Relative Atomic Mass (𝐴r) Answer Key

     Isotopes; Mahaffy, 2e, 2.8 Relative atomic mass (𝐴r ), atomic weight, molar mass (𝑀); Mahaffy, 2e, 2.9-10 Amount of substance and its units Mahaffy, 2e, 2.11 a. Mole, Atomic mass unit (u), Avogadro’s Number Naming Ionic Compounds ; Mahaffy, 2e, 3.4 Useful information: 𝑁A = 6.022140857 × 1023 mol-1, 𝑐 = 2.99792458 × 108 m/s 1. What are the units of the following? Explain the differences between them Relative atomic mass (𝐴r ): Atomic weight: Molar mass: 2. What is a connection between the following: a. Atomic weight and Relative atomic mass (𝐴r ) i. What is similar? ii. What is different? iii. How would you convert from one to another? b. Atomic weight and molar mass: i. What is similar? ii. What is different? iii. How would you convert from one to another? c. Mass of a single atom (or molecule) in grams and in Atomic mass unit (u) i. What is similar? ii. What is different? iii. How would you convert from one to another? 3. Calculate and then put the following in order of increasing mass. a) 0.500 mol Cl2 b) 4.00 𝑁A molecules of H2 c) Amount of Ca containing 4.0 × 1024 electrons d) 7.0 × 1014 u of Ba (lightest) ____ (heaviest) 4. On the scale for which one C-12 atom has mass exactly 12 u, one Mg-25 atom has mass 24.3111 u. If instead we chose the different scale for which one Mg-25 atom has a mass of exactly 25 u*, what would be the mass in grams of the atomic mass unit u*? Express your answer to five significant figures. (Hint: you need to find the new Avogadro number first). 5. How many grams of water contain the same number of hydrogen atoms as are in 92 g of dimethyl ether (CH3OCH3)? 6. Ruthenium (Ru) has 7 stable isotopes. Please answer the questions below using the table provided. A ruthenium atom has 60 neutrons. How many moles of 104Ru neutrons are in 10.1 mL of naturally found Ru (density = 12.5 g/mL)? Isotope Abundance (%) Hint: not all Ruthenium neutrons are 104Ru neutrons. 96Ru 3 98Ru 2 99Ru 13 100Ru 12 101Ru 17 102Ru 33 104Ru 20. 7. A McDonald’s cheeseburger has about 8.0 × 102 mg of salt (sodium chloride). a. How many protons that belong to a positive ion of the ionic compound are in two McDonald’s cheeseburgers? b. What is a chemical formula for the salt? c. Which ion is positive which ion is negative? 2 8. If we took all the salt in twenty cheeseburgers and made a cube from it, what would the density (in g/ml) of this salt cube be if the sides of the cube are 0.02m? (1 cm3 = 1 mL). 9. I like to have something sweet after something salty. A McDonald’s apple pie has 34.2 grams of carbohydrates. Let’s guess that 10.% by mass of those come from sucrose (C12H22O11). How many sucrose carbon atoms (that is, how many carbon atoms that come from sucrose) are in each apple pie. 10. An atom X has three known isotopes, with average mass 𝑚avg. The first isotope has mass 𝑚1 and fractional abundance 𝑓1 . The second isotope has a mass 𝑚2 and fractional abundance 𝑓2. Write an expression for the fractional abundance 𝑓3 of the third isotope of mass 𝑚3 in terms of 𝑚1 , 𝑚2 , 𝑚3 , 𝑚avg, 𝑓1, and 𝑓2. 11. In a parallel universe element X has the three stable isotopes two of them are shown in the table below. The average mass of this element is 25.5 u. a. What is the mass of the third isotope in grams? b. What is the molar mass of the third isotope? Isotope 20X 30X Mass 20.u 30. u Abundance 0.30 0.40 12. How many protons of calcium are in 286 grams of calcium hypochlorite? 13. Calculate the mass of the zinc that has the same number of atoms as 7.22 grams of copper. 14. How many protons of manganese are in 362 grams of magnesium permanganate? 15. In terms of the molar mass, 𝑀, of ammonium phosphate and the Avogadro constant, 𝑁A , write the symbolic expression for the number of ions in solution when 𝐺 grams of ammonium phosphate dissolves in water and completely ionizes. 16. An atom Y has three known isotopes, with an average mass of 𝑚avg. The first isotope has a mass of 𝑚1 and a fractional abundance 𝑓1. The second isotope has a mass of 𝑚2 and a fractional abundance 𝑓2. Write an expression for the mass, 𝑚3 , of the third isotope in terms of 𝑚1 , 𝑚2 , 𝑚avg, 𝑓1, and 𝑓2. 17. Assume that the atom in a solid are cubes with edges of length 𝐿. Derive an expression to evaluate 𝐿 in terms of molecular weight, 𝑀; density, 𝜌; and Avogadro constant, 𝑁A . Assume there is no space between the atoms. 18. Lithium has two stable isotopes: 6Li (7.5%) and 7Li. Write an expression for the atomic weight of lithium in terms of the relative atomic weights, Ar, of the isotopes. 3 19. Imagine that you decide to start your own meth lab, like in "Breaking Bad." However, because you are only in CH101, part of your product explodes at a crucial step. What explodes is 124 mL of ethylene glycol, C2H4(OH)2. If the density of ethylene glycol is 1.5 g/mL, and it takes 1.5 ×1018 atoms of C to release exactly 1 J of energy, calculate the total amount of energy released in the resultant explosion, in kJ = 103 J and to the correct number of significant figures. 20. A compound has a composition by mass of 24.1% carbon, 5.9% hydrogen, and 70.0% chlorine. What is the empirical formula of the compound? 21. Of 39K, 40K and 41K, 40K has very low abundance. Using the periodic table, which isotope (39K or 41K) is more abundant? Use that 39K A = 38.964 and 41K A = 40.962 and that K atomic weight = r r 39.083. 22. What is relative atomic mass, atomic weight and molar mass of 16O? 23. What is relative atomic mass of 12C, mass of a single 12C atom (in u), mass of a single 12C atom (in g), atomic weight of C (in u), molar mass of 12C, and molar mass of C? 24. What is the chemical name of NH4CH3COO is _________________________ 25. What is the chemical formula of sodium perchlorate _________________________ 26. If 3.0 mol of sodium phosphate is dissolved in water and ionize completely, what is the number of moles of ions in the solution? Numerical Answers 3. 4. 5. 6. 7. 8. 9. 1.61478×10–24g 110 g H2O 15 mol of 104Ru neutrons a. 1.8 × 1023 protons b. NaCl c. Na (+); Cl (-) 2 g/mL 7.2×1022 carbon atoms 10. f3 = mavg−(m1 f1 )−(m2 f2 ) m3 11. 12. 13. 14. 15. 22. 12.0000, 12.0000 u, 1.9927 × 10–23 g, 12.011 u, 12.0000 g, 12.011 g 23. Ammonium acetate 24. NaClO4 25. 12 mol a. 4.2×10-23 g b. 25 g/mol 2.4 × 1025 protons 7.43 g 4.12 × 1025 protons 𝐺𝑁 4 𝐴 𝑀 16. m3 = 3 mavg −(m1 f1 )−(m2 f2 ) 1−𝑓1−𝑓2 M 1 17. L = √ 𝑁 𝐴𝜌 18. (0.075 𝑚6 ) + (0.925 𝑚7 ) = 6.94 19. 2.4 × 103 kJ 20. CH3Cl 21. 39K 4