Lecture 27: Reaction Rates and Orders

Order of the reaction is an experimental quantity

  • Not possible to know nn and mm from a balanced equation

Rate =k[A]n= k[A]^n

  • Zero Order - Rate of reaction \rightarrow  Always the same
  • First Order - Rate proportional to the reactant concentration
  • Doubling [A][A] \rightarrow  Double the rate of the reaction
  • Second Order - Rate directly proportional to square toot of the reactant concentration
  • A rate quadruples when doubling [A][A]

Integrated Rate Law

  • Relationship between kk and the time

[A]=kt+[A]initial[A] = -kt + [A]_{initial} \rightarrow  Straight line with slope k-k

First Order Reactions

Rate == k[A]4=k[A]k[A]^4 = k [A] 

ln[A]=kt+ln[A]initial\ln [A] = -kt + \ln [A]_{initial}

kt=ln[A]initialln[A]kt = \ln [A]_{initial}-ln[A]

kt=ln([A]initial[A])kt = \ln (\frac{[A]_{initial}}{[A]})

kt1/2=ln[A]initial[A]initial/2kt_{1/2} = \frac {\ln [A]_{initial} }{[A]_{initial} / 2} \rightarrow  Half-Life

kt1/2=ln(2)kt_{1/2} = \ln (2)

kt1/2=0.693kt_{1/2} = 0.693

t1/2=0.693kt_{1/2} = \frac { 0.693}{k}

The half life of a first order reactions is constant when:

Rate ==  M/s, k=s=1M/s, \ k = s^{=1}

Zero Order

Rate =K[A]=K= K[A]^\circ = K

  • Constant rate reactions

[A]=kt+[A]initial[A] = -kt + [A]_{initial}

Rate does not change if concentration changes.

When Rate =M/s, k=M/s= M/s, \ k = M/s

t1/2=[Ainitial]2kt_{1/2}= \frac{[A_{initial}]}{2k}

First Order

Rate =k[A]4=k[A]=k[A]^4 = k[A]

ln[A]=Kt+ln[A]initial\ln [A] = -Kt + \ln [A]_{initial}

Derivation: ln[A]initialln[A]\ln [A]_{initial} - \ln [A]

Kt=ln([A]initialln[A])Kt = \ln ([A]_{initial}- \ln [A])

Kt=ln([A]initial[A]initial/2)Kt = \ln (\frac{[A]_{initial}}{[A]_{initial / 2}})

Kt1/2=ln(2)Kt_{1/2} = \ln(2)

Kt1/2=0.693Kt_{1/2} = 0.693

t1/2=0.693kt_{1/2} = \frac{0.693}{k}

The half life of first order reaction is constant.

When Rate =m/s, K=s1= m/s, \ K= s ^{-1}

*The half life, t1/2t_{1/2} of a reaction is the length f time it takes for the concentration of the reaction to fall to 12\frac{1}{2} its initial value. The half life for First order reaction, the half life is constant and independent and independent of concentration.

Second Order

Rate =K[A]2= K[A]^2 

1[A]=Kt+1[A]initial\frac{1}{[A]} = Kt + \frac {1}{[A]_{initial}}

t1/2=1K[A0]t_{1/2} = \frac{1}{K[A_0]}

When Rate =m/s, K=M1S1 = m/s, \ K=M^{-1} \cdot S^{-1}

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