   Chapter 3.8, Problem 7E

Chapter
Section
Textbook Problem

Experiments show that if the chemical reaction N 2 O → 2NO 2 + 1 2 O 2 takes place at 45°C, the rate of reaction of dinitrogen pent-oxide is proportional to its concentration as follows: − d [ N 2 O 5 ] d t = 0.0005 [ N 2 O 5 ] (See Example 3.7.4.)(a) Find an expression for the concentration [N2O5] after t seconds if the initial concentration is C.(b) How long will the reaction take to reduce the concentration of N2O5, to 90% of its original value?

(a)

To determine

To find: The concentration of [N2O5] after t seconds.

Explanation

Given:

Let [N2O5](t) be the concentration of chemical after t seconds.

The differential equation is d[N2O5]dt=0.0005[N2O5].

The initial concentration is C. That is, [N2O5](t)=C at t=0.

Calculation:

The differential equation is computed as follows,

d[N2O5]dt=0.0005[N2O5]d[N2O5][N2O5]=0.0005dt

Integrate both sides,

d[N2O5][N2O5]=0.0005dt

ln[N2O5]=0.0005t+k (1)

Apply initial condition and to find k

(b)

To determine

To find: The value of  t when the concentration of N2O5 to 90% of its original value.

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