Reviewing Fundamental Methods of Calculation and Problem Solving

Review Section 3-6 Homework

• Reading Preparation
• WebLecture
• Study Activity
• Preparation work for chat
• Online Quiz
• Lab Instructions

Reading Preparation

Textbook assignment: Read Kotz and Triechel, Chemistry and Chemical Reactivity Review Section: The tools of quantitative chemistry (pp. 32-43).

Study Notes

• 3: Mathematics of Chemistry

  In order to make certain that we use the correct orders of scale, identify the true precision of our measurements, and to simplify calculations, chemists use scientific notation, or powers-of-ten notation to record data, and significant figures to determine how precise their data really is.

  In general, always express your data values with one unit figure and the remaining significant digits as decimal values, then use powers of ten to scale the result. With this "rule", the number 354.6 grams becomes 3.546 * 10² grams.

  There are four rules to keep in mind when determining significant figures:

  • Zeroes count if they are internal to the number or not just placeholders.
  • In addition and subtraction, count the number of decimal places in the number with the fewest of them.
  • In multiplication and division, count the number of significant figures in the number with the fewest of them.
  • Round up only when the last number is 5 or more.

  When we use the two sets of concepts together, we can create data notation that is not ambiguous. We can write 35000grams as 3.5000 * 10⁴ only if all three zeros are "accurate", that is, if we know the value to 35000 grams ±1 gram. If we really only know the value to ± 100 grams, we would write this as 3.50 * 10⁴ g. The number of decimals in this notation method tells us exactly how many significant figures we have in each case.

  We've already pointed out the need to use units to help us analyze a problem. Keeping track of units not only keeps us honest but helps us understand when we've gone astray. Setting up a problem to find mass, we expect the result to be in units of kilograms or grams. If we wind up with grams/mole or 1/grams as the unit, we know that we've done something wrong in the analysis, and we need to revisit the methods we used to solve the problem.

• 4: Problem solving using dimensional analysis

  We've already pointed out the need to use units to help us analyze a problem. Keeping track of units not only keeps us honest but helps us understand when we've gone astray. Setting up a problem to find mass, we expect the result to be in units of kilograms or grams. If we wind up with grams/mole or 1/grams as the unit, we know that we've done something wrong in the analysis, and we need to revisit the methods we used to solve the problem.

  One way to check your approach is to solve for units separately from solving for the numerical answer. Do this first! You will save yourself a lot of grief and time manipulating numbers only to find out that you set the problem up incorrectly to begin with. We'll have plenty of examples of this approach as we work on homework problems.

• 5: Graphs and Graphing

  Be sure that you are comfortable with recognizing linear, quadratic or parabolic, and exponential functions. Review Appendix A if necessary. Chemists often plot values over time, and you need to be able to tell from the slope of a graph whether a value is increasing or decreasing, and whether it is doing so steadily or at a changing rate.

• 6: Chemical problem solving

  There are similar notes on problem solving methods in our own Student Guide. Be sure to look at the section on homework problem solving methods.

Web Lecture

Read the following weblecture before chat: The Mathematics of Chemistry

Take notes on any questions you have, and be prepared to discuss the lecture in chat.

Study Activity

Chat Preparation Activities

• Essay question: The Moodle forum for the session will assign a specific study question for you to prepare for chat. You need to read this question and post your answer before chat starts for this session.
• Mastery Exercise: The Moodle Mastery exercise for the chapter will contain sections related to our chat topic. Try to complete these before the chat starts, so that you can ask questions.

Chapter Quiz

• Required: Complete the Mastery exercise with a passing score of 85% or better.
• Go to the Moodle and take the quiz for this chapter.

Lab Work

Please read Illustrated Guide to Home Chemistry Experiments: All Lab, No Lecture, Chapter 2 - Lab Safety, and survey pages 52-67. Make sure that you understand how to determine the safe storage and disposal methods for a particular chemical.

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