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You are an incredibly valuable employee. Your boss wants to reward you so she offers you two options. You can either work 10 days straight and receive one million dollars or you can earn a dollar per second up to one million dollars. You would like to buy an elite condo in the Bahamas that costs exactly one million dollars. Which deal will allow you to purchase the condo first? (Assume that you work every second of every day in both cases. ) Your boss is in a hurry to a meeting so you only have five minutes to decide.
Factor –Labeling • The factor-label method was developed to keep track of units in multi-step conversion problems (also known as dimensional analysis). • Crash Course
Factor –Labeling • For example, consider the conversion of inches to centimeters (1. 00 in = 2. 54 cm). How many centimeters are in 5. 00 inches?
Hidden Conversion Factors = Sign The word per The word for The word in How many conversion factors can you find on the back of your Periodic Table?
When is factor labeling useful? A batch of French toast requires 3 eggs to make. How many eggs are needed to make 8 batches? The same French toast recipe can feed 4 people per batch. If you throw a breakfast party for 12 people, how many batches do you need to make?
Factor Labeling • By using conversion factors we can determine how many of something we have in one unit instead of the other
Converting Units (cont) Factor Labeling Steps 1. Determine what the question is asking you to solve for. • What is the ? Asking 2. Determine what is given in the problem to be converted. • Given 3. Identify and plug in the appropriate conversion factors as fractions (what is on top must also be on bottom). • Plug in the appropriate conversion factors (what’s on top must go on bottom) 4. Cancel units 5. Verify your answer. (Units must match units in step 1. If the answer doesn’t match, repeat 3 and 5).
When is factor labeling useful? You are a veterinarian’s assistant. The doctor asks you to give Lassie, a young girl’s dog, 18. 5 mg of Acepromazine before it goes into surgery. However, the medicine is in liquid form and must be given intravenously. Reading the bottle you see that Acepromazine has a density of 10 mg/ml. How many m. L of Acepromazine should you give the dog?
Self-Motivated Practice • For the rest of the year, we will be doing a lot of math and calculations. • You will also be provided a lot of practice problems to help with understanding how to correctly complete these problems.
Self-Motivated Practice • Reminder – we are doing calculations, this means that you will need your calculator every day, no exceptions.
Self-Motivated Practice • The correct answer on these quizzes are worth very little. • Therefore you will not get any credit if you do not show your work (Factor- Labeling). • If you understand the concept and can just plug the number into the calculator and get the answer, you are luckily to be able to visuals the step-up in your head but I can not grade what is in your head. Show and write out the work!
Counting Particles MOLE • The mole (mol) is an SI base unit used to measure the amount of a substance. (Also known as Avagadro’s number). • 1 mole is equal to the number 6. 02 1023 particles.
Counting Particles • Avagadro’s number is named after Amedeo Avagadro who proposed in 1811 that in any given gas, the number of atoms or molecules in a gas was directly proportional to it’s volume independent of a gas properties. • The number was valued at 6. 02 x 1023 in 1926 by Jean Perrin who proposed that the number be proposed after Avagadro for his foundational work.
Counting Particles • A mole is an enormous quantity, even for extremely small particles. • Avogadro’s number would not be convenient for measuring a quantity of eggs, roses, or paper. • One mole of marshmallows would cover the USA to a depth of 6500 miles.
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The Mass of a Mole • A mole always contains the same number of particles; however, moles of different substances have different masses.
Chemical Formulas and the Mole • Chemical formulas indicate the numbers and types of atoms contained in one unit of the compound. • Similarly, one mole of CCl 2 F 2 contains one mole of C atoms, two moles of Cl atoms, and two moles of F atoms. • One dozen molecules of CCl 2 F 2 contains 12 C atoms, 2(12) Cl atoms, and 2(12) F atoms.
The Mass of a Mole • Molecular Mass: (atomic mass, formula mass) of a molecule is its average mass as calculated by adding together the atomic weights of the atoms in the formula. MM QT MM= Molecular Mass Q= quantity T= Total
The Mass of a Mole • What is the molar mass of the following elements? – Carbon Dioxide – (NH 4)2 CO 3
The Mass of a Mole • Molar mass is the mass in grams of one mole of any pure substance. • The molar mass of any element is numerically equivalent to its molecular mass (atomic mass, formula mass) and has the units g/mol. CONVERSION FACTOR ALERT
Practice makes Perfect How many particles of Na. Cl (Sodium Chloride) are in 43. 4 moles?
Practice makes Perfect • How many moles of copper are there in 1. 54 x 1023 atoms Cu?
Practice makes Perfect • How many molecules of sucrose are in 3. 5 moles of sucrose?
Section Assessment What is the conversion factor for determining how many moles are in 7. 16 x 1024 particles? A. B. C. 1 particle 6. 02 1023 D. 1 mol 6. 02 1023 particles A. B. C. D. A B C D
Converting using Moles • How many grams of zinc are there in 1. 5 moles of Zn? • How many liters of carbon dioxide are there 4. 0 moles of carbon dioxide at STP?
Converting using Moles • Gold (Au) is one of a group of metals called coinage metals (copper, silver, and gold). How many atoms of gold are in a U. S. Eagle, a gold bullion coin with a mass of 31. 1 g Au?
Converting using Moles • The characteristic odor of garlic is due to allyl sulfate [(C 3 H 5)2 S]. What is the mass of 2. 50 mol of (C 3 H 5)2 S ?
Converting using Moles • Aluminum chloride (Al. Cl 3) is used in refining petroleum and manufacturing rubber and lubricants. A sample of aluminum chloride has a mass of 35. 6 g. How many formula units are present?
Learning Check The mass in grams of 1 mol of any pure substance is: A. molar mass B. Avogadro’s number C. atomic mass D. 1 g/mol A. B. C. D. A B C D
Practice makes Perfect • How many moles are in 28 grams of CO 2? A. 0. 636 moles B. 1232. 252 moles C. 1. 0 moles D. 0. 8 moles
Practice makes Perfect • What is the mass of 5 moles of Fe 2 O 3? A. 0. 0313 g B. 31. 937 g C. 798. 435 g D. 997. 665 g
Practice makes Perfect Find the number of moles of argon in 452 g of Ar. A. 39. 948 moles B. 11. 315 moles C. 18, 056. 496 moles D. 0. 0884 moles
Practice makes Perfect Find the mass in 2. 6 mol of Li. Br. A. 225. 797 g B. 86. 845 g C. 0. 0299 g D. 33. 402 g
Practice makes Perfect • Find the mass in grams of 2. 00 x 1023 molecules of F 2 A. 37. 996 g B. 0. 332 g C. 1. 204 x 1047 g D. 12. 623 g
Practice makes Perfect Find the mass, in grams, of 1. 00 x 1023 molecules of Cl 2. A. 6. 02 x 1046 g B. 0. 166 g C. 7. 091 x 1024 g D. 11. 778 g
Practice makes Perfect • Determine the volume in liters occupied by 14 g of N 2 at STP. A. 28. 014 L B. 11. 194 L C. 0. 4998 L D. 392. 196 L
Practice makes Perfect How many grams of H 2 SO 4 are in 13 L at STP? A. 1274. 998 g B. 98. 077 g C. 56. 920 g D. 291. 2 g
Practice makes Perfect Find the number of molecules in 28. 3 grams of HCl. A. 0. 776 molecules B. 1. 704 x 1025 molecules C. 4. 673 x 1023 molecules D. 1. 651 x 1022 molecules
Practice makes Perfect Find the number of liters in 8. 6 grams of CH 4 at STP. A. 12. 01 L B. 12. 01 g C. 192. 64 L D. 0. 536 g
Practice makes Perfect How many liters of Cu at STP are in 8. 45 x 1024 molecules? A. 14. 036 L B. 314. 419 L C. 1. 893 x 1026 L D. 14. 036 molecules