MEASUREMENTS 41 



liberate two or more H+ ions, the behavior might make the acid solu- 

 tion seem two or more times as concentrated as it actually is. To meet 

 this difficulty the chemist devised the notation, equivalents per liter 

 (eq/1); a solution of 1 m H2SO4 contains 2 eq/1. A solution containing 

 1 eq/1 is called a one normal (1 n) solution. Dilute molar, molal, or 

 equivalent solutions may be designated as millimoles per liter (mM) or 

 as microequivalents per liter (/u eq/1). For certain purposes, concentra- 

 tions expressed in percentages are adequate, particularly in the biology 

 laboratory. Two kinds of percentage solutions are possible. A 5 per cent 

 salt solution could be made by dissolving 5 g of NaCl in enough water 

 to make 100 ml of solution. This is percentage by weight, and if there 

 is likely to be any doubt, it should be so designated (w/v). A 5 per cent 

 solution of alcohol (a liquid) contains 5 ml of alcohol made up to 100 

 ml with water and does not necessarily contain 5 g of solute. Such solu- 

 tions must be designated as volume percentage solutions (v/v). Con- 

 centrations of some solutions are expressed as g/1 or mg/1, and it will be 

 be seen that these are basically similar to percentage by weight. A solu- 

 tion expressed in milligrams per liter is sometimes spoken of as parts per 

 million (p. p.m.), an expression which is awkward when dealing with 

 liquid solutions but valuable when working with gases in air or other 

 complex solutions. 



There are several ways of expressing concentrations, and even the 

 professional biologist becomes confused occasionally. If it is possible, we 

 prefer to express concentrations in moles per liter. However, we do not 

 always know the molecular weights of our material, or the reaction mix- 

 tures are so complex that it is no help to know the molar concentra- 

 tion of the various solutes. Many biologically active solutions are quite 

 dilute, and it should be no surprise to find a solution described as 

 10-«M. 



The hydrogen ion CH + ) concentration, or perhaps more properly the 

 concentration of the hydrated ion (HaO"*"), has a very profound influ- 

 ence on all kinds of biological reactions. Concentrations of H"*" ions 

 might vary from more than 1m to 10~^*^m or less, so we use the loga- 

 rithmic pH scale to denote these concentrations. If [H"^] is the concen- 

 tration of these ions in moles per liter, then 



pH = — logio [H + ] = log 



10 



[H + ] 



The notation pH 1 means 10 'm hydrogen ions, or pH 6.8 means the 

 H+ concentration is 10~^-^m. The pH of a solution might be measured 



