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576
CHAPTER 15
CHEMICAL KINETICS
Reaction Rates
10.
The reaction rate is defined as the change in concentration of a reactant or product per unit
time.
Consider the general reaction:
aA
→
products where rate =
dt
]
A
[
d
−
If we graph [A] vs. t, it would usually look like the solid line in the following plot.
An instantaneous rate is the slope of a tangent line to the graph of [A] vs. t. We can determine
the instantaneous rate at any time during the reaction. On the plot, tangent lines at t
≈
0 and t
= t
1
are drawn. The slope of these tangent lines would be the instantaneous rates at t
≈
0 and t
= t
1
. We call the instantaneous rate at t
≈
0 the initial rate. The average rate is measured over
a period of time. For example, the slope of the dashed line connecting points a and c is the
average rate of the reaction over the entire length of time 0 to t
2
(average rate =
Δ
[A]/
Δ
t). An
average rate is determined over some time period, whereas an instantaneous rate is
determined at one specific time. The rate that is largest is generally the initial rate. At t
≈
0,
the slope of the tangent line is greatest, which means the rate is largest at t
≈
0.
The initial rate is used by convention so that the rate of reaction only depends on the forward
reaction; at t
≈
0, the reverse reaction is insignificant because no products are present yet.
[A]
0
a
c
b
t
1
t
2
time
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View Full DocumentCHAPTER 15
CHEMICAL KINETICS
577
11.
0.0120/0.0080 = 1.5;
reactant B is used up 1.5 times faster than reactant A. This corres
ponds to a 3 to 2 mole ratio between B and A in the balanced equation. 0.0160/0.0080 = 2;
product C is produced twice as fast as reactant A is used up. So the coefficient for C is twice
the coefficient for A. A possible balanced equation is 2A + 3B
→
4C.
12.
The coefficients in the balanced reaction relate the rate of disappearance of reactants to the
rate of production of products.
From the balanced reaction, the rate of production of P
4
will
be 1/4 the rate of disappearance of PH
3
, and the rate of production of H
2
will be 6/4 the rate
of disappearance of PH
3
.
By convention, all rates are given as positive values.
Rate
s
)
L
0
.
2
/
mol
0048
.
0
(
t
Δ
]
PH
[
Δ
3
−
−
=
−
=
= 2.4 × 10
−
3
mol L
−
1
s
−
1
t
Δ
]
PH
[
Δ
4
1
t
Δ
]
P
[
Δ
3
4
−
=
= 2.4 × 10
−
3
/4 = 6.0 × 10
−
4
mol L
−
1
s
−
1
t
Δ
]
PH
[
Δ
4
6
t
Δ
]
H
[
Δ
3
2
−
=
= 6(2.4 × 10
−
3
)/4 = 3.6 × 10
−
3
mol L
−
1
s
−
1
13.
Using the coefficients in the balanced equation to relate the rates:
dt
]
N
[
d
2
dt
]
NH
[
d
and
dt
]
N
[
d
3
dt
]
H
[
d
2
3
2
2
−
=
=
dt
]
H
[
d
3
2
dt
]
NH
[
d
or
dt
]
NH
[
d
2
1
dt
]
H
[
d
3
1
:
So
2
3
3
2
−
=
= −
Ammonia is produced at a rate equal to 2/3 of the rate of consumption of hydrogen.
14.
a.
The units for rate are always mol L
−
1
s
−
1
.
b.
Rate = k;
k has units of mol L
−
1
s
−
1
.
c.
Rate = k[A],
⎟
⎠
⎞
⎜
⎝
⎛
=
L
mol
k
s
L
mol
d
.
R
a
t
e
=
k
[
A
]
2
,
2
L
mol
k
s
L
mol
⎟
⎠
⎞
⎜
⎝
⎛
=
k must have units of s
1
.
k must have units L mol
−
1
s
−
1
.
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 Spring '11
 Malambri,W
 pH, Kinetics

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