11.2 Reaction Rate and Concentration

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11.2 Reaction Rate and Concentration

• YOU ARE EXPECTED TO BE ABLE TO
• Define the initial rate of a reaction as the
  instantaneous rate at the start of the reaction.
• Write a rate law expression for a given reaction
  given experimental results that show the
  variation of initial rate with concentration.
• Define the concept of order of reaction and
  determine the order of a given reaction from
  initial rate vs concentration data

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Initial Rate of Reaction

• The initial rate of reaction is the instantaneous
  rate measured at the start of the reaction
• The initial rate can be used as a benchmark
• Measurements of the initial rate for a reaction
  at different starting concentrations can be used
  to determine the effect of concentration on rate

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The Rate Expression or Rate Law

• In general
• Reactions occur as a result of collisions
• The higher the concentration of molecules, the
  greater the rate
• In some reactions, the rate is directly
  proportional to the concentration
• In other cases, the rate may increase much more
  quickly than the concentration
• The relationship between rate and concentration
  is known at the rate law or rate expression

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Determining the Rate Law Expression

• The rate law MUST be determined from experiment
  it is not related to the stoichiometry of the
  equation for the reaction
• Examine the concentration vs time graph for N2O5
• Determine instantaneous rates at different times
  and concentrations of N2O5
• Plot instantaneous rate vs N2O5
• This is a straight line, (equation y mx b)
• Rate kN2O5 this is the rate law expression
  k is the rate constant

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Using Initial Rates to determine the rate Law

• Measurements of the initial rate of reaction at
  different initial concentrations can be used to
  determine the rate law expression
• If a graph of initial concentration vs initial
  rate is a straight line, then rate is directly
  proportional to concentration
• rate k reactant
• If a graph is a curve, then rate kreactantm

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Order of Reaction

• The rate law expression is of the form
• Rate kAm
• The power to which the concentration is raised is
  called the order of reaction
• If m 0, then zero order
• If m 1, then first order
• If m 2, then second order

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Calculating the Order of Reaction when there is
One Reactant

• If m is not equal to 1, the order of the reaction
  can be determined by comparing two rates at two
  different concentrations
• Rate1 kA1m
• Rate2 kA2m
• Rate1 kA1m A1 m
• Rate2 kA2m A2

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Example 11.1

• CH3CHO(g) ? CH4(g) CO(g)
• 0.10M 0.20M 0.30M
  0.40M
• Rate (mol/L.s) 0.085 0.34 0.76
  1.4
• Choose the first two concentrations
• Rate2 0.34 4.0
• Rate1 0.085
• CH3CHO2 0.20 2.0
• CH3CHO1 0.10
• 4.0 (2.0)m m 2
• Rate kCH3CHO2 The reaction is second order

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Calculate the Rate Constant

• Rate kCH3CHO2
• Choose one set of data
• 0.085mol/L.s k x (0.10 mol/L)2
• k 0.085mol/L.s 8.5 L/mol.s
• (0.10 mol/L)2

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Order of Reaction with More Than One Reactant

• Most reactions involve gt1 reactant
• aA bB ? products
• General rate law expression is
• rate kAm x Bn
• m is order with respect to A
• n is order with respect to B
• Overall order is m n

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Determining the Order

• Hold concentration of one reactant constant and
  vary other - measure initial rate
• Repeat, holding concentration of other reactant
  constant
• See Example 11.2, page 308

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Determining the Order of Reaction Graphically

• As an alternative to calculating the order of
  reaction by comparing two pieces of data, a
  graphical process can be used
• Plot rate vs concentration
• If the result is a straight line, there is a
  first order reaction, slope k
• If the result is a curve, it is necessary to
  construct a graph of (natural) log rate vs
  (natural) log concentration to determine m

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Why Use a Logarithm?

• If rate kAm
• Then ln rate ln k m ln a
• This will be a straight line with slope m

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Zero Order Reactions

• In rare cases, the rate of reaction is
  independent of the concentration of reactant(s)
• In these cases
• Rate kA0
• A plot of rate vs A would be a horizontal
  straight line