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ATOMIC MASS & ISOTOPES. Atomic mass is a relative scale Similar to comparing the distances between Cincinnati to Columbus and Cincinnati to Toledo It is twice as far to Toledo If we set the distance to Columbus as our standard making it 12; Then the distance to Toledo would be 24.
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ATOMIC MASS & ISOTOPES • Atomic mass is a relative scale • Similar to comparing the distances between Cincinnati to Columbus and Cincinnati to Toledo • It is twice as far to Toledo • If we set the distance to Columbus as our standard making it 12; Then the distance to Toledo would be 24
Chemists originally used Oxygen as the standard making it 16 but… • Today we use Carbon-12 • Remember that carbon-12 indicates a specific isotope of carbon • Since the mass of hydrogen atoms is 1/12 that carbon-12 we set the Atomic Mass of Hydrogen to 1 • Likewise, Magnesium atoms are twice as massive as C-12, hence Mg = 24 a.m.u.
Interestingly- if you add up the actual masses of an atom’s protons and neutrons, they will not equal their a.m.u. value • WHY? • Remember- the a.m.u. value is relative to carbon-12 • In fact, earliest methods involved reacting the standard element with the element to be determined • From the resulting ratio the atomic mass would be determined
Isotopes • Defined as atoms of the same element having different atomic masses due to a difference in the number of neutrons each atom possesses • Designated by giving the atomic mass along with the element’s name or symbol • carbon-12, C-12, carbon-14, C-14
Atomic Mass & Periodic Table • The value printed on the Periodic Table is a weighted average of all the element’s isotopes Average Atomic Mass =sum of the (Mass Isotope A x Percent Abundance) + (Mass Isotope B x Percent Abundance) + (Mass Isotope n x Percent Abundance) Divide by 100
Examples • Calculate the average atomic mass for Gallium made up of 60.4% Ga-68 (68.926 amu) and 39.6% Ga-71 (70.925) • Solution (68.926 x 60.4) + (70.925 x 39.6) = 100 69.7171604 calculator value 69.7 amu corrected to 3 sig figs
How many times heavier is the Gallium atom than the Carbon-12? • 69.7÷12 = 5.8083333 or 5.81 • Another solution approach is to change the percent abundance of each isotope to a decimal thereby eliminating the need to divide by 100 (68.926 x .604) + (70.925 x .396)=69.7 Same answer as before; your choice
Rubidium-85 has 84.912 amu and 72.15% abundance; Rb-87 is 27.85% of the element and has a 86.909 amu • What is the average atomic mass? • 85.4681645 calculator value • 85.47 amu correct sig figs • What is the atomic mass of silicon if 92.21% of its atoms have a mass of 27.977 amu, 4.70% have mass 28.976 and 3.09% have mass of 29.974? • Answer 28.1 amu (28.0856873)
What is the atomic mass if, out of every 100 atoms, 5 have a mass of 176 amu, 19 have mass of 177, 27 have mass of 178, 14 have mass of 179, and 35 have mass of 180? • Answer = 179 amu (178.55 calculator) Lithium is composed of two isotopes, 6Li and 7Li. The mass of 6Li is 6.015 and 7Li is 7.016. What is the percent abundance of each if average mass of Lithium is 6.941
Remember % 7Li +% 6Li = 100% • Therefore we can set the percentage of one isotope to X and the other will 100-X • 6.941 = (6.015 x X) + (7.016 x 100-X) • 100 • 6.941x100 = 6.015X + 701.6 – 7.016X • 694.1 = 6.015X + 701.6 – 7.016X • Collect like terms • 694.1 -701.6 = 6.015X – 7.016X
Solution…continued • -7.5 = -1.001X • X = -7.5÷-1.001 • X = 7.49% for Li-6 • Li-7 = 100% - 7.49% • Li-7 = 92.51% • Remember that the sum of the percentages must equal 100% • If using decimal percent than = 1.00
Additional Problems • Merrill Textbook Page 105: 33 and 34 and Page 107: 60 • Glencoe Textbook Page 104: 15 – 17 and Page 113: 67, 68, 7
