−2 and 3 (with negative signs for reactants because they are consumed) are known as stoichiometric coefficients. One molecule of A combines with two of B to form 3 of C, so if we use the symbol [X] for the number of moles of chemical X, If the reaction takes place in a closed system at constant temperature and volume, without a build-up of reaction intermediates, the reaction rate is defined as where is the stoichiometric coefficient for chemical Xi, with a negative sign for a reactant. The initial reaction rate has some functional dependence on the concentrations of the reactants, and this dependence is known as the rate equation or rate law. This law generally cannot be deduced from the chemical equation and must be determined by experiment. Power laws A common form for the rate equation is a power law: The constant is called the rate constant. The exponents, which can be fractional, are called partial orders of reaction and their sum is the overall order of reaction. In a dilute solution, an elementary reaction (one having a single step with a single transition state) is empirically found to obey the law of mass action. This predicts that the rate depends only on the concentrations of the reactants, raised to the powers of their stoichiometric coefficients. Determination of reaction order Method of initial rates The natural logarithm of the power-law rate equation is This can be used to estimate the order of reaction of each reactant. For example, the initial rate can be measured in a series of experiments at different initial concentrations of reactant with all other concentrations kept constant, so that The slope of a graph of as a function of then corresponds to the order with respect to reactant . However, this method is not always reliable because measurement of the initial rate requires accurate determination of small changes in concentration in short times (compared to the reaction half-life) and is sensitive to errors, and the rate equation will not be completely determined if the rate also depends on substances not present at the beginning of the reaction, such as intermediates or products. Integral method The tentative rate equation determined by the method of initial rates is therefore normally verified by comparing the concentrations measured over a longer time (several half-lives) with the integrated form of the rate equation; this assumes that the reaction goes