2. Average Atomic Mass A different kind of average…

3. What do these numbers mean? 82 Pb Lead 207.2 Atomic # Atomic Mass the number of p + The weighted average mass of the atoms in a naturally occurring sample of the element How is atomic mass calculated?... NOT mass number!

4. …as a weighted average unlike a normal average (or mean)  A weighted average takes into account the abundance of what is being averaged for example, if 75% of coins in your pocket are pennies and 25% are dimes, which has the greatest effect on the average value of the coins in our pocket? The pennies, of course! the weighted average value of the coins in your pocket is: 1¢ x.75=.75¢ 1¢ x.75=.75¢ 10¢ x.25= 2.50¢ 3.25¢ 3.25¢ Because the pennies are more abundant, they have the largest effect on the average THAT’S WHY THE AVERAGE IS CLOSER TO THE VALUE OF A PENNY, NOT A DIME

5. This is how it works… Here’s how you would normally calculate the average value of 7 pennies and 3 quarters: Here’s how you would normally calculate the average value of 7 pennies and 3 quarters: 1+1+1+1+1+1+1+25+25+25= 82 But it could have been calculated as a weighted average… Total amount Number of items added Average value

6. Weighted average  7 pennies, 3 quarters = 10 total coins  Since 70% of the coins are pennies, 70 % of the average value must be from the pennies  Since 30% of the coins are quarters, 30% of the average value must be from the quarters So… Coin % abundance Value (¢) Relative abundance (decimal equivalent)Subtotal penny701x.70=.7 quarter3025x.30=7.5 8.2 Weighted average value is the sum of the subtotals

7. Average atomic mass calculation example Given the following isotope data: Isotope% abundance Mass (amu) Cu-6369.2%62.93 Cu-6530.8%64.93

8. Average atomic mass calculation example Given the following isotope data: Isotope% abundance Mass (amu) % decimal equivalent Cu-6369.2%62.93 Cu-6530.8%64.93 Remember, this is just the % abundance with the decimal moved 2 places to the left

9. Average atomic mass calculation example Given the following isotope data: Isotope% abundance Mass (amu) % decimal equivalent Cu-6369.2%62.93.692 Cu-6530.8%64.93

10. Average atomic mass calculation example Given the following isotope data: Isotope% abundance Mass (amu) % decimal equivalent Cu-6369.2%62.93.692 Cu-6530.8%64.93.308

11. Average atomic mass calculation example Given the following isotope data: Isotope% abundance Mass (amu) % decimal equivalent Mass contribution Cu-6369.2%62.93x.692= Cu-6530.8%64.93x.308=

12. Average atomic mass calculation example Given the following isotope data: Isotope% abundance Mass (amu) % decimal equivalent Mass contribution Cu-6369.2%62.93x.692=43.55 Cu-6530.8%64.93x.308= ( )

13. Average atomic mass calculation example Given the following isotope data: Isotope% abundance Mass (amu) % decimal equivalent Mass contribution Cu-6369.2%62.93x.692=43.55 Cu-6530.8%64.93x.308=20.00 ( )

14. Average atomic mass calculation example Given the following isotope data: Isotope% abundance Mass (amu) % decimal equivalent Mass contribution Cu-6369.2%62.93x.692=43.55 Cu-6530.8%64.93x.308=20.00 Add the mass contributions up→ 63.55 The atomic mass of Cu is 63.55 amu

15. Example: Calculate the atomic mass for S using the natural percent abundance data listed below: Isotope Natural % abundanceMass (AMU) Relative abundance (decimal equivalent) Mass contribution S-3295.00231.972x.95002=30.374 S-330.7632.971x.0076=.2506 S-344.2233.967x.0422=1.4334 S-360.01435.967x.00014=.005035 32.06 The sum of the mass contributions is the WEIGHTED AVERAGE The atomic mass of S is 32.06 AMU