Chemical Kinetics: Rate Laws and Rate Constants

In the study of chemical kinetics, rate laws are mathematical expressions that describe the relationship between the rate of a chemical reaction and the concentrations of the reactants and products in the reaction. These laws provide a quantitatively description of how changes in the amount of a substance affect the rate of a chemical reaction and are used to calculate reaction rates and identify reaction orders and derive rate laws from rate and concentration data.

A rate law generally has the form:

rate = k[A]ⁿ

• k: rate constant, a proportionality constant in the relationship between reaction rate and concentrations of reactants
• [A]ⁿ: concentration of reactant A to the power of n, where n is the reaction order

The value of n is not related to the reaction stoichiometry and must be determined by experiment to understand the dependence of the reaction rate on the concentrations of the species and the order of the reaction that leads to various differential rate laws and integrated rate laws for different scenarios.

The rate constant k is usually determined by experiment and can be expressed in different units depending on the reaction order and the units of time used (e.x. mol/L/s for zero order, s−1 for first order, L/mol/s for second order, and mol−2 L2 s−1 for the case of a reaction with three reactants and molarity (M) instead of mol/L for the units of k).

Rate laws are used to calculate reaction rates and identify reaction orders by:

• Understand the definition of the reaction rate and be able to write down a differential equation
• Understand the difference between the differential vs. integrated rate laws and be able to recognize the order of a reaction from a plot of either rate vs. concentration or concentration vs. time
• Be able to use the integrated rate laws to solve for the half- life
• Be able to solve the integrated rate laws algebraically, given the initial concentration, to find the concentration at a later time

The initial rate of a reaction can be determined by measuring the rate of reaction at very short times before any significant changes in concentration occur and can be expressed as the derivative of concentration with respect to time or the slope of a graph of concentration against time at a particular time. As a reaction progresses, the concentrations of both reactants and products change, and the rate of the reaction depends on the concentrations of the reactants and the order of the reaction [100] [101] [102] [103] [104] [105] [106] [107] [108] [109] [110] [111] [112] [113] [114] [115] [116] [117] [118] [119] [120] [121] [122] [123] [124] [125] [126] [127] [128] [129] [130] [131] [132] [133] [134] [135] [136] [137] [138] [139] [140] [141] [142] [143] [144] [145] [146] [147] [148] [149] [150] [151] [152] [153] [154] [155] [156] [157] [158] [159] [160] [161] [162] [163] [164] [165] [166] [167] [168] [169] [170] [171] [172] [173] [174] [175] [176] [177] [178] [179] [180] [181] [182] [183] [184] [185] [186] [187] [188] [189] [190] [191] [192] [193] [194] [195] [196] [197] [198] [199] [200] [201] [202] [203] [204] [205] [206] [207] [208] [209] [210] [211] [212] [213] [214] [215] [216] [217] [218] [219] [220] [221] [222] [223] [224] [225] [226] [227] [228] [229] [230] [231] [232] [233] [234] [235] [236] [237] [238] [239] [240] [241] [242] [243] [244] [245] [246] [247] [248] [249] [250] [251] [252] [253] [254] [255] [256] [257] [258] [259] [260] [261] [262] [263] [264] [265] [266] [267] [268] [269] [270] [271] [272] [273] [274] [275] [276] [277] [278] [279] [280] [281] [282] [283] [284] [285] [286] [287] [288] [289] [290] [291] [292] [293] [294] [295] [296] [297] [298] [299] [300] [301] [302