Exponent significant figures

At 25°C, the Mark-Houwink exponent for poly(methyl methacrylate) has the value 0.69 in acetone and 0.83 in chloroform. Calculate (retaining more significant figures than strictly warranted) the value of that would be obtained for a sample with the following molecular weight distribution if the sample were studied by viscometry in each of these solvents ... 

When evaluating exponents of e, the number of significant figures generally equals the number of decimal places in the In value, hi this case, whereas = 5.62 x 10, ... 

There is often a large variation in values from source to source— in some cases, some orders of magnitude. For diis reason, only one significant figure (at most) is given before the exponent. A table of solubility products for many sulphides based on a reevaluated value for the second dissociation constant of H2S is given in Ref. 1. The values in that study are typically some orders of magnitude lower than the ones shown here. 

Significant figures for logs and exponents were discussed in Section 3-2. 

A modest value of E° produces a large equilibrium constant. The value of K is correctly expressed with one significant figure, because E° has three digits. Two are used for the exponent (14), and only one is left for the multiplier (4). 

A couple of comments are in order here. First, did you notice the value of the pH is the same as the absolute value of the exponent This will always be true when the first part of the scientific notation is exactly 1. The second comment relates to significant figures. There are two significant figures in the molarity measurement of 1.0 x 10 3 M. There are also two significant figures in the pH value of 3.00. Finally, pH values have no intrinsic units. Logarithms represent pure numbers, and as such, have no units. 

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. 

The rate of polymerization in the constant rate period is shown in Figure 5 as a function of AIBN concentration, both on logarithmic scales. At low concentrations of initiator (I) the rate varies as I0 89, but the slope drops as low as 0.33 at high rates of initiation. Similar results have been reported by Chapiro and Sebban-Danon (12) for polymerizations initiated by ionizing radiation at 19 °C. Initiator exponents significantly higher than the normal value of 0.5 have been reported by many workers (6, 10, 17, 25, 30, 31) for the polymerization of acrylonitrile under heterogeneous conditions. 

Move the decimai in an answer so that oniy one digit is to the ieft, and change the exponent accordingiy. The finai vaiue must contain the correct number of significant figures. 

It will be assumed that readers are familiar with the use of exponents, particularly powers-of-ten notation, and with the rules for significant figures. If not. Appendices A and B should be studied in conjunction with Chapter 1. 

Correlations and models approximate physical phenomena and often the fitted parameters—coefficients and exponents—have no physical meaning. Thus, the number of significant digits for these values should seldom exceed 3 for coefficients or 2 for exponents. Coefficients with seven significant figures give a false sense of certitude. 

In these numbers all the zeros to the right of the decimal point are significant (rules 1 and 3). (All significant figures come before the exponent the exponential term does not add to the number of significant figures.)... 

In addition and subtraction, all values must first be converted to numbers that have the same exponent of 10. The result is the sum or the difference of the first factors, multiplied by the same exponent of 10. Finally, the result should be rounded to the correct number of significant figures and expressed in scientific notation. 

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