11.3 Forward Reactions with More Than One Reactant 505Not only is the concentration of H 2 O nearly constant, but the concentration of KI is
also constant, since it is not consumed. We can find the pseudo order with respect to
methyl acetate and the apparent rate constant as though there were only one reactant.
See Problem 11.25.PROBLEMS
Section 11.3: Forward Reactions with More Than One
Reactant11.15The following forward reaction is first order in each
reactant, second order overall:
NO+O 3 −→NO 2 +O 2At 600 K, the rate constant for the reaction is equal to
8. 68 × 10 −^6 L mol−^1 s−^1.
a.If the initial concentration of each reactant is equal to
0.100 mol L−^1 and the initial concentration of HI is
zero, find the concentration of HI after a reaction time
of 1. 00 × 106 s (11.6 days) at 600 K.
b.What is the half-life of the reaction at this temperature
for these initial concentrations?11.16The rate constant for the forward reaction
H 3 O++OH−−→2H 2 Ois equal to 1. 4 × 1011 L mol−^1 s−^1.
a.Assuming instantaneous mixing, find the half-life of
the neutralization reaction between a strong acid and a
strong base if both the acid and the base have initial
concentrations (after mixing) of 0.150 mol L−^1.
b.Repeat the calculation for initial concentrations of
1. 00 × 10 −^3 mol L−^1.11.17The following reaction is first order in each reactant:
C 6 H 5 N(CH 3 ) 2 +CH 3 I−→C 6 H 5 N(CH 3 )+ 3 +I−Assume that the reverse reaction is negligible.
a.At 24.8◦C with nitrobenzene as the solvent, the rate
constant is 8. 39 × 10 −^5 L mol−^1 s−^1. Assuming that
both reactants have initial concentrations of
0.100 mol L−^1 , find the half-life of the reaction at this
temperature.
b. Find the time required for 75% of the reactants to react
at 24.8◦C.
c.Find the time required for 95% of the reactants to react
at 24.8◦C.11.18For the reaction of the previous problem, find the time
required at 24.8◦C for half of the methyl iodide to react if
its initial concentration is 0.100 mol L−^1 and the initial
concentration of the dimethyl phenylamine is equal to
0.0600 mol L−^1. Assume that the reverse reaction can be
neglected.
11.19Assume that the following initial-rate data were taken for
a hypothetical reaction at some temperature:A+2B+C−→products
Find the order with respect to each reactant and find the
value of the rate constant.[ A]/mol L−^1 [B]/mol L−^1 [C]/mol L−^1 initial rate/mol L−^1
min−^1
0.100 0.100 0.100 0. 120
0.200 0.100 0.100 0. 170
0.300 0.100 0.100 0. 207
0.400 0.100 0.100 0. 241
0.100 0.200 0.100 0. 239
0.100 0.300 0.100 0. 360
0.100 0.400 0.100 0. 481
0.100 0.100 0.200 0. 480
0.100 0.100 0.300 1. 079
0.100 0.100 0.400 1. 9311.20The gas-phase reaction
2NO 2 +F 2 −→2NO 2 F
is first order in each reactant, second order overall.
Assume that at some temperature,
k 4. 98 × 10 −^3 L mol−^1 s−^1.
a.If at the start of the reaction [NO 2 ] 0 .200 mol L−^1
and [F 2 ] 0 .100 mol L−^1 , find the value of [F 2 ] for a
reaction time of 30.0 minutes.
b.For the case of part a, find the half-life of the reaction.
11.21Assume that the reaction A+B−→products is second
order with respect to A and first order with respect to B.
Integrate the rate differential equation−d[A]/dtk[A]^2 [B]