Chemical MathIB Core 1.1.1 Apply the mole concept to substances. Apply: Use an idea, equation principle, theory or law in a new situation. 1.1.1 Apply the mole concept to substances. How many eggs are in a dozen? Atoms are VERY small, how small? Take a ping pong ball an placed it in the center of a soccer stadium. This is the atoms nucleus. Then take a pin and stand on the very edge of the stadium. The pin head is the electron. Avogadro's Number The mole: 6.02 x 10 23 ) atoms .02 x 10 23 1 mole atoms = 6.02 x 10 23 atoms 3 moles of atoms = 3 (6.1.1 Apply the mole concept to substances. To count small things we need a large number 1 dozen atoms is only 12 atoms We need a new number.1. That is approximately 1. The Earth is estimated to be about 4. still much less than a mole. or go around the Earth 300 trillion times.• • • • Understanding the number If you ordered a mole of donuts instead of a dozen. you would be able to cross the galaxy and back eight times. .54 billion years old.43 x 1017 seconds. that would be enough to give every person in the world over 9 trillion donuts. Spreading a mole of marbles over the Earth would produce a layer almost five kilometers thick If you traveled a mole in inches. If the average depth of sand throughout is 10 m. then the Sahara Desert would contain about 6 x 1022 grains of sand. The Sahara Desert is about 1500 km north to south and 4000 km east to west. This is still one tenth of a mole. This means there are more atoms of carbon in a 12 g sample (one mole) then there are grains of sand in the Sahara Desert . and there were about 1000 grains of sand in each cm3. 2 Determine the number of particles and the amount of substance (in moles). Determine: Find the only possible answer.1. 3) .1. (Obj. 02 x 10 23 oxygen atoms / mol .1. 1 mol oxygen 6. Ratio 1:1 There is 1 Oxygen atom for ever water molecule.2 Determine the number of particles and the amount of substance (in moles). 1 mol of water molecules has 2 moles of hydrogen atoms 2 mol Hydrogen x (6.1.04 x 10 23 hydrogen atoms.02 x 10 23 atoms/mol = 6. How many Hydrogen and Oxygen atoms are there in 1 mol of water? What is the total # of atoms? H2O Ratio 1:2: There are 2 Hydrogen atoms for every water molecule.02 x 10 23 )atoms/mol = 12. 01*1024 atoms Click for answers There are 3 mols of atoms: There are 5 mols of atoms: . Using 1 mol of substance.2 Determine the number of particles and the amount of substance (in moles).81*1024 atoms 3.1. how many atoms? HCl O3 CH4 There are 2 mols of atoms: 1.20*1024 atoms 1.1. 1. Define: Give the precise meaning of a word.2.1 Define the terms relative atomic mass (Ar) and relative molecular mass (Mr). (Obj 1) . phrase or physical quantity. The number is the ratio of the average mass per atom to 1/12 of an atom of the C-12 isotope. Relative Molecular Mass (Mr) The mass of a molecule. just use the Ar from above and -1) to the end g/mol (g add mol Relative things have NO UNITS! But!! Atomic Mass does! (g/mol) or . Indicates how heavy the molecule is compared to the C-12 isotope. To get this value. Relative Atomic Mass (Ar): You find these values on the Periodic Table Weighted mean mass of all naturally occurring isotopes of an element. .2 Calculate the mass of one mole of a species from its formula.1. Calculate: Find a numerical answer showing the relevant stages in the working (unless instructed not to do so).2. 02 g/mol all the atoms in the compound. Figs .00 g/mol For compounds or Elements with multiple atoms: M = 2(1.Don’t be lazy! Sig.008)g/mol + Add the atomic mass of =18.00) g/mol Units... Final Molar Mass of Water 1(16.Number of Atoms involved Molar Whatmass is the(M) Molar is the mass mass of one mol of atoms (g/mol) H: 1.008 g/mol of H2O? Atomic Mass (On P-table) O: 16. What is the Molar Mass of: CO2 CH4 Sodium Sulphate . . What is the Molar Mass of: Potassium Chloride Iron(III) Oxide Copper(II) Nitrate . 1. mass and molar mass.2.3 Solve problems involving the relationship between the amount of substance in moles. Solve: Obtain an answer using algebraic and/or numerical methods. . .Stoichiometry Time! Time to learn what stoichiometry is all about! Yee-haw!! Definition of stoichiometry: The relationships among the quantities of reactants and products involved in chemical reactions. desired unit Given unit x desired unit given unit . and you know what unit you are after. you can solve the problem!! • Be sure to cancel out units as you go through.• When you have something to start with. .1 mol of ANY IDEAL GAS occupies a volume of 22.T.4 dm3 at S.P. Formula n= m M n = # of moles (mol) m = mass (g) MM = Molar Mass (g/mol) Oxygen 8 O 15.999 . how many moles would you have? You have 2.904 g of sulfuric acid.00 mols of carbon dioxide. How many grams of carbon dioxide do you have? .Sample problems: If you have 4. 04999 mols 1 mol H2SO4 H2SO4 Carbon dioxide is 98.904 g H2SO4 x = 0. Sulfuric acid is H2SO4 .09 CO2.0 mol CO2 x = 88 g CO2 44.01 + (2 x 16.00) = 98. 2.01g CO2 1 mol CO2 .01 g mol-1.09 g mol-1 4.07) + (4 x 16.01) + (32.00) = 44. gSo 12. So the molar mass would be (2 x 1. The combustion of Hydrogen gas and Oxygen. 1) How many grams of oxygen will I need? 2) How many grams of product will I make? . 1) Determine the product and write the chemical equation for the reaction 2) Balance the equation 3) What is the ratio of Oxygen to Hydrogen? If I react 24 g of Hydrogen gas with oxygen. You will make 214 grams (210 using sig figs) of product (H2O) . 2H2 + O2 → 2H2O 1 mol O2 Ratio: 2 mol H2 You will need 380 grams of oxygen. 2. Distinguish: Give the difference between two or more different terms. 1. .4 Distinguish between the terms empirical formula and molecular formula. Empirical formula States the elements present in the compound. Example: Empirical formula of glucose=CH2O Molecular formula • • • The elements present in the compound Actual number of atoms of the elements in one molecule Example: Molecular formula of glucose=C6H12O6 . Simplest whole number ratio of these elements. 2. 1. Determine: Find the only possible answer (Obj.5 Determine the empirical formula from the percentage composition or from other experimental data. 3) . An analogy A test is worth 100% and there are 3 sections: Section A = 20 marks Section B = 50 marks Section C = 30 marks What % of the test is Section A? What would you make the test out of to make mark calculations easy? The easiest way to mark this test is to make the total 100. . 64% phosphorus by mass.64 g of P.409= 2. 100 is an easy number. But we need whole numbers!!!! So multiply both sides by two= 2:5 ratio.64 g 30 . so let’s start there….5.36). so make up one.523 Divide 3.523 mols Ratio = 1. there would be 43.1 = 3.5. In 100g.523 by 1.64=56. Remember.36g of O (100-43. so 1:2. You are not given a mass. and 56.409 mols Amount of oxygen = 56.1 = 1.409 : 3.36g 16. Now mole it out (find the moles!!) Amount of phosphorus = 43 .97 g mol .You need to determine the empirical formula for a compound of phosphorous and oxygen that contains 43. What is the empirical formula? .00 g mol . Empirical formula with 2:5 ratio would be: P2O5 . 11 % Nitrogen Click for answer What is the Empirical formula? Answer: CH5N .22 % Hydrogen 45. A compound was found to have a % composition of 38.67 % Carbon 16. Use your stoichiometry skills.60 g of water. You use 2.80 g of this compound. follow the mole ratios. and after it combusts. .80 g of carbon dioxide and 3. you have 8. mole it out. You run an experiment where you start with a compound containing hydrogen and carbon. and find the empirical formula. 1. Determine: Find the only possible answer (Obj.2. 3) .6 Determine the molecular formula when given the empirical formula and experimental data. Ratio = Relative Molecular Mass (Mr) Empirical Relative Molecular Mass Multiply the Empirical Formula by the ratio found . Molecular formula is related to the molar mass of the compound Sometimes the Molecular Formula is the same as the Empirical Formula. A compound was found to contain 71.65 % Cl Remember, assume a 100g sample 24.27 % C 4.07 % H The molar mass is known to be 98.96g/mol What is the empirical and molecular formula? 1.3.1 Deduce chemical equations when all reactants and products are given. Deduce: Reach a conclusion from the information given. 1) To start, balance all the metals 2) Next balance all the non metals EXCEPT for Oxygen and Hydrogen AND that are not in a complex ion. 3) Next balance all complex ions (you must be able to recognize these!!!) 4) Finally balance Oxygen and Hydrogen, if one of the 2 is in its elemental state balance it last. You already have practice and knowledge of chemical equations. Practice balancing these equations: CH4 + O2 CO2 + H2O C2H5OH(l) + O2(g) CO2(g) + H2O(g) (NH4)2Cr2O7(s) Cr2O3(s) + N2(g) + H2O(g) ? (HW) . What mass and volume of carbon dioxide will be absorbed if 1.00kg of lithium hydroxide is used at S. CH4 + O2 CO2 + H2O Don’t forget the State subscripts! C2H5OH(l) + O2(g) CO2(g) + H2O(g) (NH4)2Cr2O7(s) Cr2O3(s) + N2(g) + H2O(g) Solid lithium hydroxide is used as a carbon dioxide absorber on the space shuttle. The products formed are solid lithium carbonate and liquid water.P.T. Identify: What is the definition? Your turn…. 1.2 Identify the mole ratio of any two species in a chemical equation. (Obj 2) . Identify: Find an answer from a given number of possibilities.3. You already have practice with this as well. Yeahh! Practice makes perfect…. 2NaOH(aq) + H2SO4(aq) Na2SO4(aq) + 2H2O (l) What is the ratio of sodium hydroxide to sodium sulfate? What is the ratio of sodium hydroxide to sulfuric acid? What is the ratio of moles of oxygen atoms in sulfuric acid to moles of sulfuric acid? What is the ratio of moles of oxygen atoms in water to moles of water? . (l). principle. . equation.3.3 Apply the state symbols (s). 1. theory. or law in a new situation. Apply: Use an idea. (g). and (aq). (s) = solid (l) = liquid (g) = gas (aq) = aqueous solution . Intermission Dance Party!!!!!! . or part of an acid-base or redox reaction. Then put the ions and solid in an equation. it is often better to write the ionic equation. This is the ionic equation. For example: Pb(NO3)2(aq) + 2NaCl(aq) PbCl2(s) + 2NaNO3(aq) What are the ions which would be in solution (nonsolid) for each of these molecules? Write them down. For a reaction occurring in aqueous solution forming a precipitate (solid). just like above. . Pb2+(aq) + 2NO3 -(aq) + 2Na+(aq) + 2Cl. However. . re-write. Take these out. This would be any ions that are not involved in forming the main product. and you have the net ionic equation.(aq) PbCl2(s) + 2Na+(aq) + 2NO3-(aq) Which ones are the spectator ions? (Which appear twice?). we get rid of the spectator ions. The previous ionic equation is often referred to as the complete ionic equation. we can reduce this to the net ionic equation. To do this. Answer Net ionic equation: Pb2+(aq) + 2Cl.(aq) PbCl2(s) . 1 Calculate theoretical yield from chemical equations. 1. Calculate: Find a numerical answer showing the relevant stages in the working (unless instructed not to do so). .4. You already have practice doing this with mass to mass calculations! Practice: What mass of sodium hydrogencarbonate (NaHCO3) must be heated to give 8.6 g .80g of carbon dioxide (CO2)? 2NaHCO3 → Na2CO3 + CO2 + H2O Answer: 33. 1. . Determine: Find the only possible answer.2 Determine the limiting reactant and the reactant in excess when quantities of reacting substances are given.4. We must determine which reactant is limiting . We sometimes don’t always have perfect amounts of each reactant. We can only make as much product as the limiting reactant will allow. .Finding The Limiting Reactant 1) Balance the chemical equation 2) Find the number of mol’s of each reactant 3) Divide the # of moles by the coefficient found in the balanced equation. 4) The chemical that has the smallest value is the limiting reactant. 0g H2O = 9.01 g. NH3 left over= 8.0 g of carbon dioxide (CO2). In the reaction 2NH3 + CO2 → (NH2)2CO + H2O You have 25. Which is the limiting reactant? What is the mass of each product? How much reactant is left over? Answers: Limiting: carbon dioxide Mass of each product: (NH2)2CO = 30.5 g of ammonia (NH3) and 22.52 g . 2.50 g of methane is mixed with 3.00 g of water 1) Which reactant is the limiting one? 2) What is the mass of each product? 3) What is the mass of reactant left? CH4(g) + H2O(g) CO(g) + H2(g) . Solve: Obtain an answer using algebraic and/or numerical methods. experimental and percentage yield. 1.3 Solve problems involving theoretical.4. . Theoretical yield: Value that you should get mathematically. Percentage yield=Actual or experiment al yield 100% Theoretica l yield x . Experimental yield: The value you actually get from an experiment. Put it all together: limiting reactants and yield.37 g of iodine (I2). what would the theoretical yield of iodine (I2) be? Answer: 76.00 g of hydrogen peroxide (H2O2) and 50.00 g of KI to a solution of 12. What was the percentage yield? Answer: 81.00 g of sulfuric acid (H2SO4).59% . For the reaction H2O2(aq) + 2KI(aq) + H2SO4(aq) → I2(s) + K2SO4(aq) + 2H2O(l) If you add 100.44 g In the experiment you performed. you produced an experimental yield of 62. What is the composition by mass of 1 mol of Iron(III) Oxide? Click for answer: If it doesn’t add up to 100% something is wrong! M = 159.9% O = 30.1% .7 g/mol Fe = 69. Chemical Math . solution and concentration (g dm-3 and mol dm-3) Distinguish: Give the difference between two or more different items. . 1. solvent.5.1 Distinguish between the terms solute. So…. Concentration: Amount of substance contained within a given volume .a solution contains a solute dissolved in a solvent. Solution: Homogenous mixture of two or more substances. Solvent: Liquid in which the dispersion occurs. Solute: The substance dissolved in the solvent. 25 moles . dm3) Q: How many moles are in a 25cm3 of 10M sulphuric acid (H2SO4)? A: 0. Concentration C = Concentration or Molarity (mol/L or mol/dm3 or M) Molarity = moles of solute Liters of solvent V = volume (L. 1. Solve: Obtain an answer using algebraic and/or numerical methods.5. amount of solute and volume of solution.2 Solve problems involving concentration. . 60M HCl .56 g of gaseous HCl in enough water to make 26. Q: Calculate the molarity of a solution prepared by dissolving 1.8ml(cm3) of solution. Click for answer A: 1. 0 x 10-3 M ZnCl2 Click for answer A: 1. Calculate the number of moles of each ion in 1.75L of 1.5*10-3 mol Cl- .8*10-3 mol Zn2+ 3. # of moles does not change so. Dilutions Sometimes a concentrated solution will have solvent added to produce a more dilute one. ‘n’ is common to both!!! C1 x V 1 = C 2 x V2 . Q: What volume of 16M sulfuric acid must be used to prepare 1.5L of a 0.4 *10-3dm3 or 9.10M H2SO4 solution? Click for answer Special note: Always add acid to water not the other way around!! A: 9.4 cm3 (mL) . . . 1999 Mars Orbital Lander . .IB Core Objective 1. theory.4 Apply Avogadro’s law to calculate reacting volumes of gases. principle.4. Apply: Use an idea. or law in a new situation. equation. a given volume of any gas always contains the same number of particles. At a constant temperature and pressure. In other words. equal amounts of gases at the same temperature and pressure occupy the same volume! . what volume of hydrogen (H2) would you need to fully react with it? What is the volume of ethane (C2H6) that would be produced? Answer: 20cm3 H2 10cm3 of ethane .Using the following reaction C2H2(g) + 2H2(g) → C2H6(g) If you had 10cm3 of ethyne (C2H2). theory or law in a new situation. equation. (Obj.4.5 Apply the concept of molar volume at standard temperature and pressure in calculations. 1. 2) . principle. Apply: Use an idea. 3kPa . then molar volume can be calculated.4dm3 0oC = 273.Molar volume: The volume of any gas that contains one mole. 1atm = 760 mm Hg = 760 torr = 101.15K. If temperature and pressure are specified. At Standard Temperature and Pressure (STP): 1 mol of gas occupies 22. How many moles of oxygen (O2) are there in 5.00 dm3 of oxygen? Answer: 0.223 mol . 6 Solve problems involving the relationship between temperature. Solve: Obtain an answer using algebraic and/or numerical methods. 1. (Obj. 3) .4. pressure and volume for a fixed mass of an ideal gas. When volume decreases. .e. pressure decreases. pressure increases. there are no attractive forces between particles. Boyle’s Law: volume is inversely proportional to pressure at a constant temperature. Ideal gas: Particles have negligible volume. When volume increases. and kinetic energy is proportional to absolute temperature. i. Charles’s Law: Volume is proportional to temperature at constant pressure. Gay-Lussac’s Law: The pressure is proportional to the absolute temperature of the gas. Therefore. increasing the temperature increases the pressure. (This is for variable volume only. How do we put this all together…. doubling the temperature doubles the volume. and vice versa.? . such as a balloon) Therefore. If one of the values is constant. the two refers to the second measurement. then you can just remove that value! . P1V1/T1 = P2V2/T2 The one refers to the initial measurement. 8L at 5oC is heated to 86 oC at constant pressure.9L . Remember to convert Celsius to Kelvins! Click for answer Answer: 4. A sample of methane gas that has a volume of 3. Calculate its new volume. Solve problems using the ideal gas equation. 3) . (Obj. PV=nRT Solve: Obtain an answer using algebraic and/or numerical methods. Universal Gas Equation: PV=nRT 1L = 1000cm3 1L = 1dm3 1000cm3 = 1dm3 P = Pressure V = Volume N = # of mols T = Temperature (K) R = Universal Gas Constant = 8.314 JK-1 mol-1 OR =0.08206 (L•atm)(K•mol)-1 . 314 JK-1 mol-1 Answer: 0. A sample of hydrogen gas has a volume of 8.08206 (L•atm)(K•mol)-1 Or = 8.0 kPa. Calculate the moles of hydrogen gas present in this gas sample P= PV = nRT V= n= Click for T= answer R = 0.57 mol .00C and a pressure of 152.56dm3 at a temperature of 0. 4. 3) .8 Analyse graphs relating to the ideal gas equation. Analyse: Interpret data to reach conclusions. (Obj. 1. Homework: Look at the graphs in your textbook. Analyse: Would Gay-Lussac’s Law look the same as Boyle’s Law or Charles’s Law? .