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Dimensional Analysis: Problem-Solving with Conversion Factors

Learn how to solve problems systematically using conversion factors with dimensional analysis. Practice converting units with examples and steps explained.

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Dimensional Analysis: Problem-Solving with Conversion Factors

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  1. Unit 11 Notes You will need a calculator

  2. Dimensional Analysis: a systematic (step-by-step) approach to problem solving that uses conversion factors to convert from one unit to another Dimensional Analysis is organized as multiplied fractions, so is often referred to as railroad tracks or a grid

  3. For example: 1 mile = 5280 feet, so how many feet are in 3.5 miles? As fractions: As RR tracks (or grid):

  4. To accomplish dimensional analysis, you need a conversion factor, like 1 dollar = 0.81 euros Then there are 4 steps: Write the given with its label, in the top left box Match labels diagonally Fill in the rest of the conversion factor, cancel labels diagonally Multiply numbers on top, and divide by numbers on the bottom, bring over uncancelled label

  5. The cost of a 4 star hotel in Paris is about 500 euros a night. What is that cost in dollars? (1 dollar = 0.81 euros) Write the given with its label, in the top left box

  6. The cost of a 4 star hotel in Paris is about 500 euros a night. What is that cost in dollars? (1 dollar = 0.81 euros) Write the given with its label, in the top left box

  7. The cost of a 4 star hotel in Paris is about 500 euros a night. What is that cost in dollars? (1 dollar = 0.81 euros) 2. Match labels diagonally

  8. The cost of a 4 star hotel in Paris is about 500 euros a night. What is that cost in dollars? (1 dollar = 0.81 euros) 2. Match labels diagonally

  9. The cost of a 4 star hotel in Paris is about 500 euros a night. What is that cost in dollars? (1 dollar = 0.81 euros) Fill in the rest of the conversion factor, cancel labels diagonally

  10. The cost of a 4 star hotel in Paris is about 500 euros a night. What is that cost in dollars? (1 dollar = 0.81 euros) Fill in the rest of the conversion factor, cancel labels diagonally

  11. The cost of a 4 star hotel in Paris is about 500 euros a night. What is that cost in dollars? (1 dollar = 0.81 euros) Fill in the rest of the conversion factor, cancel labels diagonally

  12. The cost of a 4 star hotel in Paris is about 500 euros a night. What is that cost in dollars? (1 dollar = 0.81 euros) Multiply numbers on top, and divide by numbers on the bottom, bring over uncancelled label 500 × 1÷ 0.81 = 617.28

  13. The cost of a 4 star hotel in Paris is about 500 euros a night. What is that cost in dollars? (1 dollar = 0.81 euros) Multiply numbers on top, and divide by numbers on the bottom, bring over uncancelled label 500 × 1÷ 0.81 = 617.28

  14. The cost of a 4 star hotel in Paris is about 500 euros a night. What is that cost in dollars? (1 dollar = 0.81 euros) Multiply numbers on top, and divide by numbers on the bottom, bring over uncancelled label

  15. A friend gives you a 1000 peso bill from the Philippines. How many dollars did you just get? (1 dollar = 51.26 Philippine pesos)

  16. A friend gives you a 1000 peso bill from the Philippines. How many dollars did you just get? (1 dollar = 51.26 Philippine pesos)

  17. A friend gives you a 1000 peso bill from the Philippines. How many dollars did you just get? (1 dollar = 51.26 Philippine pesos)

  18. A friend gives you a 1000 peso bill from the Philippines. How many dollars did you just get? (1 dollar = 51.26 Philippine pesos)

  19. A friend gives you a 1000 peso bill from the Philippines. How many dollars did you just get? (1 dollar = 51.26 Philippine pesos)

  20. A friend gives you a 1000 peso bill from the Philippines. How many dollars did you just get? (1 dollar = 51.26 Philippine pesos)

  21. A friend gives you a 1000 peso bill from the Philippines. How many dollars did you just get? (1 dollar = 51.26 Philippine pesos)

  22. A friend gives you a 1000 peso bill from the Philippines. How many dollars did you just get? (1 dollar = 51.26 Philippine pesos)

  23. Earnest Rutherford is on the 100 New Zealand dollar. How many US dollars is he worth? (0.73 USD = 1 NZD)

  24. Earnest Rutherford is on the 100 New Zealand dollar. How many US dollars is he worth? (0.73 USD = 1 NZD)

  25. Earnest Rutherford is on the 100 New Zealand dollar. How many US dollars is he worth? (0.73 USD = 1 NZD)

  26. Earnest Rutherford is on the 100 New Zealand dollar. How many US dollars is he worth? (0.73 USD = 1 NZD)

  27. Earnest Rutherford is on the 100 New Zealand dollar. How many US dollars is he worth? (0.73 USD = 1 NZD)

  28. Earnest Rutherford is on the 100 New Zealand dollar. How many US dollars is he worth? (0.73 USD = 1 NZD)

  29. Earnest Rutherford is on the 100 New Zealand dollar. How many US dollars is he worth? (0.73 USD = 1 NZD)

  30. Practice is in Canvas Intro to Dimensional Analysis Quiz – Due by 7:30 on Monday

  31. Molar Mass Continuing the Unit 11 Notes You will need a calculator

  32. Roses and eggs are conveniently packaged as a dozen. Sheets of paper are packaged as a ream. Small item are packaged in large amounts to make life easier. The same is true for atoms. However, because atoms are really, really, really small, the amounts of them that are packaged together are really, really, really big.

  33. Roses and eggs are conveniently packaged as a dozen. Sheets of paper are packaged as a ream. Small item are packaged in large amounts to make life easier. The same is true for atoms. However, because atoms are really, really, really small, the amounts of them that are packaged together are really, really, really big. A package of atoms or compounds that chemists use is called the Mole.

  34. A mole (abbreviated “mol”) contains 602,200,000,000,000,000,000,000 of anything. This really large number is often called Avogadro’s Numberand is abbreviated 6.022 × 1023. • Typical representative particles (things) measured in moles: • atoms • Molecules (covalent only) • Compounds (ionic or covalent) • formula units (ionic only)

  35. The mole is not only handy to counting a large amount of atoms or compounds, it is even more useful when measuring out amounts of elements or compounds. The masses on the periodic table have been designed to be the amount of grams in a mole of that element, thus it is called the “molar mass”

  36. For example, look at sulfur. The information shown for sulfur tells us that 1 mol of sulfur = 32.07grams of sulfur. Likewise, 2 mols of sulfur = 2 × 32.07 or 64.14grams of sulfur, etc. This allows for amounts of elements to be easily measured in the laboratory and turned into moles.

  37. A student measures out 12.0 g of Mg in lab. How many moles does this student have?

  38. A student measures out 12.0 g of Mg in lab. How many moles does this student have?

  39. A student measures out 12.0 g of Mg in lab. How many moles does this student have?

  40. A student measures out 12.0 g of Mg in lab. How many moles does this student have?

  41. A student measures out 12 g of Mg in lab. How many moles does this student have? Notice the molar mass is unique for each element and must come from the periodic table.

  42. The opposite can also be done. A student needs 2.30 mols of B for an experiment. How many grams should this student measure out?

  43. The opposite can also be done. A student needs 2.30 mols of B for an experiment. How many grams should this student measure out?

  44. The opposite can also be done. A student needs 2.30 mols of B for an experiment. How many grams should this student measure out?

  45. The opposite can also be done. A student needs 2.30 mols of B for an experiment. How many grams should this student measure out?

  46. The opposite can also be done. A student needs 2.30 mols of B for an experiment. How many grams should this student measure out?

  47. A properly written compound shows the ratio of atoms in the compound. For example, sodium carbonate (Na2CO3) shows that for every 1 compound there are 2 atoms of Na, 1 atom of C, and 3 atoms of O.

  48. This also works with the mole. For 1 mole of the compound, there are 2 moles of Na, 1 mole of C, and 3 moles of O. This information allows us to calculate the molar mass of the entire compound, sometimes called the formula mass instead of molar mass.

  49. What is the molar mass for sodium carbonate (Na2CO3)?

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