The Foundations of Chemistry

Figure 16-3 is a plot of the hydrogen concentration versus time, using data of Table
16-1. The initial rate, or the rate at the instant of mixing the reactants, is the negative of
the slope at t0. The instantaneousrate of reaction at time t(2.0 seconds, for example)
is the negative of the slope of the tangent to the curve at time t.We see that the rate
decreases with time; lower concentrations of H 2 and ICl result in slower reaction. Had
we plotted concentration of a product versus time, the rate would have been related to
the positiveslope of the tangent at time t.

EXAMPLE 16-1 Rate of Reaction

At some time, we observe that the reaction 2N 2 O 5 (g) n 4NO 2 (g)
O 2 (g) is forming NO 2

at the rate of 0.0072 

m

L

o

s

l

.

(a) What is the rate of change of [O 2 ], 

[



O

t

^2 ], in m

L

o

s

l

, at this time?

(b) What is the rate of change of [N 2 O 5 ], 

[N



2

t

O 5 ]

, in 

m

L

o

s

l

, at this time?

(c) What is the rate of reaction at this time?

Plan

We can use the mole ratios from the balanced equation to determine the rates of change of
other products and reactants. The rate of reaction can then be derived from any one of these
individual rates.

Solution

(a) The balanced equation gives the reaction ratio 1 mol 

O

4

^2 mol NO

2.

rate of change of [O 2 ]0.0018

mol O 2



Ls

1 mol O 2



4 mol NO 2

0.0072 mol NO 2



Ls

[O 2 ]



t

Figure 16-3 Plot of H 2

concentration versus time for the

reaction of 1.000 MH 2 with

2.000 MICl. The instantaneous rate

of reaction at any time, t,equals the

negative of the slope of the tangent

to this curve at time t.The initial

rate of the reaction is equal to the

negative of the initial slope (t0).

The determination of the

instantaneous rate at t2 seconds is

illustrated. (If you do not recall how

to find the slope of a straight line,

refer to Figure 16-5.)

16-1 The Rate of a Reaction 653

Suppose a driver travels 40 miles in an

hour; we describe his average speed

(rate) as 40 mi/h. This does not

necessarily mean that he drove at a

steady speed. He might have stopped

at a few traffic signals, made a fuel

stop, driven sometimes faster,

sometimes slower—his instantaneous

rate(the rate at which he was traveling

at any instant) was quite changeable.

1.000 M

0.600 M

0.300 M

0

0 2 4 6 8 10 12 14

Time (s)

3.95

t

t

[H 2 ]

slope 

slope  initial rate

 Rate at (t  2.0 s)  0.107 Ms^1

[H 2 ]

1.15

[H

] 2 (3.95  1.15) s

(0.300  0.600) M