles of solute volume of solution in liters If you know two of these quantities, you can find the third. Solution Concentrations Determine the molarity of each solution 2.50 L of solution containing 1.25 mol of solute Molarity = moles of solute volume of solution in liters 225 ml of solution containing mole of solute 100. ml of solution containing 2.60 g of NaCl Strategy: g mol molarity Example: How many moles of HCl are present in 2.5 L of 0.10 M HCl? Given: Find: Molarity = moles of solute volume of solution in liters 2.5 L of soln 0.10M HCl mol HCl Use molarity as a conversion factor Mol HCl = 2.5 L soln x 0.10 mol HCl 1 L of soln = 0.25 mol HCl 2

3 Example: What volume of a 0.10 M NaOH solution is needed to provide 0.50 mol of NaOH? Solutions of exact concentrations are prepared by dissolving the proper amount of solute in the correct amount of solvent to give the desired final volume Determine the proper amount of solute Given: Find: 0.50 mol NaOH 0.10 M NaOH vol soln Use M as a conversion factor Vol soln = 0.50 mol NaOH x = 5.0 L solution 1 L soln 0.10 mol NaOH How is the final volume measured accurately? Example: How many grams of CuSO 4 are needed to prepare ml of 1.00 M CuSO 4? Given: ml solution 1.00 M CuSO 4 Find: g CuSO 4 Conversion factors: Molarity, molar mass Given: ml solution, 1.00 M CuSO 4 Find: g CuSO 4 Strategy: ml L mol grams g CuSO4 = ml soln x 1 L x 1.00 mol 1000 ml 1 L soln Strategy: ml L mol grams x g CuSO4 1 mol = 39.9 g CuSO4 3

4 Describe how to prepare the following: 500. ml of 1.00 M FeSO 4 Strategy: ml L mol grams Steps involved in preparing solutions from pure solids g FeSO 4 = ml x 1 L x 1.00 mol x g 1000 ml 1 L 1 mol = g 100. ml of 3.00 M glucose 250. ml of M NaCl Steps involved in preparing solutions from pure solids Calculate the amount of solid required Weigh out the solid Place in an appropriate volumetric flask Fill flask about half full with water and mix. Fill to the mark with water and invert to mix. Solutions of exact concentrations can also be prepared by diluting a more concentrated solution of the solute to the desired concentration 4

5 Many laboratory chemicals such as acids are purchased as concentrated solutions (stock solutions). 12 M HCl 12 M H 2 SO 4 More dilute solutions are prepared by taking a certain quantity of the stock solution and diluting it with water. A given volume of a stock solution contains a specific number of moles of solute. 25 ml of 6.0 M HCl contains 0.15 mol HCl (How do you know this???) If 25 ml of 6.0 M HCl is diluted with 25 ml of water, the number of moles of HCl present does not change. Still contains 0.15 mol HCl Moles solute moles solute = before dilution after dilution Although the number of moles of solute does not change, the volume of solution does change. When a solution is diluted, the concentration of the new solution can be found using: M c V c = moles = M d V d Where, M c = concentration of concentrated solution (mol/l) Vc = volume of concentrated solution M d = concentration of diluted solution (mol/l) V d = volume of diluted solution The concentration of the solution will change since Molarity = mol solute volume solution 5

6 Example: What is the concentration of a solution prepared by diluting 25.0 ml of 6.00 M HCl to a total volume of 50.0 ml? Given: V c = 25.0 ml M c = 6.00 M V d = 50.0 ml Find: M d M c x V c = M d x V d M c V c = M d V d 6.00 M x 25.0 ml = M d x 50.0 ml M d = 6.00 M x 25.0 ml = 3.00 M 50.0 ml Note: V c and V d do not have to be in liters, but they must be in the same units. Describe how to prepare 500. ml of M NaOH solution using a 6.00 M NaOH solution. Given: M c = 6.00 M M d = M V d = ml Concentrations of Acids The ph scale ph = -log [H + ] ph of vinegar = -log (1.6 x 10-3 M) = - (-2.80) = 2.80 ph of pure water = -log (1.0 x 10-7 M) = - (-7.00) = 7.00 ph of blood = -log (4.0 x 10-8 M) = - (-7.40) = 7.40 Find: V c M c V c = M d V d ph of ammonia = -log (1.0 x M) = - (-11.00) = Lower the concentration of H +, higher the ph What volume of 2.30 M NaCl should be diluted to give 250. ml of a 0.90 M solution? acidic substance, ph< 7 Basic substance, ph >7 neutral, ph = 7 6

7 Concentrations of Acids Concentrations of Acids On serial dilution of acid solution, the ph increases because the concentration of H + ions decreases with dilution Concentration ph 0.1M HCl M HCl M HCl 3 The H + concentration of a solution of known ph can be calculated using the following equation: Calculate ph of M HCl solution. Calculate the concentration of H + ion in a solution of ph 7.5. [H + ] = 10 -ph Review Review If you dissolve 9.68 g of potassium chloride in 1.50 L, what is the final molar concentration? What volume of 8.00 M sulfuric acid should be diluted to produce L of M solution? How many grams of sodium sulfate are contained in (dissolved in) 45.0 ml of 3.00 M solution? What s the ph of the final solution? 7

8 Review What volume of 2.06 M potassium permanganate contains 322 g of the solute? Conversion Factors Number of particles Moles Mass Avogadro s number Molar x mass Determine the following: The moles of potassium atoms in a 50.0 g sample 1 mol Grams x = moles grams Determine the following: The moles of FeCl 3 in a 50.0 g sample The mass of MgCl 2 in a 2.75 mole sample The mass of Mg in a 1.82 mole sample grams Moles x = grams 1 mol 8

9 glucose = C 6 H 12 O 6 (Molar mass = g) How many moles of glucose are contained in 70.0 g of C 6 H 12 O 6? 1 mol Grams x = moles grams How many moles of oxygen are contained in 70.0 g of C 6 H 12 O 6? The relative number of moles of each element in a substance can be used as a conversion factor called the molar ratio. Molar ratio = or Molar Ratios moles element A mole of substance How many grams of H are contained in 70.0 g of C 6 H 12 O 6? Molar ratio = moles element A moles element B Molar Ratios Molar Ratios H 2 O: Molar Ratio = 2 moles of H mole H 2 O Molar Ratio = 1 mole O mole H 2 O Molar Ratio = 2 moles H mole O C 6 H 12 O 6 : Molar Ratio = 6 moles of C mole C 6 H 12 O 6 Molar Ratio = 12 moles H mole C 6 H 12 O 6 Molar Ratio = 6 moles O mole C 6 H 12 O 6 Molar Ratio = 6 moles C = 1 mol C 12 moles H 2 moles H 9

10 Molar ratios can be used to determine the number of moles of a particular element in a given substance. How many moles of oxygen are contained in 70.0 g of C 6 H 12 O 6? Given: 70.0 g of C 6 H 12 O 6 Find: Moles of O Strategy: Molar mass Molar ratio grams of glucose moles of glucose moles of oxygen Moles C 6 H 12 O 6 Molar Ratio Moles O Moles of O = 70.0 g of C 6 H 12 O 6 x 1mol C 6 H 12 O x 6 6 mol O g mol C 6 H 12 O 6 = 2.33 mol O Once the number of moles of a substance present is known, we can use: Molar mass to find the number of grams Avogadro s number to find the number of atoms, ions, or molecules Grams B Molar mass Moles A Moles B Molar Ratio N A Atoms B How many grams of H are contained in 70.0 g of C 6 H 12 O 6? Grams H Molar mass Moles C 6 H 12 O 6 Moles H Molar Ratio N A Atoms H 10

11 Given: 70.0 g of C 6 H 12 O 6 Find: gram H g H = 70.0 g C 6 H 12 O 6 x 1mol C 6 H 12 O 6 x 12 mol H x g g mol C 6 H 12 O 6 mol H How many moles of nitrogen are contained in 70.0 g of C 6 H 5 NO 3? How many grams of oxygen are contained in 1.5 moles of C 6 H 5 NO 3? =4.70g H # H = 70.0 g C 6 H 12 O 6 x 1mol C 6 H 12 O 6 x 12 mol H x x atoms g mol C 6 H 12 O 6 mol H How many atoms of C are contained in 70.0 g of C 6 H 5 NO 3? = 28.1 x atoms of H Empirical and Molecular Formulas How many moles of H + ions are present in 2.5 moles of H 2 SO 4? Empirical formula: smallest whole-number ratio of atoms present in a compound Molecular formula: actual number of each type of atom present in a given compound Given: 2.5 moles H 2 SO 4 Find: moles H + Conversion factor: molar ratio Many molecular compounds have different empirical and molecular formulas Molecular Formula Empirical Formula C 6 H 6 CH Mol H + = 2.5 mol H 2 SO 4 x 2 mol H + Mol H + = 5.0 mol H + 1 mol H 2 SO 4 C 6 H 12 O 6 CH 2 O N 2 H 4 NH 2 N 2 O 4 NO 2 11

12 Percent Composition Percent Composition Empirical formulas are generally obtained by determining the percent composition of a compound: Percent composition: the percentage of the mass contributed by each element in a substance % Element X = (# atoms of X)(AW) x 100% FW of compound Formula Weight (FW): the sum of the atomic weights of all of the atoms in a chemical formula Note: Molar mass is a mass in grams that is numerically the same as the formula weight Calculate the % composition of H 2 O (i.e find %H and %O). First, find the FW of H 2 O: FW = 2( amu) + 1( amu) = amu % H = 2( amu) x 100% = 11.2% H amu % O = 1( amu) x 100% = 88.8 % O amu Mass Percentage What is the mass percentage of each element in urea (CH 4 N 2 O)? FW = amu + 4( amu) + 2 ( amu) + 1( amu) = amu % C = 1( amu) x 100% = 20.00% C amu % H = 4( amu) x 100% = 6.71 % H amu % N = 2( amu) x 100% = 46.65% C amu % O = 1( amu) x 100% = % H amu Percent composition data is commonly used to determine the empirical formula of a compound. Empirical formula: smallest whole-number ratio of atoms present in a compound Percent composition: the percentage of the mass contributed by each element in a substance Four steps: percent to mass mass to mole divide by smallest multiple til whole 12

13 A sample of nicotine has the following mass composition: 74.03% C; 8.70% H; 17.27% N. What is the empirical formula of nicotine? Step 1: % to mass If you assume g of substance, then % C g C 8.70 % H 8.70 g H Step 2: Mass to moles # moles C = g C x 1 mole C = mol C g C # moles H = 8.70 g H x 1 mole H = mol H g H # moles N = g N x 1 mole N = mol N g N % N g N Step 3: Divide by smallest (this gives the molar ratio of the elements) C: moles C = moles N H: mol H = mol N Step 4: Multiply til Whole (this step is necessary only when step 3 does not give whole number molar ratios) C: moles C = x 1 = mol C moles C H: mol H = mol C x 1 = mol H N: mol N = mol N N: mol N = mol C x 1 = mol N 13

14 Use these numbers to write the empirical formula: An iron compound contains % Fe and % O. Calculate its empirical formula mol C mol H mol N C 5 H 7 N Step 1: % to mass % Fe g Fe % O g O Step 2: Mass to Moles Step 3: Divide by smallest mol Fe = g Fe x mol Fe = mol Fe g Fe mol O = g O x mol O = mol O g O O: mol O = mol Fe Fe: mol Fe = mol Fe 14

15 Using Empirical Formulas Step 4: Multiply til whole FeO 1.5 doesn t make sense. A sample of nicotine has the following mass composition: 74.03% C; 8.70% H; 17.27% N The molar mass of nicotine is g What is the molecular formula of nicotine? mol O mol Fe x 2 = mol O x 2 = mol Fe Fe 2 O 3 Using Empirical Formulas to Find Molecular Formulas Steps: Find the empirical formula Calculate the formula weight for the empirical formula. Get the whole number ratio between MW and FW Multiply the subscripts in the empirical formula by the whole number ratio. Using Empirical Formulas to Find Molecular Formulas Step 1: Step 2: Empirical formula of nicotine: C 5 H 7 N Formula Weight = Molar mass = Molecular weight = Step 3: Ratio= MW = = 2.00 FW Step 4: Molecular formula: C (5x2) H (7x2) N (1x2) = C 10 H 14 N 2 15

16 Using Mass Percent Data Chapter 4 Combustion Analysis Ethylene glycol analyzes as %C, and 9.74 %H with the remainder being oxygen. Determine the empirical formula of ethylene glycol A g sample of a hydrocarbon was burned to produce g of CO 2 and g of H 2 O. Determine the empirical formula. Empirical and Molecular Formulas Molecular weight : Mass spectrometer % C, H, O, N : Combustion analysis Empirical and Molecular Formulas of an unknown compound 16

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