Homework Problem Set #1

Homework Policy

Generally homework papers in Chem 125 are checked off, but not graded. Checking that you have done the homework is just a way of encouraging you to keep up in the course. When letter grades are assigned at the end of the term, faithfulness in submitting homework is taken into account for students whose scores on exams put them on a borderline between letter grades. This makes a significant difference to some students every year.

One of the most valuable instructional resources for Chem 125 is your classmates. Among the benefits of working and studying together are:

(1) Reinforcement of what you know,
(2) Realization of what you don't know, and
(3) Encouragement to seek help from the professional teaching staff when you find that you are not alone in having difficulty.

Feel free to work in groups to solve problems, but make sure you master the answers (know how to wear the jewel), and submit your own answer sheets. Remember that you will be working solo on the exam covering this material.

Isotope Ratio Mass Spectrometry

The probability problem that supplies the setting for the Pepys/Newton lesson is relevant to isotopic abundance as measured by the mass spectrometer, an instrument that allows determining molecular weights of different species within a chemical sample.

If a sample is chemically pure, one might expect that all its molecules should have the same molecular weight. But there can be variation from molecule to molecule because of the occurrence of isotopes. Approximately (see Note) 75% of chlorine atoms have the mass 35, and 25% have the mass 37, so that the average atomic weight of chlorine is 35.5 (3/4 * 35 + 1/4 * 37). Thus if the mass spectrum of a compound with a single chlorine shows a peak of a certain intensity at the molecular mass M, it should also show a peak of 1/3 this intensity for the molecular weight M+2 (assuming that there are no other elements whose heavier isotopes need to be considered).

 Problem 1 Explain the formulas used in the following passage from the Pepys/Newton webpage: The chance of at least one success in throwing 6 tetrahedra is 1 - (3/4)^6 = 0.822 , while the chance of at least double success with 12 tetrahedra is 1 - (3/4)^12 - 12 * (3/4)^11 * (1/4) = 0.842. Problem 2 Sketch a bar graph (analogous to the one to the right) showing the proportion of species M+4, M+2, and M (i.e. two Cl-37 atoms, one Cl-37 atom, and no Cl-37 atoms) for a substance whose molecules have 2 chlorine atoms. Problem 3 The bar graph to the right is a portion of the mass spectrum for a chemically pure "mystery compound" showing peaks at M, M+2, and M+4 due to the presence of chlorine (for purposes of this problem neglect the peaks at 283 and 285, which are due to small amounts of carbon isotopes). Note that the peaks are scaled to the mass 282 peak, which is taken as 1. Use formulas analogous to those in Problem 1 to determine how many chlorine atoms there are in a molecule of this compound. [It might help to work with a spreadsheet.] Knowing the number of chlorine atoms, guess what other atoms are present in the compound. [Note that M comes at 282 amu.] Problem 4 In an organic compound made from petroleum 1.07% of the carbon atoms have the mass 13 instead of 12. If none of the other atoms in the molecules have a significant probability of having a heavy isotope (which is not uncommon), it is possible to count the number of carbon atoms by observing what fraction of the molecules in the mass spectrogram have only C-12 atoms, and thus the nominal molecular weight, and what fraction are heavier because they have 1 (or 2) C-13 atoms. Suppose that the molecules of a substance have 30 carbons atoms. What proportion of the molecules should have 0, or 1, or 2 C-13 atoms if the source of the substance is petroleum? If the source of the 30-carbon organic molecule is a land plant with a "C4" metabolic process, the fraction of C-13 carbon atoms is 1.10%. What should be the proportion of molecules with 0, or 1, or 2 C-13 atoms in such a substance? How accurate would a mass spectrometer have to be to identify the source of such an organic compound (from petroleum or from a plant)? Special "isotope-ratio" mass spectrometers are used for this purpose (and even to distinguish between "C4" and "C3" classes of plants). When might it be useful to be able to determine whether an organic compound comes from petroleum or from land plants?

Note

More precisely, the natural abundance of Cl-37 varies with source from 24.1% to 24.4% according to "Isotope-Abundance Variations of Selected Elements" a recent technical report from the International Union of Pure and Applied Chemistry. Pure Appl. Chem., 74, 1987-2017 (2002). Click here for PDF version of the report.