O Macmillan Learning isotopic mass: Suppose a new element with an average atomic mass of 23.202 u is discovered on Mars. This element is composed of two isotopes. The most abundant isotope has a natural abundance of 78.053% and an isotopic mass of 23.322 u. Calculate the isotopic mass of the least abundant isotope.

Average Atomic Weight Part 1: Consider the four identical spheres below, each with a mass of 2.00 g. Calculate the average mass of a sphere in this sample. Part 2: Now consider a sample that consists of four spheres, each with a different mass: blue mass is 2.00 g, red mass is 1.75 g, green mass is 3.00 g, and yellow mass is 1.25 g. a Calculate the average mass of a sphere in this sample. b How does the average mass for a sphere in this sample compare with the average mass of the sample that consisted just of the blue spheres? How can such different samples have their averages turn out the way they did? Part 3: Consider two jars. One jar contains 100 blue spheres, and the other jar contains 25 each of red, blue, green, and yellow colors mixed together. a If you were to remove 50 blue spheres from the jar containing just the blue spheres, what would be the total mass of spheres left in the jar? (Note that the masses of the spheres are given in Part 2.) b If you were to remove 50 spheres from the jar containing the mixture (assume you get a representative distribution of colors), what would be the total mass of spheres left in the jar? c In the case of the mixture of spheres, does the average mass of the spheres necessarily represent the mass of an individual sphere in the sample? d If you had 80.0 grams of spheres from the blue sample, how many spheres would you have? e If you had 60.0 grams of spheres from the mixed-color sample, how many spheres would you have? What assumption did you make about your sample when performing this calculation? Part 4: Consider a sample that consists of three green spheres and one blue sphere. The green mass is 3.00 g, and the blue mass is 1.00 g. a Calculate the fractional abundance of each sphere in the sample. b Use the fractional abundance to calculate the average mass of the spheres in this sample. c How are the ideas developed in this Concept Exploration related to the atomic weights of the elements?

Reference Section 5-2 to find the atomic masses of 12C and 13C, the relative abundance of 12C and 13C in natural carbon, and the average mass (in u) of a carbon atom. If you had a sample of natural carbon containing exactly 10,000 atoms, determine the number of 12C and 13C atoms present. What would be the average mass (in u) and the total mass (in u) of the carbon atoms in this 10,000-atom sample? If you had a sample of natural carbon containing 6.0221 1023 atoms, determine the number of 12C and 13C atoms present What would be the average mass (in u) and the total mass (in u) of this 6.0221 1023 atom sample? Given that 1 g = 6.0221 1023 u, what is the total mass of I mole of natural carbon in units of grams?

An element has the following natural abundances and isotopic masses: 90.92% abundance with 19.99 amu, 0.26% abundance with 20.99 amu, and 8.82% abundance with 21.99 amu. Calculate the average atomic mass of this element.