522 11 The Rates of Chemical ReactionsSome techniques were presented for studying fast reactions that cannot be studied
by classical experimental techniques. These techniques included continuous flow and
stopped-flow techniques, which are rapid mixing methods, as well as relaxation tech-
niques. The relaxation techniques included shock-tube methods, flash photolysis, and
T-jump and P-jump methods. Equations were derived for the relaxation of a reaction
after a small perturbation, giving an exponential relaxation for a variety of rate laws.ADDITIONAL PROBLEMS
11.42The reaction
NO+H 2 −→H 2 O+1
2
N 2has been studied in the gas phase at 826◦C by the method
of initial rates. The initial rate was monitored by
measuring the total pressure of the system, and the data
were obtained:P(H 2 )initial/kPa P(NO)initial/kPa −dPdt/kPa s−^153.3 40.0 0.137
53.3 20.3 0.033
38.5 53.3 0.213
19.6 53.3 0.105a.Find the order with respect to each reactant and find
the value of the rate constant. Use the partial pressures
in the same way as concentrations are used, since
concentrations are proportional to partial pressures in
an ideal gas mixture.b. ForP(H 2 )initial100 kPa andP(NO)initial100 kPa,
find the initial rate.c.For the initial pressures of part b, find the pressure of
each substance 1.00 s after the start of the reaction.d.ForP(NO)initial200 kPa andP(H 2 )initial
5.00 kPa, find the time for half of the H 2 to react.e.ForP(NO)initial5.00 kPa andP(H 2 )initial
200 kPa, find the time for half of the NO to react.11.43Label each of the following statements as either true or
false. If a statement is true only under special
circumstances, label it false.
a.The rate of a forward reaction can depend on the
concentrations of substances other than the substances
in the stoichiometric equation.
b.The order of a reaction with respect to a substance is
not necessarily equal to the stoichiometric coefficient
of that substance in the reaction equation.
c.The reverse reaction is unimportant during the first
half-life of any chemical reaction.
d.The method of initial rates cannot be used in
conjunction with the method of isolation.
e.At the equilibrium of a chemical reaction, the rate of
the forward reaction and the rate of the reverse
reaction cancel.
f.A rate constant is not a true constant, since it depends
on temperature and pressure.
g.In the method of initial rates, one must worry about
the effect of the reverse reaction.
h.In the case of two consecutive reactions without
reverse reactions, the final state corresponds to zero
concentration of the reactant and of the intermediate.
i.In the case of two consecutive reactions without
reverse reactions, the concentration of the
intermediate always remains small compared with the
initial concentration of the reactant.
j.The linearization of the rate equation that is done in
the study of the temperature-jump method is usually a
good approximation, because the state immediately
after the temperature jump does not deviate very much
from the final equilibrium state.
k.First-order processes occur only in chemical
processes.
l.All rate laws can be written in a form with definite
orders.