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Understanding Molar Mass and Mass Percent Composition in Chemistry

Learn about the concept of molar mass and mass percent composition in chemistry, and how to calculate them using dimensional analysis. Understand the relationship between the mass of a substance and the number of moles or atoms present.

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Understanding Molar Mass and Mass Percent Composition in Chemistry

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  1. The Mole A very large counting number = 6.022 x 1023 (6.022 followed by 23 zeros) Also known as Avogadro’s number The number shown under an element on the periodic table is the mass of 1 mole of that element (from the weighted average of naturally occurring isotopes). 1 mole of Li has a mass of 6.941 grams. 6.022 x 1023 atoms of Li has a total mass of 6.941 grams.

  2. Important concept THE MASS ON THE PERIODIC TABLE IS THE MASS IN GRAMS OF ONE MOLE OF THE ELEMENT. Avogadro’s number = # atoms in exactly 12 grams of 12C = 6.022 x 1023 atoms in exactly 12 g of 12C. 12 g of 12C has exactly 6.022 x 1023atoms of C A mole of the element carbon has a mass of 12.01 grams. Taking into account the masses of isotopes the molar mass of carbon is 12.01 grams/mole

  3. A mole of Cl has a mass of 35.45 grams. The molar mass of chlorine is 35.45 g/mole What is the mass of 6.022 x 1023 atoms of Al?

  4. From the periodic table we can see that the molar mass of Al is 26.98 g/mol

  5. Use dimensional analysis to convert 10.0 g Al to the correct number of moles

  6. 10.0 g Al x 1 mol Al = 0.371 mol Al 26.98 g Al 3 s.f. 3 s.f. Exact #

  7. How many grams of Al are there in 10.0 mol of Al? Invert the conversion factor 10.0 mol Al x 26.98g Al= 269.8 g Al mol Al How many atoms of Al are in the sample? 10 mol Al x 6.022 x 1023 atoms Al mol Al = 6.022 x 1024 atoms of Al.

  8. Molar Mass of compounds (Molecular Weight) Compounds are made up of two or more elements The molar mass of the compound is the sum of the molar masses of each element in the compound. Molar mass of O2 (the element, oxygen) is 2 x molar mass of the O atom. 2 x 16.00 grams/mol = 32.00 grams/mol The molar mass for the element O2 is 32.00 g/mol 6.022 x 1023 molecules of O2 weigh 32.00 g

  9. In the molecule CO2, there is one atom of carbon. The subscript on the symbol for oxygen tells us that there are 2 atoms of oxygen in the molecule. There is one mole of carbon in CO2 There are two moles of oxygen in CO2 The molar mass of CO2 is 1 x 12.01 g C / mol CO2 2 x 16.00 g O / mol CO2 44.01 g / mol CO2

  10. What is the molar mass of SO2? • how many moles of S? • how many moles of O?

  11. 1 mol S x 32.06 g/mol S = 32.06 g/mol 2 mol O x 16.00 g/mol of O = 32.00 g/mol 64.06 g/mol 1 mol SO2 = 64.06 g This is an equivalence statement 1 mol SO2=1 64.06 g SO2 = 1 64.06 g SO2 1 mol SO2 This is the same type of equivalence statement as 2.54 cm = 1 in and can be used as conversion factors in calculations.

  12. Calculate the number of moles of CO2 in 2.25 x 102 g of the gas.

  13. First calculate the molar mass of CO2. 1 x 12.01 g/mol C 2 x 16.00 g/mol O 44.01 g/mol CO2 1 mol CO2 = 44.01 g Second use dimensional analysis to convert grams to moles. 2.25 x 102 g CO2 x 1 mol CO2 = 5.11 mol CO2 44.01 g CO2 Is the answer in the correct # s.f.?

  14. Mass percent composition of compounds (molecules or ionic compounds) The mass percent composition of a compound is expressed by identifying the elements present and giving the mass percent of each. mass fraction, = mass of element in 1 mol compound given element mass 1 mol of compound Mass % element A = molar mass of element A x 100 molar mass of compound

  15. Mass percent of elements in ethanol, C2H5OH The molar mass of ethanol is 46.08 g/mol In each mole of ethanol there are 2 moles of carbon The mass percent of carbon in ethanol is 2 x 12.01 = 24.02 g C in each mole of ethanol 24.02 g C x 100 = 52.13% 46.08 g Ethanol 52.13% of the mass of ethanol is from the mass of carbon in the molecule.

  16. What is the mass percent of hydrogen in ethanol, C2H5OH? Total molar mass = 46.08 g. (1 mol ethanol = 46.08 g)

  17. 6 moles of hydrogen in each mole of ethanol x 1.01 g/mol = 6.06 g/mol 6.06 g/mol hydrogen /46.08 g/mol ethanol x 100 = 13.2% Do the two add up to 100%??? Where is the difference? 16.00 g/mol O / 46.08 g/mol ethanol x 100 = 34.7 %

  18. Percent composition makes it possible to determine a compound’s EMPIRICAL formula, the smallest whole number ratio of one element to others in the compound that agrees with the percent composition. CH2O is the empirical formula for formic acid, acetic acid (C2H4O2) and glucose (C6H12O6). What is the molar mass of each compound?

  19. CH2O 30.05 g / mol C2H4O2 60.06 g / mol C6H12O6 180.3 g / mol

  20. Steps - empirical forumula Assume 100 g of compound Divide the mass percent of the element by the molar mass of the element to get the number of moles of each element. Divide the # moles of each element by the smallest # moles to get the ratio of the elements, one to another. If any result is far from a whole number multiply through by a common factor that converts each number of moles to integers (or close) If each is close to a whole # round off each to nearest integer

  21. An unknown clear solution was analyzed and found to contain 84.1% carbon and 15.9% hydrogen by mass. If we assumegrams of the substance, the compound would contain 84.1 g carbon atoms and 15.9 grams of hydrogen atoms. 100

  22. Taking 84.1 g carbon and using the atomic mass and dimensional analysis, we can determine the number of moles of the two elements in the substance. 84.1 g C x 1 mol C = 7.00 mol C 12.01 g C 15.9 g H x 1 mol H = 15.8 mol H 1.01 g H divide moles of each component by smallest number of moles 15.8 mol H = 2.26 mol H 7.00 mol C 1 mol C

  23. The C-H mole ratio is 1:2.26 We can write C1H2.26 as a temporary formula. This is obviously not a true chemical formula (cannot have 2.26 atoms – violates Dalton’s law). We must multiply the formula by a number which converts the fractional number of atoms of hydrogen into a whole number. In the above instance, if we multiply by four, we get C4H9.

  24. C4H9 This is an empirical formula. The true chemical formula could be a whole number multiple of the empirical formula. The chemical formula of the substance analyzed could be C8H18 or any other whole number multiple. Molar mass of empirical formula 4 moles C x 12.01 g/mol C = 48.04 g C 9 moles of H x 1.01 g/mol H = 9.09 g H 57.13 g total

  25. Vitamin C (ascorbic acid) contains 40.92% C, 4.58% H, and 54.50% O by mass. What is the empirical formula of ascorbic acid? Assume 100 g. 40.92 g C x 1 mol C = 3.41 mol C 12.01 g 4.58 g H x 1 mol H = 4.53 mol H 1.01 g 54.50 g O x 1 mol O = 3.41 mol O 16.00 g

  26. 40.92 g C x 1 mol C = 3.41 mol C 12.01 g 4.58 g H x 1 mol H = 4.53 mol H 1.01 g 54.50 g O x 1 mol O = 3.41 mol O 16.00 g To get empirical formula divide the all by the smallest # moles 3.41 mol C / 3.41 = 1 4.53 mol H / 3.41 = 1.33 3.41 mol O / 3.41 = 1 C1H1.33O1 ???

  27. Must multiply subscripts of the derived formula, C1H1.33O1, by some factor to convert the fractional atom into a whole number. This is done by trial and error, but the multiples are usually small, whole numbers. x 2 = C2H2.66O2 x 3 = C3H4O3 molar mass = 88.07 g / mol This is the empirical formula, which may or may not be the molecular formula. It tells us only the relative numbers of atoms. What is the molecular formula for ascorbic acid whose molar mass is 176.13

  28. C3H4O3 molar mass = 88.07 g / mol molar mass compound = 176.14 g / mol 176.14 / 88.07 = 2 molecular formula ascorbic acid = C6H8O6

  29. The composition of ibuprofen is 75.7% C, 8.8% H and 15.5% O, by mass. Determine the mass percentage of each element and from that data determine the empirical formula. Start with 100 grams

  30. 75.7 g from C, 8.8 g from hydrogen, 15.5 g from O 75.7 g C x 1 mol C = 6.30 mol C 12.01 g C 8.8 g H x 1 mol H = 8.70 mol H 1.01 g H 15.5 g O x 1 mol O = 0.969 mol 16.00 g O

  31. DIVIDE EACH NUMBER OF MOLES BY THE SMALLEST TO GIVE THE FOLLOWING. 6.30 mol C / 0.969 mol O = 6.50 mol C / mol O 8.7 mol H / 0.969 mol O = 9.0 mol H / mol O 0.969 mol O / 0.969 mol O = 1 mol O / mol O Empirical formula = C6.50H9O

  32. Elemental Analysis Combustion A compound of unknown composition is decomposed by heat. The elements are carefully trapped and the number of moles of each are analyzed.

  33. A sample of a compound composed of carbon oxygen and hydrogen are combusted in a stream of O2 to produce CO2 and H2O. The H2O and CO2 are trapped and the masses of each measured.

  34. The sample has a mass of 0.255g. When the reaction is complete, 0.561 g of CO2 and 0.306g of H2O are produced. What is the empirical formula of the compound? • Determine the mass of C in the sample. For each mole of CO2, there is one mole of C. Convert moles of C to grams of C. • 0.561 g CO2 x (1 mol CO2 / 44.01 g CO2) x • (1 mol C / 1 mol CO2) (12.01 g C/ mol C) = • 0.153 g C

  35. There are 2 moles of hydrogen per mole of H2O. 0.306 g H2O x (1 mol H2O / 18.0 g H2O) x (2 mole H / mole H2O) x (1.01 g H / mol H) = 0.0343 g H Mass O = mass sample - mass H - mass C Mass sample = 0.255 g Mass O = 0.255 - 0.153 - 0.0343 = 0.068 g O

  36. To get empirical formula, convert g back to moles 0.153 g C x ( 1 mol C / 12.01 g C ) = 0.0128 mol C 0.0343 g H x (1 mol H / 1.01 g H) = 0.0340 mol H 0.068 g O x (1 mol O / 16.0 g O) = 0.0043 mol O Divide each by 0.0043 to get ratio of each element to O C 0.0128 mol C / 0.0043 mol O = 2.98 ~ 3 There are 3 moles of carbon for each mole of oxygen H 0.0340 mol H / 0.0043 mol O = 7.91 ~ 8 There are 8 moles of hydrogen per mole of oxygen Empirical Formula C3H8O

  37. Chemical Equations Short hand describing a chemical change using symbols and formulas to represent the elements and compounds involved in the change. Carbon reacts with molecular oxygen to yield carbon dioxide C + O2 CO2 The equation tells us that 1 mole of C reacts with 1 mole of O2 to yield 1 mole of CO2

  38. Stoichiometric Calculations: Stoicheion (element) ; metron (measurement) Relating mass or moles of reactants in a chemical reaction to mass or moles of products. EQUATION MUST BE BALANCED Reaction of C2H4 (g) + HCl(g) C2H5Cl(g) If we have 15.0 g of C2H4how many moles of HCl are needed to carry out the reaction to completion?

  39. C2H4(g) + HCl(g) C2H5Cl(g) The balanced equation tells us it takes 1 mole of HCl for each mole of C2H4 reacted. We must begin by converting the number of grams of C2H4 which has a molar mass of 28.08 g/mol, to moles 15.0 g C2H4 x 1 mol C2H4= 0.534 mol C2H4 28.08 g C2H4

  40. C2H4(g) + HCl(g) C2H5Cl(g) The coefficients in the balanced equation tells us that one mole of HCl is needed for each mole of C2H4 (ethylene). It therefore takes 0.534 mol of HCl to consume all of the ethylene. What mass of HCl is needed to carry the reaction through to completion?

  41. C2H4 (g) + HCl(g) C2H5Cl(g) To determine the mass of HCl needed, use molar mass. Begin with what is asked. 0.534 mol HCl x 36.5 g HCl = 19.6 g HCl mol HCl

  42. C2H4(g) + HCl(g) C2H5Cl(g) How many moles of product are made when 15.0 g of C2H4 is reacted with an excess of HCl? Pay close attention to what is being asked. Note from balanced eqn that there is one mole of C2H4 is needed to make one molecule of C2H5Cl. Note also that the question only refers to the reactant C2H4and product, not HCl.

  43. C2H4(g) + HCl(g) C2H5Cl(g) To determine moles from mass use dimensional analysis. Molar mass of C2H4 (ethylene) = 28.08 g/mol The problem states that you have 15.0 g C2H4 15.0 g C2H4 x 1mole C2H4 = 0.534 mol C2H4 28.06 g C2H4 Since the stoichiometry of the balanced equation indicates that 1 mol of C2H5Cl is produced from each mole of C2H4, the ratio is 1:1.

  44. C2H4 (g) + HCl(g) C2H5Cl(g) 0.534 mol 0.534 mol (molar mass C2H5Cl = 64.51 g/mol) Mass of product: 0.534 mol product x 64.51 g/mol = 34.448 g = 34.5 g in correct # sig fig (we started with 15.0 g reactant. Answer must be in 3 sig.fig).

  45. Calculations of product masses when the stoichiometric coefficients are not the same. N2(g) + H2(g) NH3(g) Note from the balanced equation that two moles of product are yielded when 1 mole of N2 reacts with 3 mole H2. To determine the mass of the product, we follow the same steps, but now we must consider anotherfactor, the mole ratio. 3 2

  46. N2(g) + 3H2(g) 2NH3(g) If there is enough N2 in the mixture and we have 4.8 mol H2, how many moles of NH3 are produced? The relationship is now 3:2 and we must take that into consideration. Again, begin with what you are given. You have 4.8 mol H2.

  47. N2(g) + 3H2(g) 2NH3(g) 4.8 mol H2 x 2 mol NH3 = 3.2 mol NH3 3 mol H2 Mass of NH3 is determined by calculating mass from moles using molar mass as before.

  48. N2 + 3H2 2NH3 1. Assuming there is enough hydrogen for the reaction to go to completion how many grams of nitrogen are needed to yield 0.430 moles of NH3? 2. For the reverse reaction, how many grams of nitrogen are produced by the decomposition of 3.24 grams of gaseous NH3?

  49. Limiting Reactants Suppose you do not have enough of one reactant to carry the reaction to completion? To determine the moles or masses of products, we need to know which reactant will run out first and which is in excess. We cannot use coefficients or masses to make the determination. As usual, everything is measured in moles.

  50. Limiting Reactants 1. Write the balanced equation. 2. Convert masses to moles. 3. The reactant producing the lowest moles of product will be consumed (limiting reactant).

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