Our general rate expression
tells us how the rate of the reaction changes with concentration. However, from a more practical stand point we are more interested in the relationship between time and concentration. If weare studying a reaction we would be interested in knowing how much reactant remained after 5 minutes, 1 day or several years.
It is possible to derive algebraic expressions relating the concentration to time. The form of these equations maybe very simple or quite complex depending on the order of the reaction and the number of reactants. We will discuss the simpler concentration/time equations. Those for first and second order reactions involving a single reactant.
For first order reactions of the type
we can write the differential form of the rate law (which is useful in describing how the rate of disappearance of reactant is proportional to the concentration of the reactant) as rate = ÐF(D[A],Dt) = k[A]1 which can be rearranged to Ð F(D[A],[A]1) = kDt When this relationship is integrated from tâ to tt we obtain the relationship ln B(F([A],[A]0)) = Ðkt This integrated form of the rate law for a first order reaction is handy because it provides us with a way to determine the relationship between concentration of the reacting species and time. Be sure to note that the [A] listed in the equation represents the concentration of A remaining. If we rearrange this relationship ln [A] = Ðkt + ln [A]0 The equation has the form of a straight line. Plotting ln [A] vs. time gives a straight line with a slope equal to Ðk. Remember that the rate constant, k, must be positive, therefore, the line must have a negative slope. Time [A] log [A] Time [A] log [A] 0 .310 Ð.51 3000 .116 Ð.94 600 .254 Ð.60 3600 .0964 Ð1.02 1200 .208 Ð.68 4200 .0812 Ð1.09 1800 .172 Ð.76 4800 .0669 Ð1.17 2400 .141 Ð.85 6000 .0464 Ð1.33
| Experiment # | [NO2] | [F2] | Initial Rate (M/min) |
| 1 | 0.0482 M | 0.0318 M | 1.9 x 10-3 |
| 2 | 0.0120 M | 0.0315 M | 4.69 x 10-4 |
| 3 | 0.0480 M | 0.127 M | 7.57 x 10-3 |
i) Determine the reaction order for NO2(g) and F2(g).
Show how the order with respect to NO2(g) is determined.
Show how the order with respect to F2(g) is determined.
Show how the order with respect to NO2(g) and F2(g) are determined.
ii) Determine the overall order of the reaction.
Show how the overall order for the reaction is determined.
iii) Write the specific rate law for the reaction.
Show the specific rate law for the reaction.
iv) Determine the magnitude and the units for the rate constant of this reaction.
Show how to determine therate constant for the reaction.