Calculating the Average Atomic Mass Number Where did

Calculating the Average Atomic Mass Number Where did that decimal come from?

Calculating Average Atomic Mass I CAN calculate the Average Atomic Mass Number of an element from its isotope data.

The Case for a Decimal • We learned earlier that ATOMIC MASS NUMBER is the COMBINED NUMBER of P+ and No in an atom. • Yet, the AMN given on the Periodic Table generally has a DECIMAL in it.

• We discussed earlier that the AMN on the PT represents a WEIGHTED AVERAGE of all the ISOTOPES (atoms from the same element with varying numbers of No) of an element. • Most elements have 2 OR MORE isotopes. • Each different isotope always occurs in the SAME RELATIVE AMOUNT regardless of where the sample of the element is taken from.

• • • For example: Lead has 4 isotopes: 1. 40 % of all lead atoms are Pb -204 24. 10% of all lead atoms are Pb-206 22. 10% of all lead atoms are Pb-207 52. 40% of all lead atoms are Pb-208 The UNIT for Atomic Mass is the ATOMIC MASS UNIT, abbreviated “amu” or simply “u”. How would you determine the AVERAGE ATOMIC MASS NUMBER of lead?

• First of all, why can’t we simply add all the AMNs of the four isotopes up and find the average by dividing by 4? – We can’t do this because there is NOT AN EQUAL PERCENTAGE of each isotope. It they were all 25% each we could. • Since there is not an equal percentage of each, they do not contribute equally to the overall average. • Since we can’t do a simple average, we will have to calculate a WEIGHTED AVERAGE.

Calculating a Weighted Average • To find a weighted average, EACH VALUE is MULTIPLED by its PERCENTAGE and the results are ADDED together. • For Average Atomic Mass, the equation looks like this: • Average AMN = Σ (Atomic Mass x Percentage) • Σ = sigma = “find the sum of”

Practice Problem • Lead has 4 isotopes: 1. 40 % of all lead atoms are Pb -204, 24. 10% of all lead atoms are Pb-206, 22. 10% of all lead atoms are Pb-207, and 52. 40% of all lead atoms are Pb-208. What is the average AMN for lead? STEPS 1. Multiple EACH mass by its percentage, making sure to move the decimal in the percentage TWO PLACES to the LEFT before multiplying. 2. Add the results and ROUND to SF.

• • Pb-204 Pb-206 Pb-207 Pb-208 204 u 206 u 207 u 208 u x x 0. 0140 0. 2410 0. 2210 0. 5240 = 2. 856 u = 49. 646 u = 45. 747 u = 108. 992 u _____ ≈ 207. 241 u

MORE PRACTICE Uranium has three common isotopes. If the abundance of U-234 is 0. 01%, the abundance of U-235 is 0. 71%, and the abundance of U-238 is 99. 28%, what is the average atomic mass of uranium?

U-234 u x 0. 0001 = 0. 0234 u U-235 u x 0. 0071 = U-238 u x 0. 9928 = 236. 2864 u 1. 6685 u 237. 9783 u (There are only 3 SF in 0. 0234) ≈ 237. 978 u