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Quantities in Chemistry

Quantities in Chemistry. We’ve now seen that atoms can combine in certain atom ratios to make compounds: 1 Ca atom combines with 2 Cl atoms (giving each one e-) to make 1 Ca +2 ion bound to 2 Cl -1 ions in the compound CaCl 2.

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Quantities in Chemistry

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  1. Quantities in Chemistry • We’ve now seen that atoms can combine in certain atom ratios to make compounds: 1 Ca atom combines with 2 Cl atoms (giving each one e-) to make 1 Ca+2 ion bound to 2 Cl-1 ions in the compound CaCl2

  2. Chemists often need to know how many particles of matter they have: • How many Ca atoms do they have in a sample? How many Cl atoms? • How many CaCl2 compounds can they make from them? • How many CaCl2 compounds are in a sample? • If they break up the CaCl2 compounds, how many Ca+2 ions can they get from it?

  3. 3 problems relating to counting atoms • There are trillions of atoms in even tiny samples. Need to count in ‘sets’ of trillions of atoms or so. • Atoms are too small to see – can’t count directly. Need to relate atom count to something easier to measure. • If atoms are bonded in compounds, there are several atoms but one compound. Need to clarify if you need count of compounds or count of atoms.

  4. Problem 1: Too Many! • Rather than always having to deal with such large numbers, a unit was created to count particles. It is called the mole. • (Think of the mole as a set number of atoms just like a dozen is a set number of eggs, paper clips, etc) • 1 mole = 6.02 x 1023 things

  5. Counting Units 1 dozen eggs 1 ream paper 1 gross pencils Assuming we could count these and found there were 602,300,000,000,000,000,000,000 of them … 1 mole particles

  6. What are particles in chemistry • Atoms • Formula units • Molecules • Ions _ _ _ _ _ _ _ _ _ _ _ _

  7. The mole Depending on what we’re counting, units change • 1 mole = 6.02 x 1023 things • 1 mole Al = 6.02 x 1023atoms Al • 1 mole CaCl2= 6.02 x 1023compounds CaCl2 (= 3 moles individual atoms: 1 mole Ca atoms, 2 moles Cl atoms) • 1 mole CO2 = 6.02 x 1023molecules CO2 (= 3 moles individual atoms: 1 mole C atoms, 2 moles O atoms) • 1 mole Fe3+ = 6.02 x 1023ions Fe3+ Because Al is an element Because CaCl2 is an ionic compound Because CO2 is a covalent compound Because Fe+3 is an ion

  8. Avogadro’s Number: 6.02 x 1023(= the # of things in a mole) Why did he choose such a bizarre number? To make the mass of 1 atom (in amu) the same number as the mass of 1 mole of atoms (in g) Since there are 6.02 x 1023 amu in 1 gram, choosing this number makes 1 mole weigh the same, in grams, as 1 atom weighs, in amu: 1 atom Ca = 40.08 amu AND 1 mole Ca = 40.08 g

  9. How to convert particles to moles How many of in ? Since there are 6.02 e23 in every Divide the count of By 6.02 e23

  10. How to convert particles to moles Remember, “particles” is the generic term for ions, atoms, molecules or compounds Divide by Avogadro’s number, since that is the number of particles in 1 mole:

  11. How to convert moles to particles How many of in ? Since there are 6.02 e23 in every Multiply the number of By 6.02 e23 2.5 of

  12. How to convert moles to particles multiply by Avogadro’s number:

  13. Conversion Type #1:moles  particles1 mole of X = 6.02 x 1023 atoms of X 1 mole of XY = 6.02 x 1023 molecules of XY A mole is just a large set of a number of particles (just as a dozen is a set of 12 eggs) • The number was chosen because there are the same number of amu’s in a gram. • This way a mole of atoms, in grams, weighs the same as a single atom, in amu’s. • If starting with atoms/ions/molecules, use the conversion factor with 6.02 x 1023 particles on the bottom • If starting with moles, use the conversion factor with 1 mole on the bottom

  14. Problem 2: how can we count particles that are so small??? • Remember, billions of billions of atoms can be found in a sample the size of a grain of sand. • If we can’t see the atoms, how can we find out how many there are?

  15. Solution: Use weight (mass)! If we know how much the sample weighs, and how much a single atom weighs, we can figure out how many atoms are in the sample! Mass of sample = # of atoms Mass of 1 atom

  16. How much does an atom weigh (on average)? It depends on the element • Average mass of a single atom of an element based on the natural abundance of an element’s isotopes • Average atomic mass is found on the periodic table For every 200 atoms, about 198 are 16O, 1 is 17O and 1 is 18O…. Averages to 16.999 amu

  17. Converting amu’s to grams • For your information: 6.02 x 1023 amu = 1 gram Eg. How many grams does 1 Carbon atom weigh?

  18. Molar Mass (abbreviation is MM) • Another name for the weight of 1 mole of a substance (in grams) • The Molar Mass of an element is the same number as the average atomic mass average atomic mass of Cl = 35.45 amu Molar Mass of Cl = 35.45 g/mole average atomic mass of O = 16.00 amu Molar Mass of O = 16.00 g/mole

  19. Conversion Type #2:mass  molesmolar mass of X grams = 1 mole of X • Molar Mass of an element is found on periodic table (average molar mass in grams/mole) • If starting with grams, use the conversion factor with molar mass in g on the bottom • If starting with moles, use the conversion factor with 1 mole on the bottom

  20. How to convert mass (grams) to moles(!!!!!!!) Divide grams by molar mass How many moles in 24.5 g of iron?

  21. How to convert moles to mass (grams) (!!!!!!!) Multiply moles by molar mass How many grams in 1.44 moles of iron?

  22. Names used in counting chemicalsDepending on what kind of chemical we are counting, the names change! • when counting samples of element we count Atoms • when counting samples of ionic compounds we count theoretical pieces of a crystal called Formula units • when counting samples of covalent compounds we count Molecules • when counting samples of ions we count Ions OR, we can use generic terms: • When counting chemicals, we count particles

  23. Molar Mass of Compounds How much does 1 mole of weigh? Since every mole of CaCl2 has 1 mole of Ca atoms and 2 moles of Cl atoms, we can add the known element molar masses ??? g 35.45 g 40.08 g TARE TARE TARE

  24. How much does 1 formula unit of a compound weigh? How much does “1” CaCl2 weigh? Remember, 1 CaCl2 unit is made from 1 Ca atom and 2 Cl atoms 1 formula unit CaCl2 = (40.08 amu + 2(35.45 amu)) = 110.98 amu Also, 1 mole of CaCl2 units is made from 1 mole Ca atom and 2 moles Cl atoms 1 mole CaCl2 = (40.08 g + 2(35.45 g)) = 110.98 g A compound weight can be calculated by adding together the subscript x atomic weight for each element in the compound.

  25. Molar Mass of Compounds Just as we found the mass of a formula unit of a compound using the subscripts and each element’s atomic weight, we can find the molar mass of a compound using the subscripts and the molar masses: MM CaCl2 = MM Ca + MM Cl + MM Cl = MM Ca + (MM Cl x 2) MM cmpd= Sum of (each element’s MM x its subscript)

  26. We can do all the same conversions we did with elements with compounds by just using the COMPOUND MOLAR MASS instead of the elemental molar mass: How many grams will 1.44 moles of NaOH weigh? How many moles of compound are in 24.5 grams of FeO?

  27. Problem #3: If atoms are bonded in compounds, there are several atoms but one compound. The counts are different for atoms and compounds • We need to clarify what we are counting • The subscript(s) help us convert from one to the other

  28. Conversion Type #3:atoms  atom sets (compounds)1 compound of X3Y2 = 3 atoms X 1 compound of X3Y2 = 2 atoms Y 1 compound of X3Y2 = 5 atoms total • If the ‘set’ is a compound, then the number of atoms of an element in a set is determined by the subscript for that element

  29. Compounds to individual atoms How many in How many in 1465 compounds in sample Since there is 1 in every , the count will be the same Since there are 2 in every , the # of will be double the # of

  30. Compounds to individual atoms Remember, if a compound is broken apart, you will have several atoms of different elements. The subscript tells us how many atoms of each type are in the compound To convert from # compounds to # of each type of atom, multiply by the subscript:

  31. Individual atoms to compounds Remember, a compound is formed by bonding several atoms of different elements together. The subscript tells us how many atoms of each type are in the compound To convert from # of each type of atom to # compounds, divide by the subscript:

  32. Front table

  33. How many moles in 111.6 g of Fe • 6.02 x 1023 • 2.00 moles • 6227 moles • 55.8 moles

  34. How many moles in 111.6 g of FeO • 6.02 x 1023 • 1.55 moles • 8012 moles • 71.8 moles

  35. Mole formulas for pure substances (in Ch 12 we will find another way to count moles; in CHEM 102 there is yet a 3rd way to find moles • Need to know!!

  36. How many moles in 100.0 grams of • Cu • NaCl • O2

  37. How many grams in 2.0 moles of • Cu • NaCl • O2

  38. Percent Composition vs. Empirical Formulas • % composition is defined as the %mass of an element in a compound • % composition of X = mass element  mass compound • an empirical formula’s subscripts are the lowest whole number ratio of the moles of the elements in the compounds • MxOy means that • % composition is a ratio of mass and a chemical formula represents a ratio of moles

  39. % composition is a ratio of massempirical formula is a ratio of moles Converting FromTo % composition  empirical formula is really converting (mass  moles) Empirical formula  % composition is really converting (moles  mass)

  40. Calculating % Composition % composition is a ratio of mass and a chemical formula represents a ratio of moles THUS CONVERTING FORMULA TO % COMPOSITION MEANS MOLES  MASS Steps: Pretend that you have 1.00 mole of this formula. That means you know how many moles of each element in the formula using the subscripts. Convert each element’s moles to mass of that element. Add up all the element masses to get the total compound mass. For each element (divide the mass of that element by the total mass) x 100%

  41. Sample % composition What is the % composition of N in HNO3? H: 1.00 mole H x 1.01 g H/mole H =1.01 g H 63.0 = 0.0160 x 100% = 1.60% H N: 1.00 mole N x 14.0 g N/mole N =14.0 g N 63.0 = 0.222 x 100% = 22.2% N O: 3.00 mole O x 16.0 g O/mole O =48.0 g O63.0 = 0.761 x 100% = 76.1% O TOTAL = 63.0 g HNO3 Subscript of element Molar Mass of element Divide each by the total mass, then multiply each by 100%

  42. Calculating Empirical Formula • % composition is a ratio of mass and a chemical formula represents a ratio of moles • THUS CONVERTING %COMPOSITION TO FORMULA MEANS MASS  MOLES • Steps: • Pretend that you have 100 g of this formula. So, that means if it is 25% X that you have 25 g of X; do the same for all elements in compound • Convert each element’s mass to moles of that element • Divide each mole amount by whichever amount is the smallest. (eg. 1.25 moles X / .25 moles Y means there are 5 X atoms for every 1 Y atom in the compound) NOTE: You must arrive at WHOLE numbers (you may have to multiply all the divided amounts by the same common factor to get them to be whole). • Write the chemical formula using the whole numbers as subscripts

  43. Sample empirical formulaWhat is the empirical formula of a compound that has 49.5%C, 5.2%H, 28.8%N, 16.5%O C4H5N2O Smallest # moles

  44. Sample empirical formula:What is the empirical formula of a compound that’s 31.0% B, 69.0% O B2O3 Smallest # moles

  45. How many moles of cobalt atoms are there in 77.4 g of Co?

  46. What is the mass (in g) of 1.00 E12 lead atoms?

  47. Which has more atoms?1.10 g of hydrogen atoms14.7 g of chromium atoms

  48. Which has more atoms?5.00 g of nitrogen molecules14.7 g of chromium atoms

  49. How many grams of Cl are there in 15.6 g of CaCl2?

  50. How many atoms of Cl are there in 15.6 g of CaCl2?

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