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The Mole: Avogadro's Number & Molecular Weight

Learn about the concept of the mole, Avogadro's number, molecular weight, and practice problems related to mole calculations in chemistry.

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The Mole: Avogadro's Number & Molecular Weight

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  1. The Mole A look at Avogadro's Number 6.02 x 10^23

  2. Molecular Weight • The mole is the standard method in chemistry for communicating how much of a substance is present. • What is Molecular Weight? • The weight in atomic mass units (amu) of all the atoms in a given formula • The molecular weight of a substance is needed to tell us how many grams are in one mole of that substance.

  3. Practice Problems • Calculate the following molecular formulas • 1) (NH4)2S • 2) Fe2O3 • 3) KClO4 • 4) SF6 • 5) (NH4)2SO4

  4. The Mole & Molar Mass • In one mole, there are • 6.022 x 1023 atoms, or molecules, or compounds, or doughnuts, or cups of coffee. • So one mole of ANYTHING contains 6.022 x 1023 entities.

  5. Just How Big is a Mole? • Enough soft drink cans to cover the surface of the earth to a depth of over 200 miles. • If you had Avogadro's number of unpopped popcorn kernels, and spread them across the United States of America, the country would be covered in popcorn to a depth of over 9 miles. • If we were able to count atoms at the rate of 10 million per second, it would take about 2 billion years to count the atoms in one mole.

  6. The mole and molecular weight cont. • The symbol for mole is "mol” • 6.02 x 1023 is called Avogadro's Number • When we weigh one mole of a substance on a balance, this is called a "molar mass" and has the units g/mol

  7. The mole and molecular weight practice problems • calculate the mass of one mole of these substances • 1) (NH4)2S • 2) Fe2O3 • 3) KClO4 • 4) SF6 • 5) (NH4)2SO4

  8. The mole and molecular weight practice problems • calculate the mass of one mole of these substances • Lithium Hydride • Calcium Hydroxide • Copper (II) Bromide

  9. Molar Ratios • Molar Ratios • 1) N2 + 3 H2 ---> 2 NH3 • Write the molar ratios for N2 to H2 and NH3 to H2. • 2) 4 NH3 + 3 O2 ---> 2 N2 + 6 H2O • Write the molar ratios for NH3 to N2 and H2O to O2. • 3) Fe2O3 + 3 CO ---> 2 Fe + 3 CO2 • Write the molar ratios for CO to CO2 and Fe to CO.

  10. Mole ConversionsGiven Moles, Convert to Grams • In chemistry, the mole is the standard measurement of amount. When substances react, they do so in simple ratios of moles. • There are three steps to converting moles of a substance to grams: 1. Determine how many moles are given in the problem. 2. Calculate the molar mass of the substance. 3. Multiply step one by step two.

  11. mole to gram cont. • The three steps above can be expressed in the following equation: • # of Moles X Molecular weight of substance= Grams of substance

  12. Mole to gram practice problems • Convert the following into grams • 1) 0.200 moles of H2S • 2) 0.100 moles of KI • 3) 1.500 moles of KClO • 4) 0.750 moles of NaOH • 5) 3.40 x 10^5 moles of Na2CO3

  13. Mole ConversionsGiven Grams, Convert to Moles • There are three steps to converting grams of a substance to moles. • Determine how many grams are given in the problem. • Calculate the molar mass of the substance. • Divide step one by step two.

  14. Gram to mole cont • The three steps above can be expressed in the following equation: • Given Grams x (1 mole/molecular weight)

  15. Gram to mole practice problem • Convert the following into moles • 1) 2.00 grams of H2O • 2) 75.57 grams of KBr • 3) 100. grams of KClO4 • 4) 8.76 grams of NaOH • 5) 0.750 grams of Na2CO3

  16. Avogadro Number CalculationsHow Many Atoms or Molecules? • The value for Avogadro's Number is 6.022 x 10^23 mol • Types of problems you might be asked look something like these: 1. 0.450 mole (or grams) of Fe contains how many atoms? 2. 0.200 mole (or grams) of H2O contains how many molecules?

  17. Atoms or molecules cont. • When the word grams replaces mole, you have a related set of problems which requires one more step. • Here is a graphic of the procedure steps: :

  18. Atoms or molecules • Example : 0.450 mole of Fe contains how many atoms? • Solution: start from the box labeled "mole" and move (to the right) to the box labeled "atoms." What do you have to do to get there? • 0.450 mol x 6.022 x 10^23 mol

  19. Atoms or molecules practice problems • Complete the following problems • Calculate the number of molecules in1.058 mole of H2O • Calculate the number of atoms in 0.750 mole of Fe • Calculate the number of molecules in1.058 gram of H2O • Calculate the number of atoms in 0.750 gram of Fe

  20. Molarity • Molarity is the concentration of a solution in moles per liter • The symbol for molarity is M • A 4.90M solution of NaCl means that there are 4.90 moles on NaCl in 1 liter of the solution • Molarity = mol/L

  21. Stoichiometry • What is Stoichiometry? • The word stoichiometry derives from two Greek words: stoicheion (meaning "element") and metron (meaning "measure"). • Stoichiometry deals with calculations about the masses (sometimes volumes) of reactants and products involved in a chemical reaction.

  22. Stoichiometry Cont. • What You Should Expect • The most common stoichiometric problem will present you with a certain amount of a reactant and then ask how much of a product can be formed. Here is a generic chemical equation: • 2 A + 2B ---> 3C • Here is a typically-worded problem: Given 20.0 grams of A and sufficient B, how many grams of C can be produced?

  23. Stoichiometry Cont. • Keys to solving the problem. • You will need to use molar ratios, molar masses, balancing and interpreting equations, and conversions between grams and moles.

  24. Stoichiometry Cont. • This type of problem is often called "mass-mass.“ • The Steps Involved in Solving Mass-Mass Stoichiometry Problems • Make sure the chemical equation is correctly balanced. • Using the molar mass of the given substance, convert the mass given in the problem to moles. • Construct a molar proportion (two molar ratios set equal to each other) following the guidelines set out in other files. Use it to convert to moles of the unknown. • Using the molar mass of the unknown substance, convert the moles just calculated to mass.

  25. Stoichiometry Cont. • Molar Ratios: • The sources for these ratios are the coefficients of a balanced equation. • sample equation: • 2 H2 + O2 ---> 2 H2O • What is the molar ratio between H2 and O2? • Answer: two to one. So this ratio in fractional form is: 2/1

  26. Molar ratio cont. • 2 H2 + O2 ---> 2 H2O • What is the molar ratio between O2 and H2O? • Answer: one to two. As a fraction, it is: 1/2

  27. Mole ratio practice problems. • 1) N2 + 3 H2 ---> 2 NH3 • Write the molar ratios for N2 to H2 and NH3 to H2. • 2) 2 SO2 + O2 ---> 2 SO3 • Write the molar ratios for O2 to SO3 and O2 to SO2. • 3) PCl3 + Cl2 ---> PCl5 • Write the molar ratios for PCl3 to Cl2 and PCl3 to PCl5.

  28. Mole to mole problems • The solution procedure used involves making two ratios and setting them equal to each other. • This is called a proportion. • One ratio will come from the coefficients of the balanced equation • The other will be constructed from the problem. • The ratio set up from data will almost always have one unknown in it.

  29. Mole to mole cont. • Equation: N2 + 3 H2 ---> 2 NH3 • Problem: if we have 2.00 mol of N2 reacting with sufficient H2, how many moles of NH3 will be produced? • Remember “sufficient” means there is more than enough to react with the other reactant.

  30. Equation: if we have 2.00 mol of N2 reacting with sufficient H2, how many moles of NH3 will be produced? • How to solve this problem: • Use the ratio to set up the proportion: • That means the ratio from the equation is: • The ratio from the data in the problem will be: • The proportion (setting the two ratios equal) is: • Solving by cross-multiplying gives x = 4.00 mol of NH3 produced

  31. Mole to mole practice problems: • Complete the following mole to mole conversions. • N2 + 3 H2 ---> 2 NH3 (use this equation for both problems) • Suppose 6.00 mol of H2 reacted with sufficient nitrogen. How many moles of ammonia would be produced? • We want to produce 2.75 mol of NH3. How many moles of nitrogen would be required?

  32. Mole to mass • Problem: 1.50 mol of KClO3 decomposes. How many grams of O2 will be produced? • Chemical equation: 2 KClO3 ---> 2 KCl + 3 O2 • Use the same steps for solving mole to mole problems.

  33. Problem: 1.50 mol of KClO3 decomposes. How many grams of O2 will be produced? • Let's use this ratio to set up the proportion: • That means the ratio from the equation is: • The ratio from the data in the problem will be: • The proportion (setting the two ratios equal) is: • Cross-multiplying and dividing gives x = 2.25 mol of O2 produced. • 2.25 mol x 32.0 g/mol = 72.0 grams. The 32.0 g/mol is the molar mass of O2.

  34. Mole to mass practice problems: • Here's the equation to use for all three problems: 2 H2 + O2 ---> 2 H2O • 1) How many grams of H2O are produced when 2.50 moles of oxygen are used? • 2) If 3.00 moles of H2O are produced, how many grams of oxygen must be consumed? • 3) How many grams of hydrogen gas must be used, given the data in problem two?

  35. Mass to Mass problems • There are four steps involved in solving these problems: 1. Make sure you are working with a properly balanced equation. 2. Convert grams of the substance given in the problem to moles. 3. Construct two ratios - one from the problem and one from the equation and set them equal. Solve for "x," which is usually found in the ratio from the problem. 4. Convert moles of the substance just solved for into grams.

  36. Mass to mass cont. • Double check the equation. I have seen lots of students go right ahead and solve using the unbalanced equation supplied in the problem (or test question for that matter). • DON'T use the same molar mass in steps two and four. • Don't multiply the molar mass of a substance by the coefficient in the problem BEFORE using it in one of the steps above. For example, if the formula says 2 H2O, DON'T use 36.0 g/mol, use 18.0 g/mol. • Don't round off until the very last answer. In other words, don't clear your calculator after step two and write down a value of 3 or 4 significant figures to use in the next step. Round off only once after all calculations are done.

  37. Mass to mass • This chart is used to help set up mass to mass problems.

  38. Mass to Mass • Each of the example problems below has an associated image which lays out the solution. Reading from left to right, the top row gives: • 1. the molar ratio used in the problem's solution.2. the conversion of the grams given in the problem to moles. The second row gives: • 3. the molar proportion used to convert from moles of the given to moles of the unknown.4. the conversion of moles of the unknown back to grams.

  39. Mass to Mass Cont. • How many grams of chlorine can be liberated from the decomposition of 64.0 g. of AuCl3 by this reaction: 2 AuCl3 ---> 2 Au + 3 Cl2

  40. Practice problems • Calculate the mass of AgCl that can be prepared from 200. g of AlCl3 and sufficient AgNO3, using this equation: 3AgNO3 + AlCl3 --> 3 AgCl + Al(NO3)3 • Given this equation: 2 KI + Pb(NO3)2 --> PbI2 + 2 KNO3 calculate mass of PbI2 produced by reacting of 30.0 g KI with excess Pb(NO3)2

  41. Limiting Reagents • You will see the word "excess" used in this section and in the problems. Three examples of Excess being used: a) "compound A reacts with an excess of compound B" - In this case, mentally set compound B aside for the moment. Since it is "in excess," this means there is more than enough of it. Some other compound (maybe A) will run out first.

  42. Limiting reagent Cont • b) "20 grams of A and 20 grams of B react. Which is in excess?" What we will do below is find out which substance runs out first (called the limiting reagent). Obviously (I hope), the other compound is seen to be in excess.c) "after 20 gm. of A and 20 gm. of B react, how much of the excess compound remains?" To answer this problem, we would subtract the limiting reagent amount from the excess amount.

  43. What is the Limiting Reagent? • The substance in a chemical reaction that runs out first. • Example: • Reactant A is a test tube. I have 20 of them.Reactant B is a stopper. I have 30 of them. • Product C is a stopper and test tube. • The reaction is: A + B ---> Cor: test tube plus stopper makes stopper and test tube combination. • we run out of one of the "reactants." Which one?

  44. Limiting Reagents Cont • Practice Problem: • A cup of coffee costs 50 cents. • In your possession, you have 100 grams of each coin: • nickels (5-cent pieces) • dimes (10-cent) pieces • quarters (25-cent pieces) • You know how much a single coin weighs: • one nickel = 5.00 g • one dime = 2.22 g • one quarter = 5.55 g • How many cups of coffee can you buy?

  45. Limiting reagent cont • How do you figure out HOW MANY coins there are? • Divide the total weight by the weight per one coin. • Divide the total weight by the weight per one coin. • Chemistry does the same thing. Divide total mass by the weight of one unit. In the example the unit is a coin, in chemistry it is the mole.

  46. Limiting Reagent Problems • Consider the reaction: 2 Al + 3 I2 ------> 2 AlI3 • Determine the limiting reagent and the theoretical yield of the product if one starts with: • a) 1.20 mol Al and 2.40 mol iodine.b) 1.20 g Al and 2.40 g iodinec) How many grams of Al are left over in part b?

  47. Part A solution • Take the moles of each substance and divide it by the coefficient of the balanced equation. • For aluminum: 1.20 / 2 = 0.60For iodine: 2.40 / 3 = 0.80 • The lowest number indicates the limiting reagent. • Aluminum will run out first.

  48. Part A solution cont. • "theoretical yield" depends on finding out the limiting reagent. • Once we do that, it becomes a stoichiometric calculation. • Al and AlI3 stand in a one-to-one molar relationship • so 1.20 mol of Al produces 1.20 mol of AlI3 • Notice that the amount of I2 does not play a role, since it is in excess.

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