C18 kinetics

• rate of reaction is defined as change in concentration, of any reactant or product, per unit time
• rate of reaction depends on the concentrations of the reactants, and the rate constant
• it is important to state which reactant of product you are following when working with rates of reaction because the rate will be different for different numbers of moles, and for products and reactants
• usually it is assumed that rate is measured by following concentration of a product as this increases over time
• to find the rate of reaction at a particular instant in time from a graph of concentration against time, draw a tangent to the curve at that time and find the gradient of the tangent
• the rate expression tells you about the contributions of the species which do affect the reaction rate
• the rate expression is necessary because some species may have no effect, and rate can be affected by a species which does not appear in the equation, such as a catalyst
• the rate expression is in the form:

  rate is proportional to [X]^a[Y]^b
• the rate expression can contain species not in the equation such as catalysts, there can be more than just X and Y, and the powers can be the same or different
• to get rid of the proportionality sign in the rate expression, you can add a constant represented by k called the rate constant
• once k is added, the rate expression is in the form:

  rate = k[X]^a[Y]^b
• k is different for every reaction and temperature, so the temperature it was measured at needs to be stated
• if all concentrations are 1 moldm^-3 then k equals the rate of reaction
• the order of reaction of a species is the power to which the concentration of that species is raised in the rate expression
• the order of reaction tells you how the rate depends on the concentration of the species
• the overall order of reaction is the sum of all of the orders of the species in the rate expression
• the units of the rate constant depend on the overall order of reaction
• for a zero order reaction, rate = k so there are no units
• for a first order reaction, rate = k[X] so k = rate/[X] so the units cancel to s^-1
• for a second order reaction, rate = k[X][Y] so k = rate/[X][Y] so the units cancel to mol^-1dm^3s^-1
• for a third order reaction, rate = k[X][Y]^2 so k = rate/[X][Y]^2 so the units cancel to mol^-2dm^6s^-1
• the rate expression only includes the species that affect the rate of reaction
• if the rate is not affected by the concentration of a species, the reaction is zero order with respect to that species, it is not included in the rate expression
• if the rate is directly proportional to the concentration of a species, the reaction is first order with respect to that species
• if the rate is proportional to the square of the concentration of a species, the reaction is second order with respect to that species
• one way of finding the order of reaction is using a graph of rate against concentration
• if the graph of rate against concentration is a horizontal line, the reaction is zero order with respect to that species as rate is unaffected by concentration
• if the graph of rate against concentration is a straight line through the origin, the reaction is first order with respect to that species as rate is proportional to concentration
• if the graph of rate against concentration is not a straight line, the order cannot be found directly, it could be two or more, if you plot rate against concentration^2 and get a straight line, the reaction is second order with respect to that species
• the rate constant k is affected by temperature
• small changes in temperature produce large changes in rate of reaction, and as rate = k[X][Y] and concentrations do not change with temperature, it must be k that is affected by temperature
• temperature is a measure of the average kinetic energy of particles, they will only react together if they have the activation energy
• as temperature increases, more particles have the activation energy, so rate of reaction increases
• the arrhenius equation shows how the rate equation and temperature are related exponentially
• the arrhenius equation is: $k =$$Ae^{\frac{-E_a}{RT}}$which can also be written as $\ln k =$$\frac{-E_a}{RT} +$$\ln A$
• in the arrhenius equation:

  k = rate constant

  A = pre-exponential factor, related to number of collisions

  Ea = activation energy

  R = gas constant

  T = temperature
• the form of the arrhenius equation which uses ln can be used to show it graphically as it is in the form y = mx + c
• to show the arrhenius equation graphically, plot ln K against 1/T, the gradient will be -Ea/R and the y intercept will be ln A
• not all stages of a reaction occur at the same time, but the overall rate is determined by the slowest stage of the reaction
• the rate equation contains all species involved in the stages up to and including the rate-determining step