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Wize University Chemistry Textbook > Kinetics

Rate of Reaction

Introduction to KineticsPrevious Section
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Reaction Rates

  • The reaction rate is a measure of the change in concentration of a reactant or product over time!
  • ex. In physics we know velocity= Δd/t, in chemistry, a reaction rate= Δ[ ]/t
  • The units of rate would be M/s where M=mol/L
  • A general form of a reaction rate is shown below:
aA+bB→cC+dDaA+bB \to cC+dD


rate=−1ad[A]dt=−1bd[B]dt=1cd[C]dt=1dd[D]dtrate=-\frac{1}{a}\frac{d[A]}{dt}=-\frac{1}{b}\frac{d[B]}{dt}=\frac{1}{c}\frac{d[C]}{dt}=\frac{1}{d}\frac{d[D]}{dt}

  • As the reaction proceeds are we getting more/less of the reactant?
    Less
    More/less of the product?
    More
  • The - sign indicates that the concentration of reactants are decreasing (losing reactants as the reaction proceeds)
  • The + sign indicates that the concentration of products is increasing (gaining product as the reaction proceeds )

  • **Rates must be determined through experimentation.
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Measuring Reaction Rates

  • Consider the reaction: A→B\small A\rightarrow B
  • The reaction rate can be measured using any substance in the reaction. Reaction rate units are always M/s (M stands for concentration, mol/L)
Rate=−Δ[A]Δt=ΔBΔtRate=-\cfrac{\Delta\left[A\right]}{\Delta t}=\cfrac{\Delta B}{\Delta t}
  • Instantaneous rate: the rate of reaction at an instance in time (the slope of the tangent line to a point in a concentration vs time graph)





  • Initial rate – instantaneous rate of a chemical reaction at t = 0, immediately after the reaction has begun

  • Average rate: the rate of reaction over a period of time (the slope of the line connecting 2 points in a concentration vs time graph)


Practice: Rates of Reaction

If N2 is consumed at 2 M/s, what is the rate of production of NH3 and rate of consumption of H2 in the reaction?

N2  + 3H2 → 2 NH3N_2\ \ +\ 3H_2\ \rightarrow\ 2\ NH_3

In the following reaction the average rate of formation of NO(g) is 1.12 mol/Ls. If 2 minutes passes, what is the concentration of O2(g) that is consumed?

4NH3(g) + 5O2(g) --> 4NO(g) + 6H2O(g)
Extra Practice
Rate Laws: Relative Rates of Reactions
Consider the balanced chemical equation for the reaction
2CO(g)+O2(g)⟶2CO2(g)Rate=k[CO]22CO(g)+O_2(g)⟶2CO_2(g)\qquad Rate=k[CO]^2
If the rate of the reaction is 3.2 M/s which of the following is TRUE.
Given the following data for the NH4++NO2−→N2+2H2ONH_4^++NO_2^-→N_2+2H_2O reaction, the rate law for the reaction is
Trial[NH4+][NO2–]Rate10.010M0.030M0.020M/s20.0150.0300.03030.0100.0150.005\def\arraystretch{1.5} \begin{array}{c} Trial &[NH_4^+] &[NO_2^–]& Rate \\ \hline 1 & 0.010 M & 0.030 M &0.020 M/s \\ 2& 0.015& 0.030 &0.030 \\ 3&0.010 & 0.015 &0.005 \\ \end{array}
Rate Laws: Relative Rates of Reactions
Consider the balanced chemical equation for the reaction
2CO(g)+O2(g)⟶2CO2(g)Rate=k[CO]22CO(g)+O_2(g)⟶2CO_2(g)\qquad Rate=k[CO]^2
If the rate of the reaction is 3.2 M/s which of the following is TRUE.
Given the following data for the NH4++NO2−→N2+2H2ONH_4^++NO_2^-→N_2+2H_2O reaction, the rate law for the reaction is
Trial[NH4+][NO2–]Rate10.010M0.030M0.020M/s20.0150.0300.03030.0100.0150.005\def\arraystretch{1.5} \begin{array}{c} Trial &[NH_4^+] &[NO_2^–]& Rate \\ \hline 1 & 0.010 M & 0.030 M &0.020 M/s \\ 2& 0.015& 0.030 &0.030 \\ 3&0.010 & 0.015 &0.005 \\ \end{array}
Elements: Radioactive Decay in Smoke Detectors
Americium-241 is a synthetic isotope made in nuclear reactors around the world. Chances are you have been in close proximity to this radioactive isotope thousands of time in your life because it is used in household smoke detectors. 241Am^{241}\rm Am is an alpha emitter whose decay obeys a first order rate-law (as do all nuclear decays) with a half-life of 432.6 years. What is the rate constant of its decay? How much 241Am^{241}\rm Am would remain of a 25mg sample if it were left for 300 years.
The Rate Law
Express the rate of reaction in terms of the change in concentration of each reactant and product:
A(g)+2B(g)→C(g)A_{(g)}+2B_{(g)} \to C_{(g)}
For the following reaction:
A(g)+2B(g)→C(g)A_{(g)}+2B_{(g)} \to C_{(g)}
When [B] is decreasing at 0.5 M/s, how fast is [A] decreasing?