Logarithm, Common

T = temperature equivalent at atmospheric pressure T = experimental temperature taken at pressure P P = pressure log = common logarithm (base 10)... 

Watson characterization factor log = common logarithm (base 10)... 

Unless otherwise stated, tables of logarithms are always tables of common logarithms. 

Characteristic of a Common Logarithm of a Number. Every real positive number has a real common logarithm such that f a < b, log a < log b. Neither zero nor any negative number has a real logarithm. 

A common logarithm, in general, consists of an integer, which is called the characteristic, and a decimal (usually endless), which is called the mantissa. The characteristic of any number may be determined from the following rules ... 

Mantissa of a Common Logarithm of a Number. An important consequence of the use of base 10 is that the mantissa of a number is independent of the position of the decimal point. Thus 93 600, 93.600, 0.000 936, all have the same mantissa. Hence in Tables of Common Logarithms only mantissas are given. A five-place table gives the values of the mantissa correct to five places of decimals. 

A particular concentration measure of acidity of aqueous solutions is pH which usually is regarded as the common logarithm of the reciprocal of the hydrogen-ion concentration (see Hydrogen-ION activity). More precisely, the potential difference of the hydrogen electrode in normal acid and in normal alkah solution (—0.828 V at 25°C) is divided into 14 equal parts or pH units each pH unit is 0.0591 V. Operationally, pH is defined by pH = pH(soln) + E/K, where E is the emf of the cell ... 

The common logarithm (base 10) is denoted log a or logi(/7, The natural logarithm (base e) is denoted In a (or in some texts loge ). 

Dell, m. bloom, lump, cake (of metal), dein, pron. thy, thine, your, yours, deinige, pron. thine, yours, dekadisch, a. decadic. — dekadische Logarith-men, common logarithms. 

Zetmer-logarithmus, m. logarithm to the base 10, common logarithm, -potenz, /. power of ten tenth power, -stein, m. hollow concrete block, -stelle, /. decimal place, -system, n. 

For convenience, acid strengths are normally expressed using pXa values rather than Ka values, where the pKa is the negative common logarithm of the Ka. 

Common logarithms, where the base is 10, ordinarily denoted as logm- If 10x= n, then logio n = x. Examples include the following ... 

Substituting the known values of R and F, and changing from natural to common logarithms, at a temperature of 25 °C T = 298K) ... 

If we multiply (1) throughout by 0 4343 to convert to common logarithms, and compare terms with (2) we find ... 

Notice that, as the concentration of hydronium ions increases, the pH decreases. Because pH is a common logarithm (to the base 10), a change of one pH unit means that the concentration of H30+ ions has changed by a factor of 10. For example, when the concentration of H 0+ increases by a factor of 10, from 10-5 mol-L 1 to 10 4 mol-L the pH decreases from 5 to 4. Most solutions used in chemistry have a pH ranging from 0 to 14, but values outside this range are possible. 

The common antilogarithm of a number x is the number that has x as its common logarithm. In practice, the common antilogarithm of x is simply another name for 10v, and so the common antilogarithm of 2 is 102 =100 and that of 2.18 is... 

The following relations between logarithms are useful. Written here mainly for common logarithms, they also apply to natural logarithms. 

The combination of constants RTIF often appears in electrochemical equations it has the dimensions of voltage. At 25°C (298.15 K) it has a value of 0.02569 V (or roughly 25 mV). When including the conversion factor for changing natural to common logarithms, we find a value of 0.05916 V (about 59 or 60mV) for 2.303 (RTIF) at 25°C. Values for other temperatures can be found by simple conversion, since this parameter is proportional to the absolute temperature. 

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