Logarithm keys

In this unit you will find explanations, examples, and practice dealing with the calculations encountered in the chemistry discussed in this book. The types of calculations included here involve conversion factors, metric use, algebraic manipulations, scientific notation, and significant figures. This unit can be used by itself or be incorporated for assistance with individual units. Unless otherwise noted, all answers are rounded to the hundredth place. The calculator used here is a Casio FX-260. Any calculator that has a log (logarithm) key and an exp (exponent) key is sufficient for these chemical calculations. 

Find the log (for logarithm ) key on your calculator. Enter 1000 or 103 into your calculator, then press the log key. The number 3 will be in the display. Now enter 10 000 or any other power of 10. Press the log key. What is displayed for the log of the number ... 

Using the natural logarithm key (LN) on a scientific calculator, it is relatively easy to solve for an unknown given values for the other three variables. For example, to get the time required for 6.22 X 10 atoms of a certain isotope with half-life 55.4 min to disintegrate to 8.88 X 10 " atoms, follow the steps in the left column to get the answers in the right column ... 

Dilute Polymer Solutions. The measurement of dilute solution viscosities of polymers is widely used for polymer characterization. Very low concentrations reduce intermolecular interactions and allow measurement of polymer—solvent interactions. These measurements ate usually made in capillary viscometers, some of which have provisions for direct dilution of the polymer solution. The key viscosity parameter for polymer characterization is the limiting viscosity number or intrinsic viscosity, [Tj]. It is calculated by extrapolation of the viscosity number (reduced viscosity) or the logarithmic viscosity number (inherent viscosity) to zero concentration. 

To obtain a base-10 logarithm using a calculator, all you need to do is enter the number and press the [log] key. This way you should find that... 

The method used to find inverse logarithms depends on the type of calculator. On certain calculators, you enter the number and then press, in succession, the [ihv] and either [log] or [lux] keys. With other calculators, you press the [ io ) or key. Either way, you should find that... 

Lipophilicity is an important property of molecules in relation to their biological activities. It is one of the key physiochemical parameters that determine the distribution and transport of drugs into the body and target organs. Measurements of lipophilicity, expressed as the logarithm of the... 

The key to all this is that the scale of measurement of most (if not all) variables is arbitrary. Although we are most familiar with a linear scale of measurement, there is nothing which makes this the correct scale on its own, as opposed to a logarithmic scale [familiar logarithmic measurements are that of pH values, or earthquake intensity (Richter scale)]. Transforming a set of data (converting X to X ) is really as simple as changing a scale of measurement. 

There are logarithms for all numbers, not just whole multiples of 10. What is the pH of a solution if [H3O+] = 0.004 76 mol/L Enter 0.00476. Press the [LOG] key and then the [+] key. The answer is 2.322. This result has three significant digits—the same number of significant digits as the concentration. 

When a number is not an integral power of 10, the logarithm is not a simple integer, and assistance is needed to find it. The most common forms of assistance are electronic hand calculators and log tables. With calculators, you simply enter into the keyboard the number (A) whose log you want, press the log key (or keys), and observe the log in the lighted display. For practice, and to make sure that you know how to useyour calculator for this purpose, check that... 

The connection between the microscopic description of any system in terms of individual states and its macroscopic thermodynamical behavior was provided by Boltzmann through statistical mechanics. The key connection is that the entropy of a system is proportional to the natural logarithm of the number of levels available to the system, thus ... 

There are other bases for logarithms. Your calculator should also be able to handle natural logarithms, which are based on the irrational number e , rather than 10. The natural log key is In , and the natural antilog key is e . 

Kc (or KciCo) first defined in Frame 40 and needed in logarithmic form in key equation (41.12) in Frame 41 (and later applications). 

K, the equilibrium constant was first mentioned in Section 6.3 of Frame 6 where we discussed its use as a logarithmic argument. The relevance of discussing the logarithm of equilibrium constant is readily seen by reference to the key equation (41.13) derived in Frame 41. 

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